After reading chapters 1,2,3 & 19. Answer the following questions based on the information provided. Answer should be own in own words and APA format must
1. BUSINESS ORGANIZATIONS
Jaffe Desk and Jordan Reilly just graduated from UC with a master’s degree in marketing and public health. They want to establish healthcare business that will source and distribute pharmaceutical products in the United States and internationally. Jaffe and Jordan know that before they can invest their time and other resources in the project, they must obtain financing, which means that they must raise money to pay for the investment cost and other operating expenses. Because the company might not be listed in any capital market right away, they will not be able to raise equity funding from the public. Therefore, they are considering raising long-term capital from various sources including angel investors, venture capital market, bank loans, crowdfunding, and initial coin offerings (ICOs). They learnt in corporate finance course the advantages and disadvantages of different forms of business organizations. They are worried about the legal concept of limited liability and how it will affect their personal fortunes in the future in case the business fails. They are not very sure which form of business organization to set up to protect their personal liability, reduce taxes, and access external funding. Therefore, they are considering a partnership, a limited liability, or a corporation. A cash budget they prepared shows that $5 million seed money would be needed to hire staff, buy computers, rent an office space, promote, and market the business as well as to meet other business development expenditures. They have agreed to share profits and losses equally if they decide to form a limited partnership. The general partner will, however, be paid a fixed salary of $6,000 per month before taxes and other payroll deductions.
In order to make good and right decision, Jaffe and Jordan have approached you to help them understand the concept of limited liability, advantages, and disadvantages of the various forms of business organizations and possible sources of funding for the business.
partnership,
limited liability, and
corporation
angel investors (angels)
crowdfunding
venture capital
initial coin offering, and
long-term debt
APA format mustNo Plagiarism
ros89907_fm_i-xxxii.indd i 12/05/16 03:17 PM
corporate finance
CORE PRINCIPLES & APPLICATIONS
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Stephen A. Ross
Franco Modigliani Professor of Finance and
Economics
Sloan School of Management
Massachusetts Institute of Technology
Consulting Editor
FINANCIAL MANAGEMENT
Block, Hirt, and Danielsen
Foundations of Financial Management
Sixteenth Edition
Brealey, Myers, and Allen
Principles of Corporate Finance
Twelfth Edition
Brealey, Myers, and Allen
Principles of Corporate Finance, Concise
Second Edition
Brealey, Myers, and Marcus
Fundamentals of Corporate Finance
Ninth Edition
Brooks
FinGame Online 5.0
Bruner
Case Studies in Finance: Managing for
Corporate Value Creation
Seventh Edition
Cornett, Adair, and Nofsinger
Finance: Applications and Theory
Fourth Edition
Cornett, Adair, and Nofsinger
M: Finance
Third Edition
DeMello
Cases in Finance
Third Edition
Grinblatt (editor)
Stephen A. Ross, Mentor: Influence through
Generations
Grinblatt and Titman
Financial Markets and Corporate Strategy
Second Edition
Higgins
Analysis for Financial Management
Eleventh Edition
Ross, Westerfield, Jaffe, and Jordan
Corporate Finance
Eleventh Edition
Ross, Westerfield, Jaffe, and Jordan
Corporate Finance: Core Principles and
Applications
Fifth Edition
Ross, Westerfield, and Jordan
Essentials of Corporate Finance
Ninth Edition
Ross, Westerfield, and Jordan
Fundamentals of Corporate Finance
Eleventh Edition
Shefrin
Behavioral Corporate Finance: Decisions that
Create Value
Second Edition
INVESTMENTS
Bodie, Kane, and Marcus
Essentials of Investments
Tenth Edition
Bodie, Kane, and Marcus
Investments
Tenth Edition
Hirt and Block
Fundamentals of Investment Management
Tenth Edition
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Fundamentals of Investments: Valuation and
Management
Eighth Edition
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Running Money: Professional Portfolio
Management
First Edition
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Derivatives: Principles and Practice
Second Edition
FINANCIAL INSTITUTIONS AND
MARKETS
Rose and Hudgins
Bank Management and Financial Services
Ninth Edition
Rose and Marquis
Financial Institutions and Markets
Eleventh Edition
Saunders and Cornett
Financial Institutions Management: A Risk
Management Approach
Ninth Edition
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Financial Markets and Institutions
Sixth Edition
INTERNATIONAL FINANCE
Eun and Resnick
International Financial Management
Eighth Edition
REAL ESTATE
Brueggeman and Fisher
Real Estate Finance and Investments
Fifteenth Edition
Ling and Archer
Real Estate Principles: A Value Approach
Fifth Edition
FINANCIAL PLANNING AND
INSURANCE
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Retirement Plans: 401(k)s, IRAs, and Other
Deferred Compensation Approaches
Eleventh Edition
Altfest
Personal Financial Planning
Second Edition
Harrington and Niehaus
Risk Management and Insurance
Second Edition
Kapoor, Dlabay, Hughes, and Hart
Focus on Personal Finance: An Active Approach
to Achieve Financial Literacy
Fifth Edition
Kapoor, Dlabay, Hughes, and Hart
Personal Finance
Twelfth Edition
Walker and Walker
Personal Finance: Building Your Future
Second Edition
THE MCGRAW-HILL EDUCATION SERIES IN FINANCE, INSURANCE, AND REAL ESTATE
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F I F T H E D I T I O N
corporate finance
CORE PRINCIPLES & APPLICATIONS
Stephen A. Ross
Sloan School of Management
Massachusetts Institute of Technology
Randolph W. Westerfield
Marshall School of Business
University of Southern California
Jeffrey F. Jaffe
Wharton School of Business
University of Pennsylvania
Bradford D. Jordan
Gatton College of Business and Economics
University of Kentucky
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CORPORATE FINANCE: CORE PRINCIPLES & APPLICATIONS, FIFTH EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2018 by McGraw-Hill
Education. All rights reserved. Printed in the United States of America. Previous editions © 2014, 2011, 2009,
and 2007. No part of this publication may be reproduced or distributed in any form or by any means, or stored in
a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not
limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the
United States.
This book is printed on acid-free paper.
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Library of Congress Cataloging-in-Publication Data
Name: Ross, Stephen A., author.
Title: Corporate finance : core principles & applications / Stephen A. Ross,
Sloan School of Management, Massachusetts Institute of Technology,
Randolph W. Westerfield, Marshall School of Business, University of
Southern California, Jeffrey F. Jaffe, Wharton School of Business,
University of Pennsylvania, Bradford D. Jordan, Gatton College of Business
and Economics, University of Kentucky.
Description: Fifth edition. | New York, NY : McGraw-Hill Education, [2016] |
Series: The McGraw-Hill education series in finance, insurance, and real estate
Identifiers: LCCN 2016035324 | ISBN 9781259289903 (alk. paper)
Subjects: LCSH: Corporations—Finance.
Classification: LCC HG4026 .R6755 2016 | DDC 658.15—dc23 LC record available at
https://lccn.loc.gov/2016035324
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does
not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not
guarantee the accuracy of the information presented at these sites.
mheducation.com/highered
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To our family and friends with love and gratitude.
—S.A.R. R.W.W. J.F.J. B.D.J.
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Stephen A. Ross
SLOAN SCHOOL OF MANAGEMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Stephen A. Ross is the Franco Modigliani Professor of Financial Economics at the Sloan School of
Management, Massachusetts Institute of Technology. One of the most widely published authors
in finance and economics, Professor Ross is recognized for his work in developing the arbitrage
pricing theory, as well as for having made substantial contributions to the discipline through his
research in signaling, agency theory, option pricing, and the theory of the term structure of interest
rates, among other topics. A past president of the American Finance Association, he currently serves
as an associate editor of several academic and practitioner journals and is a trustee of CalTech.
Randolph W. Westerfield
MARSHALL SCHOOL OF BUSINESS, UNIVERSITY OF SOUTHERN CALIFORNIA
Randolph W. Westerfield is Dean Emeritus of the University of Southern California’s Marshall School
of Business and is the Charles B. Thornton Professor of Finance Emeritus. Professor Westerfield
came to USC from the Wharton School, University of Pennsylvania, where he was the chairman
of the finance department and member of the finance faculty for 20 years. He is a member of the
Board of Trustees of Oak Tree Capital Mutual Funds. His areas of expertise include corporate finan-
cial policy, investment management, and stock market price behavior.
ABOUT THE AUTHORS
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Bradford D. Jordan
GATTON COLLEGE OF BUSINESS AND ECONOMICS, UNIVERSITY OF KENTUCKY
Bradford D. Jordan is professor of finance and holder of the Richard W. and Janis H. Furst Endowed
Chair in Finance at the University of Kentucky. He has a long-standing interest in both applied
and theoretical issues in corporate finance and has extensive experience teaching all levels of
corporate finance and financial management policy. Professor Jordan has published numerous
articles on issues such as cost of capital, capital structure, and the behavior of security prices. He
is a past president of the Southern Finance Association, and he is coauthor of Fundamentals of
Investments: Valuation and Management, 8th edition, a leading investments text, also published
by McGraw-Hill Education.
Jeffrey F. Jaffe
WHARTON SCHOOL OF BUSINESS, UNIVERSITY OF PENNSYLVANIA
Jeffrey F. Jaffe has been a frequent contributor to finance and economic literatures in such jour-
nals as the Quarterly Economic Journal, The Journal of Finance, The Journal of Financial and
Quantitative Analysis, The Journal of Financial Economics, and The Financial Analysts Journal. His
best-known work concerns insider trading, where he showed both that corporate insiders earn
abnormal profits from their trades and that regulation has little effect on these profits. He has also
made contributions concerning initial public offerings, the regulation of utilities, the behavior of
market makers, the fluctuation of gold prices, the theoretical effect of inflation on interest rates,
the empirical effect of inflation on capital asset prices, the relationship between small-capitalization
stocks and the January effect, and the capital structure decision.
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IN THE BEGINNING. . .
It was probably inevitable that the four of us would collaborate on
this project. Over the last 20 or so years, we have been working as
two separate “RWJ” teams. In that time, we managed (much to our
own amazement) to coauthor two widely adopted undergraduate
texts and an equally successful graduate text, all in the corporate
finance area. These three books have collectively totaled more than
31 editions (and counting), plus a variety of country-specific editions
and international editions, and they have been translated into at
least a dozen foreign languages.
Even so, we knew that there was a hole in our lineup at the
graduate (MBA) level. We’ve continued to see a need for a concise,
up-to-date, and to-the-point product, the majority of which can be
realistically covered in a typical single term or course. As we began
to develop this book, we realized (with wry chuckles all around)
that, between the four of us, we have been teaching and research-
ing finance principles for well over a century. From our own very
extensive experience with this material, we recognized that corpo-
rate finance introductory classes often have students with extremely
diverse educational and professional backgrounds. We also recog-
nized that this course is increasingly being delivered in alternative
formats ranging from traditional semester-long classes to highly
compressed modules, to purely online courses, taught both syn-
chronously and asynchronously.
OUR APPROACH
To achieve our objective of reaching out to the many different types
of students and the varying course environments, we worked to
distill the subject of corporate finance down to its core, while main-
taining a decidedly modern approach. We have always maintained
that corporate finance can be viewed as the working of a few very
powerful intuitions. We also know that understanding the “why”
is just as important, if not more so, than understanding the “how.”
Throughout the development of this book, we continued to take a
hard look at what is truly relevant and useful. In doing so, we have
worked to downplay purely theoretical issues and minimize the use
of extensive and elaborate calculations to illustrate points that are
either intuitively obvious or of limited practical use.
Perhaps more than anything, this book gave us the chance to
pool all that we have learned about what really works in a corporate
finance text. We have received an enormous amount of feedback
over the years. Based on that feedback, the two key ingredients that
we worked to blend together here are the careful attention to peda-
gogy and readability that we have developed in our undergraduate
books and the strong emphasis on current thinking and research
that we have always stressed in our graduate book.
From the start, we knew we didn’t want this text to be encyclo-
pedic. Our goal instead was to focus on what students really need to
carry away from a principles course. After much debate and consul-
tation with colleagues who regularly teach this material, we settled
on a total of 21 chapters. Chapter length is typically 30 pages, so
most of the book (and, thus, most of the key concepts and applica-
tions) can be realistically covered in a single term or module. Writing
a book that strictly focuses on core concepts and applications nec-
essarily involves some picking and choosing with regard to both
topics and depth of coverage. Throughout, we strike a balance by
introducing and covering the essentials, while leaving more special-
ized topics to follow-up courses.
As in our other books, we treat net present value (NPV) as the
underlying and unifying concept in corporate finance. Many texts
stop well short of consistently integrating this basic principle. The
simple, intuitive, and very powerful notion that NPV represents the
excess of market value over cost often is lost in an overly mechani-
cal approach that emphasizes computation at the expense of com-
prehension. In contrast, every subject we cover is firmly rooted in
valuation, and care is taken throughout to explain how particular
decisions have valuation effects.
Also, students shouldn’t lose sight of the fact that financial
management is about management. We emphasize the role of the
financial manager as decision maker, and we stress the need for
managerial input and judgment. We consciously avoid “black box”
approaches to decisions, and where appropriate, the approximate,
pragmatic nature of financial analysis is made explicit, possible pit-
falls are described, and limitations are discussed.
NEW AND NOTEWORTHY TO THE FIFTH EDITION
All chapter openers and examples have been updated to reflect the
financial trends and turbulence of the last several years. In addition,
we have updated the end-of-chapter problems in every chapter.
We have tried to incorporate the many exciting new research find-
ings in corporate finance. Several chapters have been extensively
rewritten.
• In the eight years since the “financial crisis” or “great
recession,” we see that the world’s financial markets
are more integrated than ever before. The theory and
practice of corporate finance has been moving forward
at a fast pace and we endeavor to bring the theory
and practice to life with completely updated chapter
FROM THE AUTHORS
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openers, many new modern examples, completely
updated end of chapter problems and questions.
• In recent years we have seen unprecedented high
stock and bond values and returns as well as histori-
cally low interest rates and inflation. Chapter 10 Risk
and Return: Lessons from Market History updates and
internationalizes our discussion of historical risk and
return. With updated historical data, our estimates of
the equity risk premium are on stronger footing And
our understanding of the capital market environment is
heightened.
• Given the importance of debt in most firms capital
structure, it is a mystery that many firms use no debt.
There is new and exciting research of this “no debt”
behavior that sheds new light on how firms make actual
capital structure decisions. Chapter 15 Capital Structure:
Limits to the Use of Debt explores this new research
and incorporates it into our discussion of Capital
Structure.
• Chapter 16 Dividends and Other Payouts updates the
record of earnings, dividends, and repurchases for
large U.S. firms. The recent trends show repurchases
far outpacing dividends in firm payout policy. Since
firms may use dividends or repurchases to pay out cash
to equity investors, the recent importance of repur-
chases suggests a changing financial landscape.
• There are several twists and turns to the calculation
of the firms weighted average of capital. Since the
weighted average cost of capital is the most important
benchmark we use for capital budgeting and repre-
sents a firm’s “opportunity cost,” its calculation is criti-
cal. We update our estimates of Eastman Chemical cost
of capital using readily available data from the Internet
to distinguish the nuances of this calculation.
Our attention to updating and improving also extended to
the extensive collection of support and enrichment materials that
accompany the text. Working with many dedicated and talented
colleagues and professionals, we continue to provide supplements
that are unrivaled at the graduate level (a complete description
appears in the following pages). Whether you use just the textbook,
or the book in conjunction with other products, we believe you will
be able to find a combination that meets your current as well as
your changing needs.
—Stephen A. Ross
—Randolph W. Westerfield
—Jeffrey F. Jaffe
—Bradford D. Jordan
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Corporate Finance: Core
Principles & Applications
is rich in valuable learning
tools and support to help
students succeed in learning
the fundamentals of financial
management.
Confirming Pages
CHAPTER 5 Interest Rates and Bond Valuation 147
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A convertible bond can be swapped for a fixed number of shares of stock anytime before
maturity at the holder’s option. Convertibles are relatively common, but the number has
been decreasing in recent years.
A put bond allows the holder to force the issuer to buy the bond back at a stated price.
For example, International Paper Co. has bonds outstanding that allow the holder to force
International Paper to buy the bonds back at 100 percent of the face value given that cer-
tain “risk” events happen. One such event is a change in credit rating from investment
grade to lower than investment grade by Moody’s or S&P. The put feature is therefore just
the reverse of the call provision.
BEAUTY IS IN THE EYE OF THE BONDHOLDER
Many bonds have unusual or exotic features. One of the most common types is an asset-backed, or securitized, bond.
Mortgage-backed securities were big news in 2007. For several years, there had been rapid growth in so-called sub-
prime mortgage loans, which are mortgages made to individuals with less than top-quality credit. However, a combina-
tion of cooling (and in some places dropping) housing prices and rising interest rates caused mortgage delinquencies
and foreclosures to rise. This increase in problem mortgages caused a significant number of mortgage-backed securities
to drop sharply in value and created huge losses for investors. Bondholders of a securitized bond receive interest and
principal payments from a specific asset (or pool of assets) rather than a specific company. For example, at one point
rock legend David Bowie sold $55 million in bonds backed by future royalties from his albums and songs (that’s some
serious ch-ch-ch-change!). Owners of these “Bowie” bonds received the royalty payments, so if Bowie’s record sales fell,
there was a possibility the bonds could have defaulted. Other artists have sold bonds backed by future royalties, includ-
ing James Brown, Iron Maiden, and the estate of the legendary Marvin Gaye.
Mortgage-backs are the best known type of asset-backed security. With a mortgage-backed bond, a trustee pur-
chases mortgages from banks and merges them into a pool. Bonds are then issued, and the bondholders receive pay-
ments derived from payments on the underlying mortgages. One unusual twist with mortgage bonds is that if interest
rates decline, the bonds can actually decrease in value. This can occur because homeowners are likely to refinance at
the lower rates, paying off their mortgages in the process. Securitized bonds are usually backed by assets with long-term
payments, such as mortgages. However, there are bonds securitized by car loans and credit card payments, among
other assets, and a growing market exists for bonds backed by automobile leases.
The reverse convertible is a relatively new type of structured note. This type generally offers a high coupon rate, but
the redemption at maturity can be paid in cash at par value or paid in shares of stock. For example, one recent General
Motors (GM) reverse convertible had a coupon rate of 16 percent, which is a very high coupon rate in today’s interest rate
environment. However, at maturity, if GM’s stock declined sufficiently, bondholders would receive a fixed number of GM
shares that were worth less than par value. So, while the income portion of the bond return would be high, the potential
loss in par value could easily erode the extra return.
CAT bonds are issued to cover insurance companies against natural catastrophes. The type of natural catastrophe
is outlined in the bond’s indenture. For example, about 30 percent of all CAT bonds protect against a North Atlantic
hurricane. The way these issues are structured is that the borrowers can suspend payment temporarily (or even perma-
nently) if they have significant hurricane-related losses. These CAT bonds may seem like pretty risky investments, but to
date, only three such bonds have not made their scheduled payments, courtesy of the massive destruction caused by
Hurricane Katrina, the 2011 Japanese tsunami, and an unusually active 2011 tornado season.
Perhaps the most unusual bond (and certainly the most ghoulish) is the “death bond.” Companies such as Stone
Street Financial purchase life insurance policies from individuals who are expected to die within the next 10 years.
They then sell bonds that are paid off from the life insurance proceeds received when the policyholders pass away.
The return on the bonds to investors depends on how long the policyholders live. A major risk is that if medical treat-
ment advances quickly, it will raise the life expectancy of the policyholders, thereby decreasing the return to the
bondholder.
FINANCE MATTERS
Finance Matters
By exploring information found in recent publica-
tions and building upon concepts learned in each
chapter, these boxes work through real-world
issues relevant to the surrounding text.
PEDAGOGY
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ros89907_ch08_230-261.indd 230 11/10/16 10:29 AM
230 PART 2 Valuation and Capital Budgeting
8
OPENING
CASE
Making Capital
Investment Decisions
Everyone knows that computer chips evolve quickly, getting smaller, faster, and cheaper.
In fact, the famous Moore’s Law (named after Intel cofounder Gordon Moore) predicts that the
number of transistors placed on a chip will double every two years (and this prediction has
held up very well since it was published in 1965). This growth often means that companies
need to build new fabrication facilities. For example, in 2015, GlobalFoundries announced
that it was going to spend about $646 million to further expand its manufacturing plant in
Saratoga, New York. The expansion at the plant would allow the company to produce more
of its new 14 nanometer (nm) chips. Not to be outdone, IBM announced that it was investing
$3 billion in a public-private partnership with New York State, GlobalFoundries, and Samsung
in an effort to manufacture 7 nm chips, which would be smaller, faster, and consume less
energy than current chips.
This chapter follows up on our previous one by delving more deeply into capital budget-
ing and the evaluation of projects such as these chip manufacturing facilities. We identify the
relevant cash flows of a project, including initial investment outlays, requirements for net
working capital, and operating cash flows. Further, we look at the effects of depreciation and
taxes. We also examine the impact of inflation and show how to evaluate consistently the NPV
analysis of a project.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
8.1 INCREMENTAL CASH FLOWS
Cash Flows—Not Accounting Income
You may not have thought about it, but there is a big difference between corporate finance
courses and financial accounting courses. Techniques in corporate finance generally use
cash flows, whereas financial accounting generally stresses income or earnings numbers.
Certainly, our text follows this tradition, as our net present value techniques discount cash
flows, not earnings. When considering a single project, we discount the cash flows that
the firm receives from the project. When valuing the firm as a whole, we discount the
cash flows—not earnings—that an investor receives.
Chapter Opening Case
Each chapter begins with a recent real-
world event to introduce students to chap-
ter concepts.
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ros89907_ch02_019-042.indd 19 11/10/16 09:10 AM
CHAPTER 2 Financial Statements and Cash Flow 19
2
OPENING
CASE
Financial Statements
and Cash Flow
When a company announces a “write-off,” that frequently means that the value of the compa-
ny’s assets has declined. For example, in July 2015, Microsoft announced that it would write
off $7.6 billion related to its purchase of Nokia’s phone business the previous year. What made
the write-off interesting was that Microsoft had only paid $7.2 billion for the phone business.
The oil business was also hit hard in 2015 as the five largest publicly traded oil companies
working in Wyoming wrote off a combined $41 billion for the first nine months of the year.
These write-offs were due to the declining value of oil production facilities in that state.
While Microsoft’s write-off is large, the record holder is media giant Time Warner, which
took a charge of $45.5 billion in the fourth quarter of 2002. This enormous write-off followed
an earlier, even larger, charge of $54 billion.
So, did the stockholders in these companies lose billions of dollars when these assets
were written off? Fortunately for them, the answer is probably not. Understanding why ulti-
mately leads us to the main subject of this chapter, that all-important substance known as
cash flow.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
2.1 THE BALANCE SHEET
The balance sheet is an accountant’s snapshot of the firm’s accounting value on a par-
ticular date, as though the firm stood momentarily still. The balance sheet has two sides:
On the left are the assets and on the right are the liabilities and stockholders’ equity. The
balance sheet states what the firm owns and how it is financed. The accounting definition
that underlies the balance sheet and describes the balance is
Assets ≡ Liabilities + Stockholders’ equity [2.1]
We have put a three-line equality in the balance equation to indicate that it must always
hold, by definition. In fact, the stockholders’ equity is defined to be the difference between
the assets and the liabilities of the firm. In principle, equity is what the stockholders would
have remaining after the firm discharged its obligations.
Table 2.1 gives the 2016 and 2017 balance sheets for the fictitious U.S. Composite
Corporation. The assets in the balance sheet are listed in order by the length of time it
normally would take an ongoing firm to convert them to cash. The asset side depends on
the nature of the business and how management chooses to conduct it. Management must
make decisions about cash versus marketable securities, credit versus cash sales, whether
ExcelMaster
coverage online
www.mhhe.com/RossCore5e
Two excellent sources
for company financial
information are finance.
yahoo.com and money.
cnn.com.
Core Calculator Skills
This icon, located in the margins of the text near key con-
cepts and equations, indicates that additional coverage is
available describing how to use a financial calculator when
studying the topic. This additional coverage can be found
in a special calculator section, Appendix C.
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Spreadsheet Techniques
This feature helps students to improve their Excel spreadsheet
skills, particularly as they relate to corporate finance. This feature
appears in self-contained sections and shows students how to set
up spreadsheets to analyze common financial problems—a vital
part of every business student’s education. For even more help
using Excel, students have access to Excel Master, an in-depth
online tutorial.
Confirming Pages
PART 2 Valuation and Capital Budgeting
ros89907_ch05_130-164.indd 138 11/10/16 04:18 PM
138
How to Calculate Bond Pr ices and
Yie lds Us ing a Spreadsheet SPREADSHEET TECHNIQUES
Most spreadsheets have fairly elaborate routines available for calculating bond values and yields; many of
these routines involve details that we have not discussed. However, setting up a simple spreadsheet to cal-
culate prices or yields is straightforward, as our next two spreadsheets show:
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
A B C D E F G H
Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a yield to
maturity of 9 percent. If the bond makes semiannual payments, what is its price today?
Settlement date: 1/1/00
Maturity date: 1/1/22
Annual coupon rate: .08
Yield to maturity: .09
Face value (% of par): 100
Coupons per year: 2
Bond price (% of par): 90.49
The formula entered in cell B13 is =PRICE(B7,B8,B9,B10,B11,B12); notice that face value and bond
price are given as a percentage of face value.
Using a spreadsheet to calculate bond values
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
A B C D E F G H
Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a price of
$960.17. If the bond makes semiannual payments, what is its yield to maturity?
Settlement date: 1/1/00
Maturity date: 1/1/22
Annual coupon rate: .08
Bond price (% of par): 96.017
Face value (% of par): 100
Coupons per year: 2
Yield to maturity: .084
The formula entered in cell B13 is =YIELD(B7,B8,B9,B10,B11,B12); notice that face value and bond
price are entered as a percentage of face value.
Using a spreadsheet to calculate bond yields
1 7
In our spreadsheets, notice that we had to enter two dates, a settlement date and a maturity date. The
settlement date is just the date you actually pay for the bond, and the maturity date is the day the bond
actually matures. In most of our problems, we don’t explicitly have these dates, so we have to make them
up. For example, since our bond has 22 years to maturity, we just picked 1/1/2000 (January 1, 2000) as
the settlement date and 1/1/2022 (January 1, 2022) as the maturity date. Any two dates would do as long
as they are exactly 22 years apart, but these are particularly easy to work with. Finally, notice that we had
to enter the coupon rate and yield to maturity in annual terms and then explicitly provide the number of
coupon payments per year.
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530 PART 5 Special Topics
As indicated, this ratio is called the delta of the call. In words, a $1 swing in the price of
the stock gives rise to a $1/2 swing in the price of the call. Because we are trying to dupli-
cate the call with the stock, it seems sensible to buy one-half a share of stock instead of
buying one call. In other words, the risk of buying one-half a share of stock should be the
same as the risk of buying one call.
DETERMINING THE AMOUNT OF BORROWING How did we know how much to borrow?
Buying one-half a share of stock brings us either $30 or $20 at expiration, which is exactly
$20 more than the payoffs of $10 and $0, respectively, from the call. To duplicate the call
through a purchase of stock, we should also borrow enough money so that we have to pay
back exactly $20 of interest and principal. This amount of borrowing is merely the present
value of $20, which is $18.18 (= $20/1.10).
Now that we know how to determine both the delta and the amount of borrowing, we
can write the value of the call as:
Value of call = Stock price × Delta − Amount borrowed [17.2]
$ 6.82 = $50 × 1 __
2
− $18.18
We will find this intuition very useful in explaining the Black−Scholes model.
RISK-NEUTRAL VALUATION Before leaving this simple example, we should comment on
a remarkable feature. We found the exact value of the option without even knowing the
probability that the stock would go up or down! If an optimist thought the probability
of an up move was very high and a pessimist thought it was very low, they would still
agree on the option value. How could that be? The answer is that the current $50 stock
price already balances the views of the optimist and the pessimist. The option reflects that
balance because its value depends on the stock price.
This insight provides us with another approach to valuing the call. If we don’t need the
probabilities of the two states to value the call, perhaps we can select any probabilities
we want and still come up with the right answer. Suppose we selected probabilities such
that the return on the stock is equal to the risk-free rate of 10 percent. We know that the
stock return given a rise is 20 percent (= $60/$50 − 1) and the stock return given a fall is
−20 percent (= $40/$50 − 1). Thus, we can solve for the probability of a rise necessary to
achieve an expected return of 10 percent as:
10% = Probability of a rise × 20% + 1 − Probability of a rise × − 20%
Solving this formula, we find that the probability of a rise is 3/4 and the probability of a
fall is 1/4. If we apply these probabilities to the call, we can value it as:
Value of call =
3 __
4
× $10 + 1 __
4
× $0
_______________
1.10
= $6.82
the same value that we got from the duplicating approach.
Why did we select probabilities such that the expected return on the stock is 10 percent?
We wanted to work with the special case where investors are risk-neutral. This case occurs
when the expected return on any asset (including both the stock and the call) is equal to the
risk-free rate. In other words, this case occurs when investors demand no additional com-
pensation beyond the risk-free rate, regardless of the risk of the asset in question.
What would have happened if we had assumed that the expected return on the stock was
greater than the risk-free rate? The value of the call would still be $6.82. However, the cal-
culations would be more difficult. For example, if we assumed that the expected return on
Numbered Equations
Key equations are numbered within the text and listed on the
back end sheets for easy reference.
END-OF-CHAPTER MATERIAL
The end-of-chapter material reflects
and builds on the concepts learned
from the chapter and study features.
Questions and Problems
Because solving problems is so critical to students’ learning,
we provide extensive end-of-chapter questions and prob-
lems. The questions and problems are segregated into three
learning levels: Basic, Intermediate, and Challenge. All prob-
lems are fully annotated so that students and instructors can
readily identify particular types. Also, most of the problems
are available in McGraw-Hill’s Connect—see the next section
of this preface for more details.
www.mhhe.com/RossCore5e
Confirming Pages
ros89907_ch02_019-042.indd 34 11/10/16 09:10 AM
PART 1 Overview34
5. Book Values versus Market Values Under standard accounting rules, it is possible for a company’s
liabilities to exceed its assets. When this occurs, the owners’ equity is negative. Can this happen with
market values? Why or why not?
6. Cash Flow from Assets Suppose a company’s cash flow from assets was negative for a particular
period. Is this necessarily a good sign or a bad sign?
7. Operating Cash Flow Suppose a company’s operating cash flow was negative for several years
running. Is this necessarily a good sign or a bad sign?
8. Net Working Capital and Capital Spending Could a company’s change in net working capital
be negative in a given year? (Hint: Yes.) Explain how this might come about. What about net capital
spending?
9. Cash Flow to Stockholders and Creditors Could a company’s cash flow to stockholders be negative
in a given year? (Hint: Yes.) Explain how this might come about. What about cash flow to creditors?
10. Firm Values Referring back to the Microsoft example used at the beginning of the chapter, note that
we suggested that Microsoft’s stockholders probably didn’t suffer as a result of the reported loss. What
do you think was the basis for our conclusion?
QUESTIONS AND PROBLEMS
1. Building a Balance Sheet Burnett, Inc., has current assets of $6,800, net fixed assets of $29,400,
current liabilities of $5,400, and long-term debt of $13,100. What is the value of the shareholders’
equity account for this firm? How much is net working capital?
2. Building an Income Statement Bradds, Inc., has sales of $528,600, costs of $264,400, depreciation
expense of $41,700, interest expense of $20,700, and a tax rate of 35 percent. What is the net income
for the firm? Suppose the company paid out $27,000 in cash dividends. What is the addition to retained
earnings?
3. Market Values and Book Values Klingon Cruisers, Inc., purchased new cloaking machinery three
years ago for $7 million. The machinery can be sold to the Romulans today for $5.3 million. Klingon’s
current balance sheet shows net fixed assets of $3.9 million, current liabilities of $1.075 million, and
net working capital of $320,000. If all the current accounts were liquidated today, the company would
receive $410,000 cash. What is the book value of Klingon’s total assets today? What is the sum of the
market value of NWC and market value of assets?
4. Calculating Taxes The Alexander Co. had $328,500 in taxable income. Using the rates from Table 2.3
in the chapter, calculate the company’s income taxes. What is the average tax rate? What is the marginal
tax rate?
5. Calculating OCF Timsung, Inc., has sales of $30,700, costs of $11,100, depreciation expense of $2,100,
and interest expense of $1,140. If the tax rate is 40 percent, what is the operating cash flow, or OCF?
6. Calculating Net Capital Spending Busch Driving School’s 2016 balance sheet showed net fixed assets
of $3.75 million, and the 2017 balance sheet showed net fixed assets of $4.45 million. The company’s
2017 income statement showed a depreciation expense of $395,000. What was the company’s net
capital spending for 2017?
7. Building a Balance Sheet The following table presents the long-term liabilities and stockholders’
equity of Information Control Corp. one year ago:
Basic
(Questions 1–10)
Long-term debt
Preferred stock
Common stock ($1 par value)
Capital surplus
Accumulated retained earnings
$37,000,000
2,100,000
8,900,000
41,000,000
75,300,000
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Excel Problems
Indicated by the Excel icon in the margin, these problems
are integrated in the Questions and Problems section of
almost all chapters. Located on the book’s website, Excel
templates have been created for each of these problems.
Students can use the data in the problem to work out the
solution using Excel skills.
www.mhhe.com/RossCore5e
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CHAPTER 11 Return and Risk: The Capital Asset Pricing Model (CAPM) 349
QUESTIONS AND PROBLEMS
1. Determining Portfolio Weights What are the portfolio weights for a portfolio that has 125 shares of
Stock A that sell for $38 per share and 175 shares of Stock B that sell for $26 per share?
2. Portfolio Expected Return You own a portfolio that has $3,850 invested in Stock A and $6,100
invested in Stock B. If the expected returns on these stocks are 7.2 percent and 13.1 percent,
respectively, what is the expected return on the portfolio?
3. Portfolio Expected Return You own a portfolio that is 20 percent invested in Stock X, 35 percent
invested in Stock Y, and 45 percent invested in Stock Z. The expected returns on these three stocks are
9.2 percent, 11.8 percent, and 14.3 percent, respectively. What is the expected return on the portfolio?
4. Portfolio Expected Return You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an
expected return of 12.4 percent and Stock Y with an expected return of 10.2 percent. If your goal is to create
a portfolio with an expected return of 10.9 percent, how much money will you invest in Stock X? In Stock Y?
5. Calculating Expected Return Based on the following information, calculate the expected return.
STATE OF
ECONOMY
PROBABILITY OF
STATE OF ECONOMY
RATE OF RETURN
IF STATE OCCURS
Recession .35 –.09
Normal .50 .15
Boom .15 .34
6. Calculating Returns and Standard Deviations Based on the following information, calculate the
expected return and standard deviation for the two stocks.
STATE OF
ECONOMY
PROBABILITY OF
STATE OF ECONOMY
RATE OF RETURN IF STATE OCCURS
STOCK A STOCK B
Recession .15 .01 –.19
Normal .50 .09 .11
Boom .35 .13 .37
7. Calculating Returns and Standard Deviations Based on the following information, calculate the
expected return and standard deviation of the following stock.
STATE OF
ECONOMY
PROBABILITY OF
STATE OF ECONOMY
RATE OF RETURN
IF STATE OCCURS
Depression .10 –.279
Recession .20 –.128
Normal .45 .141
Boom .25 .365
8. Calculating Expected Returns A portfolio is invested 25 percent in Stock G, 60 percent in Stock J, and
15 percent in Stock K. The expected returns on these stocks are 8.6 percent, 10.8 percent, and 13.4
percent, respectively. What is the portfolio’s expected return? How do you interpret your answer?
9. Returns and Standard Deviations Consider the following information:
STATE OF
ECONOMY
PROBABILITY OF
STATE OF ECONOMY
RATE OF RETURN IF STATE OCCURS
STOCK A STOCK B STOCK C
Boom .15 .26 .40 .38
Good .45 .10 .18 .15
Poor .35 .02 –.19 –.03
Bust .05 –.08 –.32 –.06
Basic
(Questions 1–19)
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ros89907_ch11_316-356.indd 354 11/17/16 01:53 PM
PART 3 Risk and Return354
b. What are the expected return and standard deviation of a portfolio consisting of 70 percent of Stock
A and 30 percent of Stock B?
c. What is the beta of the portfolio in part (b)?
38. Minimum Variance Portfolio Assume Stocks A and B have the following characteristics:
STOCK EXPECTED RETURN (%) STANDARD DEVIATION (%)
A 13 34
B 11 58
The covariance between the returns on the two stocks is .01.
a. Suppose an investor holds a portfolio consisting of only Stock A and Stock B. Find the portfolio
weights, XA and XB , such that the variance of his portfolio is minimized. (Hint: Remember that the
sum of the two weights must equal 1.)
b. What is the expected return on the minimum variance portfolio?
c. If the covariance between the returns on the two stocks is –.15, what are the minimum variance
weights?
d. What are the variance and standard deviation of the portfolio in part (c)?
WHAT’S ON THE WEB?
1. Expected Return You want to find the expected return for Honeywell using the CAPM. First you need
the market risk premium. Go to money.cnn.com and find the current interest rate for three-month
Treasury bills. Use the historic market risk premium from Chapter 10 as the market risk premium. Next,
go to finance.yahoo.com, enter the ticker symbol HON for Honeywell, and find the beta for Honeywell.
What is the expected return for Honeywell using CAPM? What assumptions have you made to arrive at
this number?
2. Portfolio Beta You have decided to invest in an equally weighted portfolio consisting of American
Express, Procter & Gamble, Home Depot, and DuPont and need to find the beta of your portfolio. Go to
finance.yahoo.com and find the beta for each of the companies. What is the beta for your portfolio?
3. Beta Which companies currently have the highest and lowest betas? Go to finance.yahoo.com and find
the “Stock Screener” link. Enter 0 as the maximum beta and search. How many stocks currently have a
beta less than or equal to 0? What is the lowest beta? Go back to the stock screener and enter 3 as the
minimum. How many stocks have a beta above 3? What stock has the highest beta?
4. Security Market Line Go to finance.yahoo.com and enter the ticker symbol IP for International Paper.
Follow the “Key Statistics” link to get the beta for the company. Next, find the estimated (or “target”)
price in 12 months according to market analysts. Using the current share price and the mean target
price, compute the expected return for this stock. Don’t forget to include the expected dividend
payments over the next year. Now go to money.cnn.com and find the current interest rate for three-
month Treasury bills. Using this information, calculate the expected return on the market using the
reward-to-risk ratio. Does this number make sense? Why or why not?
The CAPM is one of the most thoroughly researched models in financial economics. When beta is estimated
in practice, a variation of CAPM called the market model is often used. To derive the market model, we start
with the CAPM:
E( R i ) = R F × β[E( R M ) − R F ]
Since CAPM is an equation, we can subtract the risk-free rate from both sides, which gives us
E( R i ) − R F = β[E( R M ) − R F ]
EXCEL MASTER IT ! PROBLEM
What’s On the Web?
These end-of-chapter activities show students how to use and learn from
the vast amount of financial resources available on the Internet.
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Excel Master-It! Problems
These more in-depth mini-case studies highlight higher-
level Excel skills. Students are encouraged to use Excel
to solve real-life financial problems using the concepts
they have learned in the chapter and the Excel skills
they have acquired thus far.
www.mhhe.com/RossCore5e
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CHAPTER 5 Interest Rates and Bond Valuation 163
EXCEL MASTER IT ! PROBLEM
Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated
portfolio because the proceeds of the portfolio are dedicated to the future liability. In such a case, the port-
folio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the
coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at
a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if
interest rates increase, the portfolio value at maturity will be higher than needed.
Suppose Ice Cubes, Inc., has the following liability due in five years. The company is going to buy five-year
bonds today to meet the future obligation. The liability and current YTM are below:
Amount of liability:
Current YTM:
$100,000,000
8%
a. At the current YTM, what is the face value of the bonds the company has to purchase today to meet
its future obligation? Assume that the bonds in the relevant range will have the same coupon rate as
the current YTM and these bonds make semiannual coupon payments.
b. Assume the interest rates remain constant for the next five years. Thus, when the company reinvests
the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in five years?
c. Assume that immediately after the company purchases the bonds, interest rates either rise or fall by
1 percent. What is the value of the portfolio in five years under these circumstances?
One way to eliminate reinvestment risk is called immunization. Rather than buying bonds with the same maturity
as the liability, the company instead buys bonds with the same duration as the liability. If you think about the ded-
icated portfolio, if the interest rate falls, the future value of the reinvested coupon payments decreases. However,
as interest rates fall, the price of bonds increases. These effects offset each other in an immunized portfolio.
Another advantage of using duration to immunize a portfolio is that the duration of a portfolio is the
weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a portfo-
lio, you simply take the weight of each asset multiplied by its duration and then sum the results.
d. What is the duration of the liability for Ice Cubes, Inc.?
e. Suppose the two bonds shown below are the only bonds available to immunize the liability. What
face amount of each bond will the company need to purchase to immunize the portfolio?
FINANCING EAST COAST YACHTS’ EXPANSION PLANS
WITH A BOND ISSUE
After Dan’s EFN analysis for East Coast Yachts (see the Closing Case in Chapter 3), Larissa has decided to expand
the company’s operations. She has asked Dan to enlist an underwriter to help sell $45 million in new 30-year
bonds to finance new construction. Dan has entered into discussions with Renata Harper, an underwriter from
the firm of Crowe & Mallard, about which bond features East Coast Yachts should consider and also what coupon
CLOSING CASE
BOND A BOND B
Settlement
Maturity
Coupon rate
YTM
Coupons per year
1/1/2000
1/1/2003
7.00%
7.50%
2
1/1/2000
1/1/2008
8.00%
9.00%
2
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CHAPTER 12 Risk, Cost of Capital, and Valuation 389
ros89907_ch12_357-389.indd 389 11/17/16 02:28 PM
THE COST OF CAPITAL FOR SWAN MOTORS
You have recently been hired by Swan Motors, Inc. (SMI), in its relatively new treasury management depart-
ment. SMI was founded eight years ago by Joe Swan. Joe found a method to manufacture a cheaper battery
with much greater energy density than was previously possible, giving a car powered by the battery a range of
700 miles before requiring a charge. The cars manufactured by SMI are midsized and carry a price that allows
the company to compete with other mainstream auto manufacturers. The company is privately owned by Joe
and his family, and it had sales of $97 million last year.
SMI primarily sells to customers who buy the cars online, although it does have a limited number of
company-owned dealerships. The customer selects any customization and makes a deposit of 20 percent of
the purchase price. After the order is taken, the car is made to order, typically within 45 days. SMI’s growth to
date has come from its profits. When the company had sufficient capital, it would expand production. Relatively
little formal analysis has been used in its capital budgeting process. Joe has just read about capital budget-
ing techniques and has come to you for help. For starters, the company has never attempted to determine its
cost of capital, and Joe would like you to perform the analysis. Because the company is privately owned, it
is difficult to determine the cost of equity for the company. Joe wants you to use the pure play approach to
estimate the cost of capital for SMI, and he has chosen Tesla Motors as a representative company. The follow-
ing questions will lead you through the steps to calculate this estimate.
1. Most publicly traded corporations are required to submit 10Q (quarterly) and 10K (annual) reports to the
SEC detailing their financial operations over the previous quarter or year, respectively. These corporate
filings are available on the SEC website at www.sec.gov. Go to the SEC website and enter “TSLA” for
Tesla in the “Search for Company Filings” link and search for SEC filings made by Tesla. Find the most
recent 10Q or 10K and download the form. Look on the balance sheet to find the book value of debt
and the book value of equity. If you look further down the report, you should find a section titled either
“Long-Term Debt” or “Long-Term Debt and Interest Rate Risk Management” that will list a breakdown of
Tesla’s long-term debt.
2. To estimate the cost of equity for Tesla, go to finance.yahoo.com and enter the ticker symbol “TSLA.”
Follow the various links to find answers to the following questions: What is the most recent stock
price listed for Tesla? What is the market value of equity, or market capitalization? How many shares of
stock does Tesla have outstanding? What is the beta for Tesla? Now go back to finance.yahoo.com and
follow the “Bonds” link. What is the yield on three-month Treasury bills? Using a 7 percent market risk
premium, what is the cost of equity for Tesla using the CAPM?
3. Go to www.reuters.com and find the list of competitors in the industry. Find the beta for each of these
competitors, and then calculate the industry average beta. Using the industry average beta, what is the
cost of equity? Does it matter if you use the beta for Tesla or the beta for the industry in this case?
4. You now need to calculate the cost of debt for Tesla. Go to http://finra-markets.morningstar.com/
BondCenter/Default.jsp, enter Tesla as the company, and find the yield to maturity for each of Tesla’s
bonds. What is the weighted average cost of debt for Tesla using the book value weights and the
market value weights? Does it make a difference in this case if you use book value weights or market
value weights?
5. You now have all the necessary information to calculate the weighted average cost of capital for Tesla.
Calculate the weighted average cost of capital for Tesla using book value weights and market value
weights, assuming Tesla has a 35 percent marginal tax rate. Which cost of capital number is more
relevant?
6. You used Tesla as a representative company to estimate the cost of capital for SMI. What are some of
the potential problems with this approach in this situation? What improvements might you suggest?
CLOSING CASE
End-of-Chapter Cases
Located at the end of each chapter, these mini-cases focus
on common company situations that embody important
corporate finance topics. Each case presents a new sce-
nario, data, and a dilemma. Several questions at the end of
each case require students to analyze and focus on all of
the material they learned in that chapter.
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COMPREHENSIVE TEACHING
INSTRUCTOR SUPPORT
∙ Instructor’s Manual
prepared by Melissa Frye, University of Central Florida, Ann Marie Whyte,
University of Central Florida, and Joseph Smolira, Belmont University
A great place to find new lecture ideas. The IM has three main sections. The first
section contains a chapter outline and other lecture materials. The annotated outline
for each chapter includes lecture tips, real-world tips, ethics notes, suggested
PowerPoint slides, and, when appropriate, a video synopsis. Detailed solutions for
all end-of-chapter problems appear in Section three.
∙ Test Bank
prepared by Kay Johnson
Great format for a better testing process. The Test Bank has 75–100 questions per
chapter that closely link with the text material and provide a variety of question
formats (multiple-choice questions/problems and essay questions) and levels of
difficulty (basic, intermediate, and challenge) to meet every instructor’s testing
needs. Problems are detailed enough to make them intuitive for students, and
solutions are provided for the instructor.
∙ Computerized Test Bank
TestGen is a complete, state-of-the-art test generator and editing application
software that allows instructors to quickly and easily select test items from
McGraw-Hill’s testbank content. The instructors can then organize, edit, and
customize questions and answers to rapidly generate tests for paper or online
administration. Questions can include stylized text, symbols, graphics, and
equations that are inserted directly into questions using built-in mathematical
templates. TestGen’s random generator provides the option to display different text
or calculated number values each time questions are used. With both quick-and-
simple test creation and flexible and robust editing tools, TestGen is a complete test
generator system for today’s educators.
∙ PowerPoint Presentation System
prepared by Melissa Frye, University of Central Florida, and Ann Marie Whyte,
University of Central Florida
Customize our content for your course. This presentation has been thoroughly
revised to include more lecture-oriented slides, as well as exhibits and examples
both from the book and from outside sources. Applicable slides have web links that
take you directly to specific Internet sites, or a spreadsheet link to show an example
in Excel. You can also go to the Notes Page function for more tips on presenting the
slides. This customizable format gives you the ability to edit, print, or rearrange the
complete presentation to meet your specific needs.
Online Videos
Available in DVD format and online. Current set of videos on hot topics! McGraw-Hill
Education has produced a series of finance videos that are 10-minute case studies on
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topics such as financial markets, careers, rightsizing, capital budgeting, EVA (economic
value added), mergers and acquisitions, and foreign exchange. Discussion questions for
these videos, as well as video clips, are available in the Instructor’s Center in Connect.
STUDENT SUPPORT
∙ Excel Master
Created by Brad Jordan and Joseph Smolira, this extensive Excel tutorial is fully
integrated with the text. Learn Excel and corporate finance at the same time.
PACKAGE OPTIONS AVAILABLE FOR PURCHASE & PACKAGING
You may also package either version of the text with a variety of additional learning tools
that are available for your students.
FinGame Online 5.0
by LeRoy Brooks, John Carroll University
(ISBN 10: 0077219880/ISBN 13: 9780077219888)
Just $15.00 when packaged with this text. In this comprehensive simulation game,
students control a hypothetical company over numerous periods of operation. As students
make major financial and operating decisions for their company, they will develop and
enhance their skills in financial management and financial accounting statement analysis.
Financial Analysis with an Electronic Calculator, Sixth Edition
by Mark A. White, University of Virginia, McIntire School of Commerce
(ISBN 10: 0073217093/ISBN 13: 9780073217093)
The information and procedures in this supplementary text enable students to master the
use of financial calculators and develop a working knowledge of financial mathematics
and problem solving. Complete instructions are included for solving all major problem
types on three popular models: HP 10B and 12C, TI BA II Plus, and TI-84. Hands-on
problems with detailed solutions allow students to practice the skills outlined in the text
and obtain instant reinforcement. Financial Analysis with an Electronic Calculator is a
self-contained supplement to the introductory financial management course.
MCGRAW-HILL CUSTOMER CARE CONTACT INFORMATION
At McGraw-Hill, we understand that getting the most from new technology can be
challenging. That’s why our services don’t stop after you purchase our products.
You can e-mail our Product Specialists 24 hours a day to get product training online.
Or you can search our knowledge bank of Frequently Asked Questions on our support
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of our Technical Support Analysts will be able to assist you in a timely fashion.
AND LEARNING PACKAGE
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Required=Results
McGraw-Hill Connect®
Learn Without Limits
Connect is a teaching and learning platform
that is proven to deliver better results for
students and instructors.
Connect empowers students by continually
adapting to deliver precisely what they
need, when they need it, and how they need
it, so your class time is more engaging and
effective.
Connect Insight®
Connect Insight is Connect’s new one-
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ACKNOWLEDGMENTS xix
A
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S
To borrow a phrase, writing a finance textbook is
easy—all you do is sit down at a word processor and
open a vein. We never would have completed this
book without the incredible amount of help and sup-
port we received from our colleagues, students, edi-
tors, family members, and friends. We would like to
thank, without implicating, all of you.
Clearly, our greatest debt is to our many col-
leagues (and their students). Needless to say, without
this support and feedback we would not be publish-
ing this text.
We owe a special thanks to Joseph Smolira of
Belmont University for his work on this book. Joe
worked closely with us to develop portions of the
Instructor’s Manual, along with the many vignettes
and real-world examples. In addition, we would like
to thank Melissa Frye, University of Central Florida,
and Ann Marie Whyte, University of Central Florida,
for their work on the PowerPoint and Instructor’s
Manual. We would also like to thank Kay Johnson for
her terrific work and attention to detail in updating
our test bank.
Steve Hailey did outstanding work on this edition.
To him fell the unenviable task of technical proofread-
ing, and in particular, careful checking of each calcu-
lation throughout the text and Instructor’s Manual.
Finally, in every phase of this project, we have
been privileged to have had the complete and
unwavering support of a great organization, McGraw-
Hill Education. We especially thank the McGraw-Hill
Education sales organization. The suggestions they
provide, their professionalism in assisting potential
adopters, and the service they provide have been a
major factor in our success.
We are deeply grateful to the select group of pro-
fessionals who served as our development team on
this edition: Chuck Synovec, director; Jennifer Upton,
senior product developer; Trina Maurer, senior mar-
keting manager; Kathryn Wright, core content proj-
ect manager; Bruce Gin, senior assessment project
manager; and Matt Diamond, senior designer. Others
at McGraw-Hill Education, too numerous to list here,
have improved the book in countless ways.
Finally, we wish to thank our families, Carol, Kate,
Jon, Suh-Pyng, Mark, Lynne, and Susan, for their for-
bearance and help.
Throughout the development of this edition,
we have taken great care to discover and eliminate
errors. Our goal is to provide the best textbook avail-
able on the subject. To ensure that future editions are
error-free, we gladly offer $10 per arithmetic error to
the first individual reporting it as a modest token of
our appreciation. More than this, we would like to
hear from instructors and students alike. Please write
and tell us how to make this a better text. Forward
your comments to: Dr. Brad Jordan, c/o Editorial-
Finance, McGraw-Hill Education, 1333 Burr Ridge
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—Stephen A. Ross
—Randolph W. Westerfield
—Jeffrey F. Jaffe
—Bradford D. Jordan
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BRIEF CONTENTS xxi
PART ONE OVERVIEW
CHAPTER ONE Introduction to Corporate Finance 1
CHAPTER TWO Financial Statements and Cash Flow 19
CHAPTER THREE Financial Statements Analysis and Financial
Models 43
PART TWO VALUATION AND CAPITAL BUDGETING
CHAPTER FOUR Discounted Cash Flow Valuation 83
CHAPTER FIVE Interest Rates and Bond Valuation 130
CHAPTER SIX Stock Valuation 165
CHAPTER SEVEN Net Present Value and Other Investment
Rules 195
CHAPTER EIGHT Making Capital Investment Decisions 230
CHAPTER NINE Risk Analysis, Real Options, and Capital
Budgeting 262
PART THREE RISK AND RETURN
CHAPTER TEN Risk and Return: Lessons from Market
History 287
CHAPTER ELEVEN Return and Risk: The Capital Asset Pricing Model
(CAPM) 316
CHAPTER TWELVE Risk, Cost of Capital, and Valuation 357
PART FOUR CAPITAL STRUCTURE AND DIVIDEND POLICY
CHAPTER THIRTEEN Efficient Capital Markets and Behavioral
Challenges 390
CHAPTER FOURTEEN Capital Structure: Basic Concepts 423
CHAPTER FIFTEEN Capital Structure: Limits to the Use of Debt 451
CHAPTER SIXTEEN Dividends and Other Payouts 480
PART FIVE SPECIAL TOPICS
CHAPTER SEVENTEEN Options and Corporate Finance 515
CHAPTER EIGHTEEN Short-Term Finance and Planning 550
CHAPTER NINETEEN Raising Capital 582
CHAPTER TWENTY International Corporate Finance 618
CHAPTER TWENTY ONE Mergers and Acquisitions (web only)
APPENDIX A Mathematical Tables 644
APPENDIX B Solutions to Selected End-of-Chapter
Problems 653
APPENDIX C Using the HP 10B and TI BA II Plus Financial
Calculators 658
Indexes 662
B
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CONTENTSxxii
PART ONE OVERVIEW
CHAPTER ONE
Introduction to Corporate
Finance 1
1.1 What Is Corporate Finance? 1
The Balance Sheet Model of the Firm 1
The Financial Manager 3
1.2 The Corporate Firm 3
The Sole Proprietorship 4
The Partnership 4
The Corporation 5
A Corporation by Another Name . . . 6
1.3 The Importance of Cash Flows 7
1.4 The Goal of Financial Management 9
Possible Goals 10
The Goal of Financial Management 10
A More General Goal 11
1.5 The Agency Problem and Control of the
Corporation 11
Agency Relationships 12
Management Goals 12
Do Managers Act in the Stockholders’
Interests? 13
Stakeholders 14
1.6 Regulation 14
The Securities Act of 1933 and the Securities
Exchange Act of 1934 16
Summary and Conclusions 16
Closing Case: East Coast Yachts 18
CHAPTER TWO
Financial Statements and Cash
Flow 19
2.1 The Balance Sheet 19
Accounting Liquidity 20
Debt versus Equity 21
Value versus Cost 21
2.2 The Income Statement 22
Generally Accepted Accounting Principles 22
Noncash Items 23
Time and Costs 24
2.3 Taxes 24
Corporate Tax Rates 24
Average versus Marginal Tax Rates 25
2.4 Net Working Capital 27
2.5 Cash Flow of the Firm 28
2.6 The Accounting Statement of Cash Flows 31
Cash Flow from Operating Activities 31
Cash Flow from Investing Activities 32
Cash Flow from Financing Activities 32
Summary and Conclusions 33
Closing Case: Cash Flows at East Coast
Yachts 41
CHAPTER THREE
Financial Statements Analysis and
Financial Models 43
3.1 Financial Statements Analysis 43
Standardizing Statements 43
Common-Size Balance Sheets 44
Common-Size Income Statements 45
3.2 Ratio Analysis 46
Short-Term Solvency or Liquidity
Measures 47
Long-Term Solvency Measures 49
Asset Management or Turnover
Measures 50
Profitability Measures 52
Market Value Measures 54
3.3 The DuPont Identity 57
A Closer Look at ROE 57
Problems with Financial Statement
Analysis 59
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3.4 Financial Models 60
A Simple Financial Planning Model 60
The Percentage of Sales Approach 62
3.5 External Financing and Growth 66
EFN and Growth 67
Financial Policy and Growth 69
A Note about Sustainable Growth Rate
Calculations 73
3.6 Some Caveats Regarding Financial Planning
Models 73
Summary and Conclusions 74
Closing Case: Ratios and Financial Planning at East
Coast Yachts 80
PART TWO VALUATION AND CAPITAL
BUDGETING
CHAPTER FOUR
Discounted Cash Flow Valuation 83
4.1 Valuation: The One-Period Case 83
4.2 The Multiperiod Case 86
Future Value and Compounding 86
The Power of Compounding: A Digression 89
Present Value and Discounting 90
The Algebraic Formula 94
4.3 Compounding Periods 96
Distinction between Annual Percentage Rate and
Effective Annual Rate 98
Compounding over Many Years 99
Continuous Compounding 99
4.4 Simplifications 101
Perpetuity 101
Growing Perpetuity 102
Annuity 104
Trick 1: A Delayed Annuity 106
Trick 2: Annuity Due 107
Trick 3: The Infrequent Annuity 108
Trick 4: Equating Present Value of Two Annuities 108
Growing Annuity 109
4.5 Loan Types and Loan Amortization 111
Pure Discount Loans 111
Interest-Only Loans 111
Amortized Loans 112
4.6 What Is a Firm Worth? 115
Summary and Conclusions 117
Closing Case: The MBA Decision 128
CHAPTER FIVE
Interest Rates and Bond Valuation 130
5.1 Bonds and Bond Valuation 130
Bond Features and Prices 131
Bond Values and Yields 131
Interest Rate Risk 134
Finding the Yield to Maturity: More Trial and Error 136
5.2 More on Bond Features 137
Long-Term Debt: The Basics 139
The Indenture 140
Terms of a Bond 140
Security 141
Seniority 141
Repayment 141
The Call Provision 142
Protective Covenants 142
5.3 Bond Ratings 143
5.4 Some Different Types of Bonds 144
Government Bonds 144
Zero Coupon Bonds 145
Floating-Rate Bonds 146
Other Types of Bonds 146
5.5 Bond Markets 148
How Bonds Are Bought and Sold 148
Bond Price Reporting 148
A Note on Bond Price Quotes 151
5.6 Inflation and Interest Rates 152
Real versus Nominal Rates 152
The Fisher Effect 153
5.7 Determinants of Bond Yields 154
The Term Structure of Interest Rates 154
Bond Yields and the Yield Curve: Putting It All Together 155
Conclusion 157
Summary and Conclusions 158
Closing Case: Financing East Coast Yachts’ Expansion
Plans with a Bond Issue 163
CHAPTER SIX
Stock Valuation 165
6.1 The Present Value of Common Stocks 165
Dividends versus Capital Gains 165
Valuation of Different Types of Stocks 166
Case 1 (Zero Growth) 167
Case 2 (Constant Growth) 167
Case 3 (Differential Growth) 168
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xxiv
6.2 Estimates of Parameters in the Dividend Discount
Model 170
Where Does g Come From? 170
Where Does R Come From? 171
A Healthy Sense of Skepticism 172
The No-Payout Firm 174
6.3 Comparables 174
Price-to-Earnings Ratio 174
Enterprise Value Ratios 176
6.4 Valuing Stocks Using Free Cash Flows 177
6.5 Some Features of Common and Preferred Stocks 179
Common Stock Features 179
Shareholder Rights 179
Proxy Voting 180
Classes of Stock 180
Other Rights 181
Dividends 181
Preferred Stock Features 182
Stated Value 182
Cumulative and Noncumulative Dividends 182
Is Preferred Stock Really Debt? 182
6.6 The Stock Markets 182
Dealers and Brokers 183
Organization of the NYSE 183
Members 183
Operations 184
Floor Activity 184
NASDAQ Operations 185
ECNs 187
Stock Market Reporting 188
Summary and Conclusions 188
Closing Case: Stock Valuation at Ragan Engines 194
CHAPTER SEVEN
Net Present Value and Other Investment
Rules 195
7.1 Why Use Net Present Value? 195
7.2 The Payback Period Method 197
Defining the Rule 197
Problems with the Payback Method 198
Problem 1: Timing of Cash Flows within the Payback
Period 199
Problem 2: Payments after the Payback Period 199
Problem 3: Arbitrary Standard for Payback Period 199
Managerial Perspective 199
Summary of Payback 200
7.3 The Discounted Payback Period Method 200
7.4 The Average Accounting Return Method 201
Defining the Rule 201
Step 1: Determining Average Net Income 202
Step 2: Determining Average Investment 202
Step 3: Determining AAR 202
Analyzing the Average Accounting Return Method 202
7.5 The Internal Rate of Return 203
7.6 Problems with the IRR Approach 206
Definition of Independent and Mutually Exclusive
Projects 206
Two General Problems Affecting Both Independent and
Mutually Exclusive Projects 206
Problem 1: Investing or Financing? 206
Problem 2: Multiple Rates of Return 208
NPV Rule 208
Modified IRR 209
The Guarantee against Multiple IRRs 209
General Rules 210
Problems Specific to Mutually Exclusive Projects 210
The Scale Problem 210
The Timing Problem 212
Redeeming Qualities of IRR 214
A Test 214
7.7 The Profitability Index 215
Calculation of Profitability Index 215
Application of the Profitability Index 215
7.8 The Practice of Capital Budgeting 217
Summary and Conclusions 219
Closing Case: Bullock Gold Mining 229
CHAPTER EIGHT
Making Capital Investment Decisions 230
8.1 Incremental Cash Flows 230
Cash Flows—Not Accounting Income 230
Sunk Costs 231
Opportunity Costs 231
Side Effects 232
Allocated Costs 232
8.2 The Baldwin Company: An Example 233
An Analysis of the Project 234
Investments 234
Income and Taxes 235
Salvage Value 236
Cash Flow 237
Net Present Value 237
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Which Set of Books? 237
A Note on Net Working Capital 237
A Note on Depreciation 238
Interest Expense 239
8.3 Inflation and Capital Budgeting 239
Discounting: Nominal or Real? 240
8.4 Alternative Definitions of Operating Cash Flow 242
The Bottom-Up Approach 243
The Top-Down Approach 243
The Tax Shield Approach 244
Conclusion 244
8.5 Some Special Cases of Discounted Cash
Flow Analysis 244
Setting the Bid Price 244
Evaluating Equipment Options with Different Lives 246
The General Decision to Replace 248
Summary and Conclusions 250
Closing Case: Expansion at East Coast Yachts 260
Closing Case: Bethesda Mining Company 261
CHAPTER NINE
Risk Analysis, Real Options, and Capital
Budgeting 262
9.1 Decision Trees 262
Warning 264
9.2 Sensitivity Analysis, Scenario Analysis, and Break-Even
Analysis 264
Sensitivity Analysis and Scenario Analysis 264
Revenues 265
Costs 266
Break-Even Analysis 268
Accounting Profit 268
Financial Breakeven 270
9.3 Monte Carlo Simulation 271
Step 1: Specify the Basic Model 271
Step 2: Specify a Distribution for Each Variable in the
Model 271
Step 3: The Computer Draws One Outcome 273
Step 4: Repeat the Procedure 273
Step 5: Calculate NPV 273
9.4 Real Options 274
The Option to Expand 274
The Option to Abandon 275
Timing Options 277
Summary and Conclusions 278
Closing Case: Bunyan Lumber, LLC 285
PART THREE RISK AND RETURN
CHAPTER TEN
Risk and Return: Lessons from Market
History 287
10.1 Returns 287
Dollar Returns 287
Percentage Returns 289
10.2 Holding Period Returns 291
10.3 Return Statistics 297
10.4 Average Stock Returns and Risk-Free Returns 298
10.5 Risk Statistics 300
Variance 300
Normal Distribution and Its Implications for Standard
Deviation 301
10.6 The U.S. Equity Risk Premium: Historical and International
Perspectives 302
10.7 2008: A Year of Financial Crisis 305
10.8 More on Average Returns 306
Arithmetic versus Geometric Averages 306
Calculating Geometric Average Returns 307
Arithmetic Average Return or Geometric Average
Return? 308
Summary and Conclusions 309
Closing Case: A Job at East Coast Yachts, Part 1 313
CHAPTER ELEVEN
Return and Risk: The Capital Asset Pricing
Model (CAPM) 316
11.1 Individual Securities 316
11.2 Expected Return, Variance, and Covariance 317
Expected Return and Variance 317
Covariance and Correlation 318
11.3 The Return and Risk for Portfolios 321
The Expected Return on a Portfolio 321
Variance and Standard Deviation of a
Portfolio 322
The Variance 322
Standard Deviation of a Portfolio 322
The Diversification Effect 323
An Extension to Many Assets 324
11.4 The Efficient Set 324
The Two-Asset Case 324
The Efficient Set for Many Securities 328
11.5 Riskless Borrowing and Lending 329
The Optimal Portfolio 331
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11.6 Announcements, Surprises, and Expected Returns 333
Expected and Unexpected Returns 333
Announcements and News 334
11.7 Risk: Systematic and Unsystematic 335
Systematic and Unsystematic Risk 335
Systematic and Unsystematic Components of Return 335
11.8 Diversification and Portfolio Risk 336
The Effect of Diversification: Another Lesson from Market
History 336
The Principle of Diversification 336
Diversification and Unsystematic Risk 338
Diversification and Systematic Risk 338
11.9 Market Equilibrium 339
Definition of the Market Equilibrium Portfolio 339
Definition of Risk When Investors Hold the Market Portfolio 339
The Formula for Beta 342
A Test 343
11.10 Relationship between Risk and Expected Return (CAPM) 344
Expected Return on Individual Security 344
Summary and Conclusions 347
Closing Case: A Job at East Coast Yachts, Part 2 355
CHAPTER TWELVE
Risk, Cost of Capital, and Valuation 357
12.1 The Cost of Equity Capital 357
12.2 Estimating the Cost of Equity Capital with the CAPM 358
The Risk-Free Rate 360
Market Risk Premium 361
Method 1: Using Historical Data 361
Method 2: Using the Dividend Discount Model (DDM) 361
12.3 Estimation of Beta 362
Real-World Betas 362
Stability of Beta 363
Using an Industry Beta 364
12.4 Determinants of Beta 365
Cyclicality of Revenues 365
Operating Leverage 366
Financial Leverage and Beta 366
12.5 Dividend Discount Model 367
Comparison of DDM and CAPM 368
12.6 Cost of Capital for Divisions and Projects 369
12.7 Cost of Fixed Income Securities 370
Cost of Debt 370
Cost of Preferred Stock 371
12.8 The Weighted Average Cost of Capital 372
12.9 Valuation With RWACC 374
Project Evaluation and the RWACC 374
Firm Valuation with the RWACC 374
12.10 Estimating Eastman Chemical’s Cost of Capital 377
Eastman’s Cost of Equity 377
Eastman’s Cost of Debt 379
Eastman’s WACC 380
12.11 Flotation Costs and the Weighted Average Cost of
Capital 380
The Basic Approach 380
Flotation Costs and NPV 381
Internal Equity and Flotation Costs 382
Summary and Conclusions 382
Closing Case: The Cost of Capital for
Swan Motors 389
PART FOUR CAPITAL STRUCTURE AND
DIVIDEND POLICY
CHAPTER THIRTEEN
Efficient Capital Markets and Behavioral
Challenges 390
13.1 A Description of Efficient Capital Markets 390
Foundations of Market Efficiency 392
Rationality 392
Independent Deviations from Rationality 392
Arbitrage 393
13.2 The Different Types of Efficiency 393
The Weak Form 393
The Semistrong and Strong Forms 393
Some Common Misconceptions about the Efficient Market
Hypothesis 395
The Efficacy of Dart Throwing 395
Price Fluctuations 396
Stockholder Disinterest 396
13.3 The Evidence 396
The Weak Form 396
The Semistrong Form 398
Event Studies 398
The Record of Mutual Funds 400
The Strong Form 401
13.4 The Behavioral Challenge to Market Efficiency 401
Rationality 401
Independent Deviations from Rationality 402
Arbitrage 402
13.5 Empirical Challenges to Market Efficiency 403
13.6 Reviewing the Differences 408
Representativeness 409
Conservatism 409
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13.7 Implications for Corporate Finance 409
1. Accounting Choices, Financial Choices, and Market
Efficiency 410
2. The Timing Decision 410
3. Speculation and Efficient Markets 412
4. Information in Market Prices 413
Summary and Conclusions 415
Closing Case: Your 401(K) Account at East Coast Yachts 421
CHAPTER FOURTEEN
Capital Structure: Basic Concepts 423
14.1 The Capital Structure Question and the Pie Theory 423
14.2 Maximizing Firm Value versus Maximizing Stockholder
Interests 424
14.3 Financial Leverage and Firm Value: An Example 426
Leverage and Returns to Shareholders 426
The Choice between Debt and Equity 428
A Key Assumption 430
14.4 Modigliani and Miller: Proposition II (No Taxes) 430
Risk to Equityholders Rises with Leverage 430
Proposition II: Required Return to Equityholders Rises with
Leverage 431
MM: An Interpretation 436
14.5 Taxes 437
The Basic Insight 437
Present Value of the Tax Shield 439
Value of the Levered Firm 439
Expected Return and Leverage under Corporate Taxes 441
The Weighted Average Cost of Capital (RWACC) and Corpo-
rate Taxes 442
Stock Price and Leverage under Corporate Taxes 442
Summary and Conclusions 444
Closing Case: Stephenson Real Estate Recapitalization 450
CHAPTER FIFTEEN
Capital Structure: Limits to the Use of
Debt 451
15.1 Costs of Financial Distress 451
Direct Bankruptcy Costs 452
Indirect Bankruptcy Costs 452
Agency Costs 453
Selfish Investment Strategy 1: Incentive to Take Large
Risks 453
Selfish Investment Strategy 2: Incentive Toward
Underinvestment 454
Selfish Investment Strategy 3: Milking the Property 455
Summary of Selfish Strategies 455
15.2 Can Costs of Debt be Reduced? 456
Protective Covenants 456
Consolidation of Debt 457
15.3 Integration of Tax Effects and Financial Distress Costs 457
Pie Again 457
15.4 Signaling 460
15.5 Shirking, Perquisites, and Bad Investments: A Note on
Agency Cost of Equity 461
Effect of Agency Costs of Equity on Debt–Equity
Financing 463
Free Cash Flow 463
15.6 The Pecking-Order Theory 464
Rules of the Pecking Order 465
Rule #1 Use Internal Financing 465
Rule #2 Issue Safe Securities First 466
Implications 466
15.7 How Firms Establish Capital Structure 467
15.8 A Quick Look at the Bankruptcy Process 472
Liquidation and Reorganization 472
Bankruptcy Liquidation 472
Bankruptcy Reorganization 473
Financial Management and the Bankruptcy Process 474
Agreements to Avoid Bankruptcy 475
Summary and Conclusions 475
Closing Case: Dugan Corporation’s Capital
Budgeting 479
CHAPTER SIXTEEN
Dividends and Other Payouts 480
16.1 Different Types of Dividends 480
16.2 Standard Method of Cash Dividend Payment 481
16.3 The Benchmark Case: An Illustration of the Irrelevance of
Dividend Policy 483
Current Policy: Dividends Set Equal to Cash Flow 483
Alternative Policy: Initial Dividend Is Greater than Cash
Flow 483
The Indifference Proposition 484
Homemade Dividends 485
A Test 486
Dividends and Investment Policy 486
16.4 Repurchase of Stock 487
Dividend versus Repurchase: Conceptual Example 488
Dividends versus Repurchases: Real-World
Considerations 489
1. Flexibility 489
2. Executive Compensation 489
3. Offset to Dilution 489
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4. Undervaluation 489
5. Taxes 490
16.5 Personal Taxes, Issuance Costs, and Dividends 490
Firms without Sufficient Cash to Pay a Dividend 490
Firms with Sufficient Cash to Pay a Dividend 491
Summary on Personal Taxes 493
16.6 Real-World Factors Favoring A High-Dividend Policy 493
Desire for Current Income 493
Behavioral Finance 494
Agency Costs 495
Information Content of Dividends and Dividend
Signaling 495
16.7 The Clientele Effect: A Resolution of Real-World
Factors? 496
16.8 What We Know and Do Not Know about Dividend Policy 498
Corporate Dividends Are Substantial 498
Fewer Companies Pay Dividends 498
Corporations Smooth Dividends 499
Some Survey Evidence about Dividends 500
16.9 Putting It All Together 501
16.10 Stock Dividends and Stock Splits 503
Example of a Small Stock Dividend 504
Example of a Stock Split 504
Example of a Large Stock Dividend 505
Value of Stock Splits and Stock Dividends 505
The Benchmark Case 505
Popular Trading Range 505
Reverse Splits 506
Summary and Conclusions 507
Closing Case: Electronic Timing, Inc. 513
PART FIVE SPECIAL TOPICS
CHAPTER SEVENTEEN
Options and Corporate Finance 515
17.1 Options 515
17.2 Call Options 516
The Value of a Call Option at Expiration 516
17.3 Put Options 517
The Value of a Put Option at Expiration 517
17.4 Selling Options 519
17.5 Option Quotes 520
17.6 Combinations of Options 521
17.7 Valuing Options 524
Bounding the Value of a Call 524
Lower Bound 524
Upper Bound 524
The Factors Determining Call Option Values 524
Exercise Price 524
Expiration Date 525
Stock Price 525
The Key Factor: The Variability of the Underlying
Asset 526
The Interest Rate 527
A Quick Discussion of Factors Determining Put Option
Values 527
17.8 An Option Pricing Formula 528
A Two-State Option Model 529
Determining the Delta 529
Determining the Amount of Borrowing 530
Risk-Neutral Valuation 530
The Black–Scholes Model 531
17.9 Stocks and Bonds as Options 535
The Firm Expressed in Terms of Call Options 536
The Stockholders 536
The Bondholders 537
The Firm Expressed in Terms of Put Options 537
The Stockholders 537
Cash Flow Is Less Than $800 538
Cash Flow Is Greater Than $800 538
The Bondholders 538
Cash Flow Is Less Than $800 538
Cash Flow Is Greater Than $800 538
A Resolution of the Two Views 538
A Note on Loan Guarantees 539
Summary and Conclusions 540
Closing Case: Exotic Cuisines Employee Stock
Options 548
CHAPTER EIGHTEEN
Short-Term Finance and Planning 550
18.1 Tracing Cash and Net Working Capital 551
18.2 The Operating Cycle and the Cash Cycle 552
Defining the Operating and Cash Cycles 552
The Operating Cycle 553
The Cash Cycle 553
The Operating Cycle and the Firm’s Organization
Chart 554
Calculating the Operating and Cash Cycles 554
The Operating Cycle 556
The Cash Cycle 557
Interpreting the Cash Cycle 558
18.3 Some Aspects of Short-Term Financial Policy 558
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The Size of the Firm’s Investment in Current Assets 559
Alternative Financing Policies for Current Assets 560
An Ideal Case 560
Different Policies for Financing Current Assets 562
Which Financing Policy Is Best? 563
Current Assets and Liabilities in Practice 564
18.4 The Cash Budget 564
Sales and Cash Collections 565
Cash Outflows 566
The Cash Balance 566
18.5 Short-Term Borrowing 567
Unsecured Loans 567
Compensating Balances 568
Cost of a Compensating Balance 568
Letters of Credit 568
Secured Loans 569
Accounts Receivable Financing 569
Inventory Loans 570
Commercial Paper 570
Trade Credit 570
Understanding Trade Credit Terms 570
Cash Discounts 570
18.6 A Short-Term Financial Plan 571
Summary and Conclusions 572
Closing Case: Keafer Manufacturing Working
Capital Management 581
CHAPTER NINETEEN
Raising Capital 582
19.1 Early-Stage Financing and Venture Capital 582
Venture Capital 583
Stages of Financing 584
Some Venture Capital Realities 585
Crowdfunding 586
19.2 Selling Securities to the Public: The Basic
Procedure 586
19.3 Alternative Issue Methods 587
19.4 Underwriters 589
Choosing an Underwriter 589
Types of Underwriting 590
Firm Commitment Underwriting 590
Best Efforts Underwriting 590
Dutch Auction Underwriting 590
The Green Shoe Provision 591
The Aftermarket 591
Lockup Agreements 591
The Quiet Period 592
19.5 IPOs and Underpricing 592
Evidence on Underpricing 593
IPO Underpricing: The 1999–2000 Experience 594
Why Does Underpricing Exist? 594
The Partial Adjustment Phenomenon 598
19.6 What CFOs Say About the IPO Process 599
19.7 SEOs and the Value of the Firm 599
19.8 The Cost of Issuing Securities 600
19.9 Rights 603
The Mechanics of a Rights Offering 605
Subscription Price 605
Number of Rights Needed to Purchase a Share 606
Effect of Rights Offering on Price of Stock 606
Effects on Shareholders 608
The Underwriting Arrangements 608
The Rights Puzzle 608
19.10 Dilution 609
Dilution of Proportionate Ownership 609
Dilution of Value: Book versus Market Values 609
A Misconception 610
The Correct Arguments 610
19.11 Issuing Long-Term Debt 611
19.12 Shelf Registration 611
Summary and Conclusions 612
Closing Case: East Coast Yachts Goes Public 617
CHAPTER TWENTY
International Corporate Finance 618
20.1 Terminology 619
20.2 Foreign Exchange Markets and Exchange
Rates 620
Exchange Rates 621
Exchange Rate Quotations 621
Cross-Rates and Triangle Arbitrage 622
Types of Transactions 623
20.3 Purchasing Power Parity 624
Absolute Purchasing Power Parity 624
Relative Purchasing Power Parity 626
The Basic Idea 626
The Result 627
Currency Appreciation and Depreciation 628
20.4 Interest Rate Parity, Unbiased Forward Rates, and the
International Fisher Effect 628
Covered Interest Arbitrage 628
Interest Rate Parity 629
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xxx
Forward Rates and Future Spot Rates 630
Putting It All Together 631
Uncovered Interest Parity 631
The International Fisher Effect 631
20.5 International Capital Budgeting 632
Method 1: The Home Currency Approach 633
Method 2: The Foreign Currency Approach 633
Unremitted Cash Flows 634
20.6 Exchange Rate Risk 634
Short-Run Exposure 634
Long-Run Exposure 635
Translation Exposure 636
Managing Exchange Rate Risk 637
20.7 Political Risk 637
Summary and Conclusions 638
Closing Case: East Coast Yachts Goes International 643
CHAPTER TWENTY ONE
Mergers and Acquisitions (web only)
APPENDIX A
Mathematical Tables 644
APPENDIX B
Solutions to Selected End-of-Chapter
Problems 653
APPENDIX C
Using the HP 10B and TI BA II Plus Financial
Calculators 658
NAME INDEX 662
COMPANY INDEX 664
SUBJECT INDEX 666
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LIST OF BOXES xxxi
L
IS
T
O
F
B
O
X
E
S FINANCE MATTERS
CHAPTER 1 Sarbanes-Oxley 15
CHAPTER 2 What is Warren Buffett’s Tax Rate? 27
CHAPTER 3 What’s in a Ratio? 60
CHAPTER 4 Jackpot! 96
CHAPTER 5 Beauty Is in the Eye of the Bondholder 147
CHAPTER 6 How Fast Is Too Fast? 173
The Wild, Wild West of Stock Trading 186
CHAPTER 9 When Things Go Wrong . . . 265
CHAPTER 11 Beta, Beta, Who’s Got the Beta? 343
CHAPTER 12 The Cost of Capital, Texas Style 378
CHAPTER 13 Can Stock Market Investors Add and Subtract? 405
CHAPTER 16 Stock Buybacks: No End in Sight 492
CHAPTER 18 A Look at Operating and Cash Cycles 555
CHAPTER 19 IPO Underpricing around the World 596
Anatomy of an IPO 603
CHAPTER 20 McPricing 626
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CHAPTER 1 Introduction to Corporate Finance 1
1
OPENING
CASE
Introduction to
Corporate Finance
George Zimmer, founder of The Men’s Wearhouse, for years ap peared in television ads prom-
ising “You’re going to like the way you look. I guarantee it.” But, in mid-2013, Zimmer evi-
dently didn’t look so good to the company’s board of directors, which abruptly fired him. It
was reported that Zimmer had a series of dis agreements with the board, including a desire to
take the company private. Evidently, Zimmer’s ideas did not “suit” the board. Of course, you
can’t keep a good entrepreneur down: After Zimmer was fired, he started zTailors, a market-
place for customers to contact tailors and have them visit the customer’s home, as well as
Generation Tux, an online tuxedo rental company with home delivery.
Understanding Zimmer’s journey from the founder of a clothing store that used a cigar
box as a cash register, to corporate execu tive, and finally to ex-employee takes us into issues
involving the corporate form of organization, corporate goals, and corporate con trol, all of
which we discuss in this chapter. You’re going to learn a lot if you read it. We guarantee it.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
1.1 WHAT IS CORPORATE FINANCE?
Suppose you decide to start a firm to make tennis balls. To do this you hire managers to
buy raw materials, and you assemble a workforce that will produce and sell finished ten-
nis balls. In the language of finance, you make an investment in assets such as inventory,
machinery, land, and labor. The amount of cash you invest in assets must be matched by an
equal amount of cash raised by financing. When you begin to sell tennis balls, your firm
will generate cash. This is the basis of value creation. The purpose of the firm is to create
value for you, the owner. The value is reflected in the framework of the simple balance
sheet model of the firm.
The Balance Sheet Model of the Firm
Suppose we take a financial snapshot of the firm and its activities at a single point in time.
Figure 1.1 shows a graphic conceptualization of the balance sheet, and it will help intro-
duce you to corporate finance.
The assets of the firm are on the left side of the balance sheet. These assets can be
thought of as current and fixed. Fixed assets are those that will last a long time, such as
buildings. Some fixed assets are tangible, such as machinery and equipment. Other fixed
assets are intangible, such as patents and trademarks. The other category of assets, current
assets, comprises those that have short lives, such as inventory. The tennis balls that your
firm has made, but has not yet sold, are part of its inventory. Unless you have overpro-
duced, they will leave the firm shortly.
Before a company can invest in an asset, it must obtain financing, which means that it
must raise the money to pay for the investment. The forms of financing are represented on
PART ONE: OVERVIEW
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2
the right side of the balance sheet. A firm will issue (sell) pieces of paper called debt (loan
agreements) or equity shares (stock certificates). Just as assets are classified as long-lived
or short-lived, so too are liabilities. A short-term debt is called a current liability. Short-
term debt represents loans and other obligations that must be repaid within one year. Long-
term debt is debt that does not have to be repaid within one year. Shareholders’ equity
represents the difference between the value of the assets and the debt of the firm. In this
sense, it is a residual claim on the firm’s assets.
From the balance sheet model of the firm, it is easy to see why finance can be thought
of as the study of the following three questions:
1. In what long-lived assets should the firm invest? This question concerns the
left side of the balance sheet. Of course the types and proportions of assets the
firm needs tend to be set by the nature of the business. We use the term capital
budgeting to describe the process of making and managing expenditures on
long-lived assets.
2. How can the firm raise cash for required capital expenditures? This question
concerns the right side of the balance sheet. The answer to this question involves
the firm’s capital structure, which represents the proportions of the firm’s
financing from current liabilities, long-term debt, and equity.
3. How should short-term operating cash flows be managed? This question con-
cerns the upper portion of the balance sheet. There is often a mismatch between
the timing of cash inflows and cash outflows during operating activities.
Furthermore, the amount and timing of operating cash flows are not known with cer-
tainty. Financial managers must attempt to manage the gaps in cash flow.
From a balance sheet perspective, short-term management of cash flow is associated
with a firm’s net working capital. Net working capital is defined as current assets minus
current liabilities. From a financial perspective, short-term cash flow problems come from
the mismatching of cash inflows and outflows. This is the subject of short-term finance.
FIGURE 1.1
The Balance Sheet Model of
the Firm
Long-term
debt
Current assets
Fixed assets
1. Tangible fixed
assets
2. Intangible fixed
assets
Net
working
capital
Current
liabilities
Shareholders’
equity
Total Value of Assets Total Value of the Firm to Investors=
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The Financial Manager
In large firms, the finance activity is usually associated with a top officer of the firm,
such as the vice president and chief financial officer, and some lesser officers. Figure 1.2
depicts a general organizational structure emphasizing the finance activity within the firm.
Reporting to the chief financial officer are the treasurer and the controller. The treasurer is
responsible for handling cash flows, managing capital expenditure decisions, and making
financial plans. The controller handles the accounting function, which includes taxes, cost
and financial accounting, and information systems.
1.2 THE CORPORATE FIRM
The firm is a way of organizing the economic activity of many individuals. A basic prob-
lem of the firm is how to raise cash. The corporate form of business—that is, organizing
the firm as a corporation—is the standard method for solving problems encountered in
raising large amounts of cash. However, businesses can take other forms. In this section we
For current issues facing
CFOs, see www.cfo.com.
FIGURE 1.2
Hypothetical Organization
ChartBoard of Directors
Chairman of the Board and
Chief Executive O�cer (CEO)
President and Chief
Operations O�cer (COO)
Vice President and Chief
Financial O�cer (CFO)
Treasurer Controller
Cash Manager Credit Manager Tax Manager
Cost Accounting
Manager
Information
Systems
Manager
Financial
Accounting
Manager
Financial
Planning
Capital
Expenditures
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4
consider the three basic legal forms of organizing firms, and we see how firms go about the
task of raising large amounts of money under each form.
The Sole Proprietorship
A sole proprietorship is a business owned by one person. Suppose you decide to start a
business to produce mousetraps. Going into business is simple: You announce to all who
will listen, “Today, I am going to build a better mousetrap.”
Most large cities require that you obtain a business license. Afterward, you can begin to
hire as many people as you need and borrow whatever money you need. At year-end all the
profits or the losses will be yours.
Here are some factors that are important in considering a sole proprietorship:
1. The sole proprietorship is the cheapest business to form. No formal charter is
required, and few government regulations must be satisfied for most industries.
2. A sole proprietorship pays no corporate income taxes. All profits of the business
are taxed as individual income.
3. The sole proprietorship has unlimited liability for business debts and obligations.
No distinction is made between personal and business assets.
4. The life of the sole proprietorship is limited by the life of the sole proprietor.
5. Because the only money invested in the firm is the proprietor’s, the equity
money that can be raised by the sole proprietor is limited to the proprietor’s per-
sonal wealth.
The Partnership
Any two or more people can get together and form a partnership. Partnerships fall into
two categories: (1) general partnerships and (2) limited partnerships.
In a general partnership all partners agree to provide some fraction of the work and cash
and to share the profits and losses. Each partner is liable for all of the debts of the partner-
ship. A partnership agreement specifies the nature of the arrangement. The partnership
agreement may be an oral agreement or a formal document setting forth the understanding.
Limited partnerships permit the liability of some of the partners to be limited to the
amount of cash each has contributed to the partnership. Limited partnerships usually
require that (1) at least one partner be a general partner and (2) the limited partners do
not participate in managing the business. Here are some things that are important when
considering a partnership:
1. Partnerships are usually inexpensive and easy to form. Written documents are
required in complicated arrangements. Business licenses and filing fees may be
necessary.
2. General partners have unlimited liability for all debts. The liability of limited
partners is usually limited to the contribution each has made to the partnership.
If one general partner is unable to meet his or her commitment, the shortfall
must be made up by the other general partners.
3. The general partnership is terminated when a general partner dies or withdraws
(but this is not so for a limited partner). It is difficult for a partnership to transfer
ownership without dissolving. Usually all general partners must agree. However,
limited partners may sell their interest in a business.
4. It is difficult for a partnership to raise large amounts of cash. Equity contribu-
tions are usually limited to a partner’s ability and desire to contribute to the part-
nership. Many companies, such as Apple Computer, start life as a proprietorship
or partnership, but at some point they choose to convert to corporate form.
5. Income from a partnership is taxed as personal income to the partners.
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6. Management control resides with the general partners. Usually a majority vote is
required on important matters, such as the amount of profit to be retained in the
business.
It is difficult for large business organizations to exist as sole proprietorships or partner-
ships. The main advantage to a sole proprietorship or partnership is the cost of getting
started. Afterward, the disadvantages, which may become severe, are (1) unlimited liabil-
ity, (2) limited life of the enterprise, and (3) difficulty of transferring ownership. These
three disadvantages lead to (4) difficulty in raising cash.
The Corporation
Of the forms of business enterprises, the corporation is by far the most important. It is a
distinct legal entity. As such, a corporation can have a name and enjoy many of the legal
powers of natural persons. For example, corporations can acquire and exchange property.
Corporations can enter contracts and may sue and be sued. For jurisdictional purposes the
corporation is a citizen of its state of incorporation (it cannot vote, however).
Starting a corporation is more complicated than starting a proprietorship or partnership.
The incorporators must prepare articles of incorporation and a set of bylaws. The articles
of incorporation must include the following:
1. Name of the corporation.
2. Intended life of the corporation (it may be forever).
3. Business purpose.
4. Number of shares of stock that the corporation is authorized to issue, with a
statement of limitations and rights of different classes of shares.
5. Nature of the rights granted to shareholders.
6. Number of members of the initial board of directors.
The bylaws are the rules to be used by the corporation to regulate its own existence,
and they concern its shareholders, directors, and officers. Bylaws range from the briefest
possible statement of rules for the corporation’s management to hundreds of pages of text.
In its simplest form, the corporation comprises three sets of distinct interests: the share-
holders (the owners), the directors, and the corporation officers (the top management).
Traditionally, the shareholders control the corporation’s direction, policies, and activities.
The shareholders elect a board of directors, who in turn select top management. Members
of top management serve as corporate officers and manage the operations of the corpora-
tion in the best interest of the shareholders. In closely held corporations with few share-
holders, there may be a large overlap among the shareholders, the directors, and the top
management. However, in larger corporations, the shareholders, directors, and the top
management are likely to be distinct groups.
The potential separation of ownership from management gives the corporation several
advantages over proprietorships and partnerships:
1. Because ownership in a corporation is represented by shares of stock, ownership
can be readily transferred to new owners. Because the corporation exists inde-
pendently of those who own its shares, there is no limit to the transferability of
shares as there is in partnerships.
2. The corporation has unlimited life. Because the corporation is separate from its
owners, the death or withdrawal of an owner does not affect the corporation’s
legal existence. The corporation can continue on after the original owners have
withdrawn.
3. The shareholders’ liability is limited to the amount invested in the owner-
ship shares. For example, if a shareholder purchased $1,000 in shares of a
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6
corporation, the potential loss would be $1,000. In a partnership, a general part-
ner with a $1,000 contribution could lose the $1,000 plus any other indebtedness
of the partnership.
Limited liability, ease of ownership transfer, and perpetual succession are the major
advantages of the corporate form of business organization. These give the corporation an
enhanced ability to raise cash.
There is, however, one great disadvantage to incorporation. The federal government
taxes corporate income (the states do as well). This tax is in addition to the personal
income tax that shareholders pay on dividend income they receive. This is double taxation
for shareholders when compared to taxation on proprietorships and partnerships. Table 1.1
summarizes our discussion of partnerships and corporations.
Today all 50 states have enacted laws allowing for the creation of a relatively new
form of business organization, the limited liability company (LLC). The goal of this
entity is to operate and be taxed like a partnership but retain limited liability for owners,
so an LLC is essentially a hybrid of partnership and corporation. Although states have
differing definitions for LLCs, the more important scorekeeper is the Internal Revenue
Service (IRS). The IRS will consider an LLC a corporation, thereby subjecting it to
double taxation, unless it meets certain specific criteria. In essence, an LLC cannot be
too corporation-like, or it will be treated as one by the IRS. LLCs have become common.
For example, Goldman, Sachs and Co., one of Wall Street’s last remaining partnerships,
decided to convert from a private partnership to an LLC (it later “went public,” becom-
ing a publicly held corporation). Large accounting firms and law firms by the score have
converted to LLCs.
A Corporation by Another Name . . .
The corporate form of organization has many variations around the world. The exact laws
and regulations differ from country to country, of course, but the essential features of pub-
lic ownership and limited liability remain. These firms are often called joint stock compa-
nies, public limited companies, or limited liability companies, depending on the specific
nature of the firm and the country of origin.
Table 1.2 gives the names of a few well-known international corporations, their coun-
tries of origin, and a translation of the abbreviation that follows each company name.
To find out more
about LLCs, visit
www.incorporate.com.
CORPORATION PARTNERSHIP
Liquidity and
marketability
Shares can be exchanged without termination of the
corporation. Common stock can be listed on a stock
exchange.
Units are subject to substantial restrictions on transferability.
There is usually no established trading market for
partnership units.
Voting rights Usually each share of common stock entitles the holder
to one vote per share on matters requiring a vote and
on the election of the directors. Directors determine top
management.
Some voting rights by limited partners. However, general
partners have exclusive control and management of
operations.
Taxation Corporations have double taxation: Corporate income is
taxable, and dividends to shareholders are also taxable.
Partnerships are not taxable. Partners pay personal taxes on
partnership profits.
Reinvestment and
dividend payout
Corporations have broad latitude on dividend payout
decisions.
Partnerships are generally prohibited from reinvesting
partnership profits. All profits are distributed to partners.
Liability Shareholders are not personally liable for obligations of
the corporation.
Limited partners are not liable for obligations of partner-
ships.
General partners may have unlimited liability.
Continuity of
existence
Corporations may have a perpetual life. Partnerships have limited life.
TABLE 1.1 A Comparison of Partnerships and Corporations
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1.3 THE IMPORTANCE OF CASH FLOWS
The most important job of a financial manager is to create value from the firm’s capital
budgeting, financing, and net working capital activities. How do financial managers create
value? The answer is that the firm should create more cash flow than it uses.
The cash flows paid to bondholders and stockholders of the firm should be greater than
the cash flows put into the firm by the bondholders and stockholders. To see how this is
done, we can trace the cash flows from the firm to the financial markets and back again.
The interplay of the firm’s activities with the financial markets is illustrated in
Figure 1.3. The arrows in Figure 1.3 trace cash flow from the firm to the financial markets
and back again. Suppose we begin with the firm’s financing activities. To raise money, the
firm sells debt and equity shares to investors in the financial markets. This results in cash
flows from the financial markets to the firm (A). This cash is invested in the investment
TYPE OF COMPANY
COMPANY COUNTRY OF ORIGIN IN ORIGINAL LANGUAGE INTERPRETATION
Bayerische
Motoren Werke (BMW) AG Germany Aktiengesellschaft Corporation
Rolls-Royce PLC United Kingdom Public limited company Public limited company
Shell UK Ltd. United Kingdom Limited Corporation
Unilever NV Netherlands Naamloze Vennootschap Joint stock company
Fiat SpA Italy Società per Azioni Joint stock company
Volvo AB Sweden Aktiebolag Joint stock company
Peugeot SA France Société Anonyme Joint stock company
TABLE 1.2 International Corporations
FIGURE 1.3 Cash Flows between the Firm and the Financial Markets
Total Value of Assets
Firm invests
in assets
(B)
Current assets
Fixed assets
Cash for securities issued by the firm (A)
Retained cash
flows (E )
Government
(D)
Cash flow from
firm (C)
Dividends and
debt payments (F )
Financial
markets
Short-term debt
Long-term debt
Equity shares
Total Value of the Firm
to Investors in
the Financial Markets
Taxes
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8
activities (assets) of the firm (B) by the firm’s management. The cash generated by the
firm (C) is paid to shareholders and bondholders (F). The shareholders receive cash in the
form of dividends; the bondholders who lent funds to the firm receive interest and, when
the initial loan is repaid, principal. Not all of the firm’s cash is paid out. Some is retained
(E), and some is paid to the government as taxes (D).
Over time, if the cash paid to shareholders and bondholders (F) is greater than the cash
raised in the financial markets (A), value will be created.
IDENTIFICATION OF CASH FLOWS Unfortunately, it is sometimes not easy to observe
cash flows directly. Much of the information we obtain is in the form of accounting state-
ments, and much of the work of financial analysis is to extract cash flow information from
accounting statements. The following example illustrates how this is done.
E
X
A
M
P
L
E
1.
1
The Midland Company refines and trades gold. At the end of the year, it sold 2,500 ounces of gold for
$1 million. The company had acquired the gold for $900,000 at the beginning of the year. The company
paid cash for the gold when it was purchased. Unfortunately it has yet to collect from the customer to
whom the gold was sold. The following is a standard accounting of Midland’s financial circumstances at
year-end:
By generally accepted accounting principles (GAAP), the sale is recorded even though the customer has
yet to pay. It is assumed that the customer will pay soon. From the accounting perspective, Midland seems
to be profitable. However, the perspective of corporate finance is different. It focuses on cash flows:
The perspective of corporate finance is interested in whether cash flows are being created by the
gold trading operations of Midland. Value creation depends on cash flows. For Midland, value creation
depends on whether and when it actually receives $1 million.
Accounting Profit versus Cash Flows
THE MIDLAND COMPANY
Account ing View
Income Statement
Year Ended December 31
Sales $1,000,000
−Costs −900,000
Profit $ 100,000
THE MIDLAND COMPANY
F inancia l V iew
Income Statement
Year Ended December 31
Cash inflow $ 0
Cash outflow −900,000
$−900,000
TIMING OF CASH FLOWS The value of an investment made by a firm depends on the tim-
ing of cash flows. One of the most important principles of finance is that individuals prefer
to receive cash flows earlier rather than later. One dollar received today is worth more than
one dollar received next year.
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RISK OF CASH FLOWS The firm must consider risk. The amount and timing of cash flows
are not usually known with certainty. Most investors have an aversion to risk.
E
X
A
M
P
L
E
1.
2
The Midland Company is attempting to choose between two proposals for new products. Both proposals
will provide additional cash flows over a four-year period and will initially cost $10,000. The cash flows
from the proposals are as follows:
At first it appears that new Product A would be best. However, the cash flows from Product B come ear-
lier than those of A. Without more information, we cannot decide which set of cash flows would create
the most value for the bondholders and shareholders. It depends on whether the value of getting cash
from B up front outweighs the extra total cash from A. Bond and stock prices reflect this preference for
earlier cash, and we will see how to use them to decide between A and B.
Cash Flow Timing
YEAR NEW PRODUCT A NEW PRODUCT B
1 $ 0 $ 4,000
2 0 4,000
3 0 4,000
4 20,000 4,000
Total $20,000 $16,000
E
X
A
M
P
L
E
1.
3
The Midland Company is considering expanding operations overseas. It is evaluating Europe and Japan
as possible sites. Europe is considered to be relatively safe, whereas operating in Japan is seen as very
risky. In both cases the company would close down operations after one year.
After doing a complete financial analysis, Midland has come up with the following cash flows of the
alternative plans for expansion under three scenarios—pessimistic, most likely, and optimistic:
If we ignore the pessimistic scenario, perhaps Japan is the best alternative. When we take the pessimis-
tic scenario into account, the choice is unclear. Japan appears to be riskier, but it also offers a higher
expected level of cash flow. What is risk and how can it be defined? We must try to answer this impor-
tant question. Corporate finance cannot avoid coping with risky alternatives, and much of our book is
devoted to developing methods for evaluating risky opportunities.
Risk
PESSIMISTIC MOST L IKELY OPTIMISTIC
Europe $75,000 $100,000 $125,000
Japan 0 150,000 200,000
1.4 THE GOAL OF FINANCIAL MANAGEMENT
Assuming that we restrict our discussion to for-profit businesses, the goal of financial
management is to make money or add value for the owners. This goal is a little vague,
of course, so we examine some different ways of formulating it to come up with a more
precise definition. Such a definition is important because it leads to an objective basis for
making and evaluating financial decisions.
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10
Possible Goals
If we were to consider possible financial goals, we might come up with some ideas like the
following:
∙ Survive.
∙ Avoid financial distress and bankruptcy.
∙ Beat the competition.
∙ Maximize sales or market share.
∙ Minimize costs.
∙ Maximize profits.
∙ Maintain steady earnings growth.
These are only a few of the goals we could list. Furthermore, each of these possibilities
presents problems as a goal for the financial manager.
For example, it’s easy to increase market share or unit sales: All we have to do is lower
our prices or relax our credit terms. Similarly, we can always cut costs by doing away with
things such as research and development. We can avoid bankruptcy by never borrowing
any money or never taking any risks, and so on. It’s not clear that any of these actions are
in the stockholders’ best interests.
Profit maximization would probably be the most commonly cited goal, but even this is not
a precise objective. Do we mean profits this year? If so, then we should note that actions such
as deferring maintenance, letting inventories run down, and taking other short-run cost-cutting
measures will tend to increase profits now, but these activities aren’t necessarily desirable.
The goal of maximizing profits may refer to some sort of “long-run” or “average” prof-
its, but it’s still unclear exactly what this means. First, do we mean something like account-
ing net income or earnings per share? As we will see in more detail in the next chapter,
these accounting numbers may have little to do with what is good or bad for the firm. We
are actually more interested in cash flows. Second, what do we mean by the long run? As
a famous economist once remarked, in the long run, we’re all dead! More to the point, this
goal doesn’t tell us what the appropriate trade-off is between current and future profits.
The goals we’ve listed here are all different, but they tend to fall into two classes. The
first of these relates to profitability. The goals involving sales, market share, and cost control
all relate, at least potentially, to different ways of earning or increasing profits. The goals in
the second group, involving bankruptcy avoidance, stability, and safety, relate in some way
to controlling risk. Unfortunately, these two types of goals are somewhat contradictory. The
pursuit of profit normally involves some element of risk, so it isn’t really possible to maxi-
mize both safety and profit. What we need, therefore, is a goal that encompasses both factors.
The Goal of Financial Management
The financial manager in a corporation makes decisions for the stockholders of the firm.
So, instead of listing possible goals for the financial manager, we really need to answer a
more fundamental question: From the stockholders’ point of view, what is a good financial
management decision?
If we assume that stockholders buy stock because they seek to gain financially, then
the answer is obvious: Good decisions increase the value of the stock, and poor decisions
decrease the value of the stock.
From our observations, it follows that the financial manager acts in the shareholders’
best interests by making decisions that increase the value of the stock. The appropriate goal
for the financial manager can thus be stated quite easily:
The goal of financial management is to maximize the current value per share of the
existing stock.
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The goal of maximizing the value of the stock avoids the problems associated with
the different goals we listed earlier. There is no ambiguity in the criterion, and there is no
short-run versus long-run issue. We explicitly mean that our goal is to maximize the cur-
rent stock value.
If this goal seems a little strong or one-dimensional to you, keep in mind that the stockhold-
ers in a firm are residual owners. By this we mean that they are entitled only to what is left after
employees, suppliers, and creditors (and everyone else with legitimate claims) are paid their
due. If any of these groups go unpaid, the stockholders get nothing. So if the stockholders are
winning in the sense that the leftover, residual portion is growing, it must be true that everyone
else is winning also. In other words, managers should make decisions that they believe will
achieve the highest firm value because by doing so shareholders will benefit the most.
Because the goal of financial management is to maximize the value of the stock, we
need to learn how to identify investments and financing arrangements that favorably
impact the value of the stock. This is precisely what we will be studying. In the previous
section we emphasized the importance of cash flows in value creation. In fact, we could
have defined corporate finance as the study of the relationship between business decisions,
cash flows, and the value of the stock in the business.
A More General Goal
If our goal is to maximize the value of the stock, as stated in the preceding section, an obvi-
ous question comes up: What is the appropriate goal when the firm has no traded stock?
Corporations are certainly not the only type of business; and the stock in many corporations
rarely changes hands, so it’s difficult to say what the value per share is at any particular time.
As long as we are considering for-profit businesses, only a slight modification is needed.
The total value of the stock in a corporation is equal to the value of the owners’ equity.
Therefore, a more general way of stating our goal is
Maximize the value of the existing owners’ equity.
With this in mind, we don’t care whether the business is a proprietorship, a partnership,
or a corporation. For each of these, good financial decisions increase the value of the own-
ers’ equity, and poor financial decisions decrease it. In fact, although we choose to focus
on corporations in the chapters ahead, the principles we develop apply to all forms of busi-
ness. Many of them even apply to the not-for-profit sector.
Finally, our goal does not imply that the financial manager should take illegal or unethi-
cal actions in the hope of increasing the value of the equity in the firm. What we mean is that
the financial manager best serves the owners of the business by identifying goods and ser-
vices that add value to the firm because they are desired and valued in the free marketplace.
1.5 THE AGENCY PROBLEM AND CONTROL
OF THE CORPORATION
The processes, policies, laws, and institutions that direct a company’s actions are all
included under the broad category of corporate governance. Corporate governance can
also include the relationships among various stakeholders including shareholders, manage-
ment, employees, the board of directors, suppliers, and the community at large, among
others. As such, corporate governance is a wide-ranging topic.
We’ve seen that the financial manager acts in the best interests of the stockholders by
taking actions that increase the value of the firm and thus the stock. However, in large cor-
porations, ownership can be spread over a huge number of stockholders. This dispersion
of ownership arguably means that stockholders cannot directly control the firm and that
management effectively controls the firm. In this case, will management necessarily act in
Business ethics are
considered at business-
ethics.com.
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12
the best interests of the stockholders? Put another way, might not management pursue its
own goals at the stockholders’ expense?
Corporate governance varies quite a bit around the world. For example, in most coun-
tries other than the U.S. and the U.K., publicly traded companies are usually controlled
by one or more large shareholders. Moreover, in countries with limited shareholder pro-
tection, when compared to countries with strong shareholder protection like the U.S. and
the U.K., large shareholders may have a greater opportunity to take advantage of minor-
ity shareholders. Research shows that a country’s investor protection framework is
important to understanding a firm’s cash holdings and dividend payouts. For example,
studies find that shareholders do not highly value cash holdings in firms in countries
with low investor protection when compared to firms in the U.S. where investor protec-
tion is high.1
In the basic corporate governance setup, the shareholders elect the board of directors
who in turn appoint the top corporate managers, such as the CEO. The CEO is usually a
member of the board of directors. One aspect of corporate governance that has received
attention recently concerns the chair of a firm’s board of directors. In a large number of
U.S. corporations, the CEO and the board chair are the same person. An argument can be
made that combining the CEO and board chair positions can contribute to poor corporate
governance. When comparing corporate governance in the U.S. and the U.K., an edge is
often given to the U.K., partly because over 90 percent of U.K. companies are chaired by
outside directors rather than the CEO.2 This is a contentious issue confronting many U.S.
corporations. For example, in 2015, 29 percent of the S&P 500 companies had named an
independent outsider as board chair, up from only 10 percent eight years earlier.
Agency Relationships
The relationship between stockholders and management is called an agency relationship.
Such a relationship exists whenever someone (the principal) hires another (the agent) to
represent his or her interests. For example, you might hire someone (an agent) to sell a car
that you own while you are away at school. In all such relationships there is a possibility
of a conflict of interest between the principal and the agent. Such a conflict is called an
agency problem.
Suppose you hire someone to sell your car and you agree to pay that person a flat fee
when he or she sells the car. The agent’s incentive in this case is to make the sale, not nec-
essarily to get you the best price. If you offer a commission of, say, 10 percent of the sales
price instead of a flat fee, then this problem might not exist. This example illustrates that
the way in which an agent is compensated is one factor that affects agency problems.
Management Goals
To see how management and stockholder interests might differ, imagine that a firm is con-
sidering a new investment. The new investment is expected to favorably impact the share
value, but it is also a relatively risky venture. The owners of the firm will wish to take the
investment (because the stock value will rise), but management may not because there is
the possibility that things will turn out badly and management jobs will be lost. If manage-
ment does not take the investment, then the stockholders may lose a valuable opportunity.
This is one example of an agency cost.
1 See, for example, “Investor Protection and Corporate Valuation,” by Rafael La Porta, Florencio Lopez-de-Silanes, Andrei Shleifer, and Robert
Vishny, Journal of Finance 57 (2002), pp. 1147–1170; and “Cash Holdings, Dividend Policy, and Corporate Governance: A Cross-Country
Analysis,” by Lee Pinkowitz, René M. Stulz, and Rohan Williamson, Journal of Applied Corporate Finance, Vol. 19, No. 1 (2007), pp. 81–87.
2 “U.S. Corporate Governance: Accomplishments and Failings, a Discussion with Michael Jensen and Robert Monks” (moderated by Ralph
Walkling), Journal of Applied Corporate Finance, Vol. 20, No. 1 (Winter 2008), pp. 28–46.
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More generally, the term agency costs refers to the costs of the conflict of interest
between stockholders and management. These costs can be indirect or direct. An indirect
agency cost is a lost opportunity, such as the one we have just described.
Direct agency costs come in two forms. The first type is a corporate expenditure that
benefits management but costs the stockholders. Perhaps the purchase of a luxurious and
unneeded corporate jet would fall under this heading. The second type of direct agency
cost is an expense that arises from the need to monitor management actions. Paying outside
auditors to assess the accuracy of financial statement information could be one example.
It is sometimes argued that, left to themselves, managers would tend to maximize the
amount of resources over which they have control or, more generally, corporate power or
wealth. This goal could lead to an overemphasis on corporate size or growth. For example,
cases in which management is accused of overpaying to buy up another company just to
increase the size of the business or to demonstrate corporate power are not uncommon.
Obviously, if overpayment does take place, such a purchase does not benefit the stockhold-
ers of the purchasing company.
Our discussion indicates that management may tend to overemphasize organizational
survival to protect job security. Also, management may dislike outside interference, so
independence and corporate self-sufficiency may be important goals.
Do Managers Act in the Stockholders’ Interests?
Whether managers will, in fact, act in the best interests of stockholders depends on two
factors. First, how closely are management goals aligned with stockholder goals? This
question relates, at least in part, to the way managers are compensated. Second, can man-
agers be replaced if they do not pursue stockholder goals? This issue relates to control of
the firm. As we will discuss, there are a number of reasons to think that, even in the largest
firms, management has a significant incentive to act in the interests of stockholders.
MANAGERIAL COMPENSATION Management will frequently have a significant economic
incentive to increase share value for two reasons. First, managerial compensation, par-
ticularly at the top, is usually tied to financial performance in general and often to share
value in particular. For example, managers are frequently given the option to buy stock at a
bargain price. The more the stock is worth, the more valuable is this option. In fact, options
are often used to motivate employees of all types, not just top management. Many firms
also give managers an ownership stake in the company by granting stock or stock options.
In 2015, the total compensation of David Zaslav, CEO of Discovery Communications, was
$156.1 million. His base salary and cash bonus was $11 million with stock and options of
$145.1 million. Although there are many critics of the high level of CEO compensation,
from the stockholders’ point of view, sensitivity of compensation to firm performance is
usually more important.
The second incentive managers have relates to job prospects. Better performers within
the firm will tend to get promoted. More generally, managers who are successful in pursu-
ing stockholder goals will be in greater demand in the labor market and thus command
higher salaries.
In fact, managers who are successful in pursuing stockholder goals can reap enormous
rewards. For example, also in 2015, Michael Fries, the CEO of Liberty Global made about
$111.9 million. By way of comparison, Floyd Mayweather made $300 million and Robert
Downey, Jr., made about $80 million.3
3 This raises the issue of the level of top management pay and its relationship to other employees. According to recent research by the
Economic Policy Institute, the average CEO compensation was 20 times greater than that of the average employee in 1965, 383 times
greater in 2000, and 231 times greater in 2011 (http://www.epi.org/publication/ib331-ceo-pay-top-1-percent/). However, there is no precise
formula that governs the gap between top management compensation and that of other employees.
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14
CONTROL OF THE FIRM Control of the firm ultimately rests with stockholders. They elect
the board of directors, who, in turn, hire and fire management.
An important mechanism by which unhappy stockholders can replace existing man-
agement is called a proxy fight. A proxy is the authority to vote someone else’s stock.
A proxy fight develops when a group solicits proxies in order to replace the existing board
and thereby replace existing management. In 2002, the proposed merger between HP and
Compaq triggered one of the most widely followed, bitterly contested, and expensive proxy
fights in history, with an estimated price tag of well over $100 million.
Another way that management can be replaced is by takeover. Firms that are poorly man-
aged are more attractive as acquisitions than well-managed firms because a greater profit
potential exists. Thus, avoiding a takeover by another firm gives management another incen-
tive to act in the stockholders’ interests. Unhappy prominent shareholders can suggest differ-
ent business strategies to a firm’s top management. This was the case in 2015, when digital
imaging company Shutterfly lost a proxy fight with Marathon Partners, which won two seats
on the board of directors in June 2015. However, another activist investor, Ancora Advisors,
threatened Shutterfly with another proxy fight in late 2015. Ancora felt that Shutterfly hadn’t
adequately addressed corporate strategy, capital allocation, and compensation.
Historically, proxy fights have been relatively rare. One reason is that the expenses in
a proxy fight can become quite large. Further, outsiders waging a proxy fight must cover
their own expenses, while the current directors use company finances to back their bid to
retain board seats. In recent years, proxy fights appear to have become more civil. In 2014,
about 50 percent of proxy fights went the distance, meaning they ultimately resulted in a
shareholder vote. Before that, it was not uncommon for 70 percent or more of proxy fights
to result in shareholder votes. Companies today appear to be more willing to work with
activist shareholders, perhaps because both parties have become more concerned with the
potential high costs of a long, bitter proxy fight.
CONCLUSION The available theory and evidence are consistent with the view that stock-
holders control the firm and that stockholder wealth maximization is the relevant goal of
the corporation. Even so, there will undoubtedly be times when management goals are
pursued at the expense of the stockholders, at least temporarily.
Stakeholders
Our discussion thus far implies that management and stockholders are the only parties with
an interest in the firm’s decisions. This is an oversimplification, of course. Employees, cus-
tomers, suppliers, and even the government all have a financial interest in the firm.
Taken together, these various groups are called stakeholders in the firm. In general,
a stakeholder is someone other than a stockholder or creditor who potentially has a claim
on the cash flows of the firm. Such groups will also attempt to exert control over the firm,
perhaps to the detriment of the owners.
1.6 REGULATION
Until now, we have talked mostly about the actions that shareholders and boards of direc-
tors can take to reduce the conflicts of interest between themselves and management. We
have not talked about regulation.4 Until recently the main thrust of federal regulation has
been to require that companies disclose all relevant information to investors and
4 At this stage in our book, we focus on the regulation of disclosure of relevant information and corporate governance. We do not talk about
many other regulators in financial markets such as the Federal Reserve Board. In Chapter 5, we discuss the nationally recognized statistical
rating organizations (NRSROs) in the U.S., such as Fitch Ratings, Moody’s, and Standard & Poor’s. Their ratings are used by market partici-
pants to help value securities such as corporate bonds. Many critics of the rating agencies blame the 2007–2009 subprime credit crisis on
weak regulatory oversight of these agencies.
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SARBANES-OXLEY
In response to corporate scandals at companies such as Enron, WorldCom, Tyco, and Adelphia, Congress enacted the
Sarbanes-Oxley Act in 2002. The act, better known as “Sarbox,” is intended to protect investors from corporate abuses.
For example, one section of Sarbox prohibits personal loans from a company to its officers, such as the ones that were
received by WorldCom CEO Bernie Ebbers.
One of the key sections of Sarbox took effect on November 15, 2004. Section 404 requires, among other things, that
each company’s annual report must have an assessment of the company’s internal control structure and financial report-
ing. The auditor must then evaluate and attest to management’s assessment of these issues.
Sarbox contains other key requirements. For example, the officers of the corporation must review and sign the annual
reports. They must explicitly declare that the annual report does not contain any false statements or material omissions;
that the financial statements fairly represent the financial results; and that they are responsible for all internal controls.
Finally, the annual report must list any deficiencies in internal controls. In essence, Sarbox makes company management
responsible for the accuracy of the company’s financial statements.
Of course, as with any law, there are costs. Sarbox has increased the expense of corporate audits, sometimes dra-
matically. In 2004, the average compliance cost was $4.51 million. By 2007, however, the average compliance cost had
fallen to $1.7 million. More recent numbers show that Sarbox costs are becoming more manageable. In 2012, 10 years
after Sarbox was passed, it was reported that most small companies spent less than $100,000 on compliance annually,
and a third of midsized companies spent $100,000 to $500,000. And there appear to be economies in Sarbox costs. By
the fourth year of Sarbox compliance, a company is expected to spend between $100,000 and $500,000, regardless
of size.
However, the added expense of Sarbox compliance has led to several unintended results. Over the seven-year period
from 1998 to 2004, 484 firms delisted their shares from exchanges, or “went dark.” Within the first two years alone of
Sarbox, 370 companies delisted. Many of the companies that delisted stated the reason was to avoid the cost of compli-
ance with Sarbox. And small companies are not the only ones to delist because of Sarbox. For example, German insurer
Allianz applied to delist its shares from the New York Stock Exchange. The company estimated that canceling its listings
outside of its home exchange of Frankfurt could save 5 million euros (about $6 million) per year.
A company that goes dark does not have to file quarterly or annual reports. Annual audits by independent auditors
are not required, and executives do not have to certify the accuracy of the financial statements, so the savings can be
huge. Of course, there are costs. Stock prices typically fall when a company announces it is going dark. Further, such
companies will typically have limited access to capital markets and usually will have a higher interest cost on bank loans.
Sarbox has also probably affected the number of companies choosing to go public in the United States. For exam-
ple, when Peach Holdings, based in Boynton Beach, Florida, decided to go public, it shunned the U.S. stock markets,
instead choosing the London Stock Exchange’s Alternative Investment Market (AIM). To go public in the United States,
the firm would have paid a $100,000 fee, plus about $2 million to comply with Sarbox. Instead, the company spent only
$500,000 on its AIM stock offering.
FINANCE MATTERS
potential investors.5 Disclosure of relevant information by corporations is intended to
put all investors on a level information playing field and, thereby to reduce conflicts of
interest. More recent regulation has been aimed at corporate governance. Of course,
regulation imposes costs on corporations, and any analysis of regulation must include
both benefits and costs. Our nearby Finance Matters box discusses some of the costs
exchange-listed companies face arising from corporate governance requirements.
5 Here, we are speaking mostly of public companies and not private companies. You will learn more about this distinction in Chapter 19. If you
can’t wait, go to investopedia.com and search “public vs. private companies.”
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16
The Securities Act of 1933 and the Securities Exchange
Act of 1934
The Securities Act of 1933 (the 1933 Act) and the Securities Exchange Act of 1934 (the 1934
Act) provide the basic regulatory framework in the United States for the public trading of
securities.
The 1933 Act focuses on the issuing of new securities. Basically, the 1933 Act requires
a corporation to file a registration statement with the Securities and Exchange Commission
(SEC) that must be made available to every buyer of a new security. The intent of the reg-
istration statement is to provide potential stockholders with all the necessary information to
make a reasonable decision. The 1934 Act extends the disclosure requirements of the 1933
Act to securities trading in markets after they have been issued. The 1934 Act establishes the
SEC and covers a large number of issues including corporate reporting, tender offers, and
insider trading. The 1934 Act requires corporations to file reports to the SEC on an annual
basis (Form 10K), on a quarterly basis (Form 10Q), and on a monthly basis (Form 8K).
As mentioned, the 1934 Act deals with the important issue of insider trading. Illegal
insider trading occurs when any person who has acquired nonpublic, special information
(i.e., inside information) buys or sells securities based upon that information. One section
of the 1934 Act deals with insiders such as directors, officers, and large shareholders,
while another deals with any person who has acquired inside information. The intent of
these sections of the 1934 Act is to prevent insiders or persons with inside information
from taking unfair advantage of this information when trading with outsiders.
To illustrate, suppose you learned that ABC firm was about to publicly announce that
it had agreed to be acquired by another firm at a price significantly greater than its current
price. This is an example of inside information. The 1934 Act prohibits you from buying
ABC stock from shareholders who do not have this information. This prohibition would be
especially strong if you were the CEO of the ABC firm. Other kinds of inside information
could be knowledge of an initial dividend about to be paid, the discovery of a drug to cure
cancer, or the default of a debt obligation.
A recent example of insider trading involved Mathew Martoma, a portfolio manager at SAC
Capital, who was convicted of insider trading in 2014. SAC Capital had already plead guilty
to fraud charges and paid $1.8 billion in fines. Martoma was found guilty of trading on inside
information he learned about a new Alzheimer’s drug and received a nine-year prison term.
SUMMARY AND CONCLUSIONS
This chapter introduced you to some of the basic ideas in corporate finance:
1. Corporate finance has three main areas of concern:
a. Capital budgeting: What long-term investments should the firm take?
b. Capital structure: Where will the firm get the short-term and long-term financing to pay for its invest-
ments? Also, what mixture of debt and equity should it use to fund operations?
c. Working capital management: How should the firm manage its everyday financial activities?
2. The goal of financial management in a for-profit business is to make decisions that increase the value of
the stock, or, more generally, increase the value of the equity.
3. The corporate form of organization is superior to other forms when it comes to raising money and trans-
ferring ownership interests, but it has the significant disadvantage of double taxation.
4. There is the possibility of conflicts between stockholders and management in a large corporation. We
called these conflicts agency problems and discussed how they might be controlled and reduced.
5. To create value companies must generate more cash than they use.
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CHAPTER 1 Introduction to Corporate Finance 17
6. Until recently the main thrust of federal regulation has been to require companies to disclose all relevant
information to investors and potential investors. More recent regulation has been aimed at corporate
governance.
Of the topics we’ve discussed thus far, the most important is the goal of financial management: maxi-
mizing the value of the stock. Throughout the text we will be analyzing many different financial decisions,
but we will always ask the same question: How does the decision under consideration affect the value of
the stock?
1. Forms of Business What are the three basic legal forms of organizing a business? What are the
advantages and disadvantages of each? What business form do most start-up companies take? Why?
2. Goal of Financial Management What goal should always motivate the actions of the firm’s financial
manager?
3. Agency Problems Who owns a corporation? Describe the process whereby the owners control the
firm’s management. What is the main reason that an agency relationship exists in the corporate form of
organization? In this context, what kinds of problems can arise?
4. Not-for-Profit Firm Goals Suppose you were the financial manager of a not-for-profit business (a not-
for-profit hospital, perhaps). What kinds of goals do you think would be appropriate?
5. Goal of the Firm Evaluate the following statement: Managers should not focus on the current stock
value because doing so will lead to an overemphasis on short-term profits at the expense of long-term
profits.
6. Ethics and Firm Goals Can our goal of maximizing the value of the stock conflict with other goals,
such as avoiding unethical or illegal behavior? In particular, do you think subjects like customer and
employee safety, the environment, and the general good of society fit in this framework, or are they
essentially ignored? Try to think of some specific scenarios to illustrate your answer.
7. International Firm Goal Would our goal of maximizing the value of the stock be different if we were
thinking about financial management in a foreign country? Why or why not?
8. Agency Problems Suppose you own stock in a company. The current price per share is $25. Another
company has just announced that it wants to buy your company and will pay $35 per share to acquire
all the outstanding stock. Your company’s management immediately begins fighting off this hostile bid.
Is management acting in the shareholders’ best interests? Why or why not?
9. Agency Problems and Corporate Ownership Corporate ownership varies around the world.
Historically, individuals have owned the majority of shares in public corporations in the United States. In
Germany and Japan, however, banks, other large financial institutions, and other companies own most
of the stock in public corporations. Do you think agency problems are likely to be more or less severe
in Germany and Japan than in the United States? Why? In recent years, large financial institutions such
as mutual funds and pension funds have been becoming the dominant owners of stock in the United
States, and these institutions are becoming more active in corporate affairs. What are the implications
of this trend for agency problems and corporate control?
10. Executive Compensation Critics have charged that compensation to top management in the United
States is too high and should be cut back. For example, focusing on large corporations, Mario Gabelli
of GAMCO Investors was been one of the best-compensated CEOs in the United States, earning about
$88.5 million in 2015. Are such amounts excessive?
In answering, it might be helpful to recognize that superstar athletes such as LeBron James, top people
in entertainment such as Oprah Winfrey and Jerry Bruckheimer, and many others at the peak of their
respective fields can earn at least as much, if not a great deal more.
CONCEPT QUESTIONS
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EAST COAST YACHTS
In 1969, Tom Warren founded East Coast Yachts. The company’s operations are located near Hilton Head
Island, South Carolina, and the company is structured as a sole proprietorship. The company has manufactured
custom midsize, high-performance yachts for clients, and its products have received high reviews for safety
and reliability. The company’s yachts have also recently received the highest award for customer satisfaction.
The yachts are primarily purchased by wealthy individuals for pleasure use. Occasionally, a yacht is manufac-
tured for purchase by a company for business purposes.
The custom yacht industry is fragmented, with a number of manufacturers. As with any industry, there are
market leaders, but the diverse nature of the industry ensures that no manufacturer dominates the market.
The competition in the market, as well as the product cost, ensures that attention to detail is a necessity. For
instance, East Coast Yachts will spend 80 to 100 hours on hand-buffing the stainless steel stem-iron, which is
the metal cap on the yacht’s bow that conceivably could collide with a dock or another boat.
Several years ago, Tom retired from the day-to-day operations of the company and turned the operations
of the company over to his daughter, Larissa. Because of the dramatic changes in the company, Larissa has
approached you to help manage and direct the company’s growth. Specifically, she has asked you to answer
the following questions.
1. What are the advantages and disadvantages of changing the company organization from a sole
proprietorship to an LLC?
2. What are the advantages and disadvantages of changing the company organization from a sole
proprietorship to a corporation?
3. Ultimately, what action would you recommend the company undertake? Why?
CLOSING CASE
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PART 1 Overview18
WHAT’S ON THE WEB?
1. Listing Requirements This chapter mentioned listing requirements for public companies. Find the
complete listing requirements for NYSE Euronext at www.nyse.com and NASDAQ at www.nasdaq.com.
Which exchange has more stringent listing requirements? Why don’t the exchanges have the same
listing requirements?
2. Business Formation As you may (or may not) know, many companies incorporate in Delaware for a
variety of reasons. Visit BizFilings at www.bizfilings.com to find out why. Which state has the highest
fee for incorporation? For an LLC? While at the site, look at the FAQ section regarding corporations
and LLCs.
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CHAPTER 2 Financial Statements and Cash Flow 19
2
OPENING
CASE
Financial Statements
and Cash Flow
When a company announces a “write-off,” that frequently means that the value of the compa-
ny’s assets has declined. For example, in July 2015, Microsoft announced that it would write
off $7.6 billion related to its purchase of Nokia’s phone business the previous year. What made
the write-off interesting was that Microsoft had only paid $7.2 billion for the phone business.
The oil business was also hit hard in 2015 as the five largest publicly traded oil companies
working in Wyoming wrote off a combined $41 billion for the first nine months of the year.
These write-offs were due to the declining value of oil production facilities in that state.
While Microsoft’s write-off is large, the record holder is media giant Time Warner, which
took a charge of $45.5 billion in the fourth quarter of 2002. This enormous write-off followed
an earlier, even larger, charge of $54 billion.
So, did the stockholders in these companies lose billions of dollars when these assets
were written off? Fortunately for them, the answer is probably not. Understanding why ulti-
mately leads us to the main subject of this chapter, that all-important substance known as
cash flow.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
2.1 THE BALANCE SHEET
The balance sheet is an accountant’s snapshot of the firm’s accounting value on a par-
ticular date, as though the firm stood momentarily still. The balance sheet has two sides:
On the left are the assets and on the right are the liabilities and stockholders’ equity. The
balance sheet states what the firm owns and how it is financed. The accounting definition
that underlies the balance sheet and describes the balance is
Assets ≡ Liabilities + Stockholders’ equity [2.1]
We have put a three-line equality in the balance equation to indicate that it must always
hold, by definition. In fact, the stockholders’ equity is defined to be the difference between
the assets and the liabilities of the firm. In principle, equity is what the stockholders would
have remaining after the firm discharged its obligations.
Table 2.1 gives the 2016 and 2017 balance sheets for the fictitious U.S. Composite
Corporation. The assets in the balance sheet are listed in order by the length of time it
normally would take an ongoing firm to convert them to cash. The asset side depends on
the nature of the business and how management chooses to conduct it. Management must
make decisions about cash versus marketable securities, credit versus cash sales, whether
ExcelMaster
coverage online
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Two excellent sources
for company financial
information are finance.
yahoo.com and money.
cnn.com.
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20
Annual and quarterly
financial statements for
most public U.S. corpora-
tions can be found in the
EDGAR database at www.
sec.gov.
TABLE 2.1 The Balance Sheet of the U.S. Composite Corporation
U.S. COMPOSITE CORPORATION
Balance Sheet
2016 and 2017
( in $ mi l l ions)
ASSETS 2016 2017
LIABIL IT IES (DEBT) AND
STOCKHOLDERS’ EQUITY 2016 2017
Current assets:
Cash and equivalents
Accounts receivable
Inventories
Total current assets
$ 157
270
280
$ 707
$ 198
294
269
$ 761
Current liabilities:
Accounts payable
Total current liabilities
$ 455
$ 455
$ 486
$ 486
Long-term liabilities:
Deferred taxes
Long-term debt*
Total long-term liabilities
$ 104
458
$ 562
$ 117
471
$ 588
Fixed assets:
Property, plant, and equipment
Less accumulated depreciation
Net property, plant, and equipment
Intangible assets and others
Total fixed assets
$ 1,274
460
$ 814
221
$ 1,035
$ 1,423
550
$ 873
245
$ 1,118
Stockholders’ equity:
Preferred stock
Common stock ($1 par value)
Capital surplus
Accumulated retained earnings
Less treasury stock†
Total equity
$ 39
32
327
347
20
$ 725
$ 39
55
347
390
26
$ 805
Total assets $ 1,742 $ 1,879
Total liabilities and
stockholders’ equity‡ $ 1,742 $ 1,879
* Long-term debt rose by $471 million – 458 million = $13 million. This is the difference between $86 million new debt and $73 million in retirement of old debt.
† Treasury stock rose by $6 million. This reflects the repurchase of $6 million of U.S. Composite’s company stock.
‡ U.S. Composite reports $43 million in new equity. The company issued 23 million shares at a price of $1.87. The par value of common stock increased by $23 million, and capital surplus
increased by $20 million.
to make or buy commodities, whether to lease or purchase items, the types of business in
which to engage, and so on.
The liabilities and stockholders’ equity side reflects the types and proportions of financ-
ing, which depend on management’s choice of capital structure, as between debt and equity
and between current debt and long-term debt. The liabilities and the stockholders’ equity
are listed in the order in which they would typically be paid over time.
When analyzing a balance sheet, the financial manager should be aware of three con-
cerns: accounting liquidity, debt versus equity, and value versus cost.
Accounting Liquidity
Accounting liquidity refers to the ease and quickness with which assets can be converted
to cash. Current assets are the most liquid and include cash and those assets that will be
turned into cash within a year from the date of the balance sheet. Accounts receivable are
amounts not yet collected from customers for goods or services sold to them (after adjust-
ment for potential bad debts). Inventory is composed of raw materials to be used in produc-
tion, work in process, and finished goods. Fixed assets are the least liquid kind of assets.
Tangible fixed assets include property, plant, and equipment. These assets do not convert
to cash from normal business activity, and they are not usually used to pay expenses such
as payroll.
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Some fixed assets are not tangible. Intangible assets have no physical existence but can
be very valuable. Examples of intangible assets are the value of a trademark or the value
of a patent. The more liquid a firm’s assets, the less likely the firm is to experience prob-
lems meeting short-term obligations. Thus, the probability that a firm will avoid financial
distress can be linked to the firm’s liquidity. Unfortunately, liquid assets frequently have
lower rates of return than fixed assets; for example, cash generates no investment income.
To the extent a firm invests in liquid assets, it sacrifices an opportunity to invest in more
profitable investment vehicles.
Debt versus Equity
Liabilities are obligations of the firm that require a payout of cash within a stipulated time
period. Many liabilities involve contractual obligations to repay a stated amount at some
point, along with interest over a period. Thus, liabilities are debts and are frequently asso-
ciated with nominally fixed cash burdens, called debt service, that put the firm in default
of a contract if they are not paid. Stockholders’ equity is a claim against the firm’s assets
that is residual and not fixed. In general terms, when the firm borrows, it gives the bond-
holders first claim on the firm’s cash flow.1 Bondholders can sue the firm if the firm
defaults on its bond contracts. This may lead the firm to declare itself bankrupt.
Stockholders’ equity is the residual difference between assets and liabilities:
Assets – Liabilities ≡ Stockholders’ equity [2.2]
This is the stockholders’ share in the firm stated in accounting terms. The account-
ing value of stockholders’ equity increases when retained earnings are added. This occurs
when the firm retains part of its earnings instead of paying them out as dividends.
Value versus Cost
The accounting value of a firm’s assets is frequently referred to as the carrying value or the
book value of the assets.2 Under generally accepted accounting principles (GAAP),
audited financial statements of firms in the United States carry the assets at cost.3 Thus the
terms carrying value and book value are unfortunate. They specifically say “value,” when
in fact the accounting numbers are based on cost. This misleads many readers of financial
statements to think that the firm’s assets are recorded at true market values. Market value
is the price at which willing buyers and sellers would trade the assets. It would be only a
coincidence if accounting value and market value were the same. In fact, management’s
job is to create value for the firm that exceeds its cost.
Many people use the balance sheet, but the information each may wish to extract is not
the same. A banker may look at a balance sheet for evidence of accounting liquidity and
working capital. A supplier may also note the size of accounts payable and therefore the
general promptness of payments. Many users of financial statements, including managers
and investors, want to know the value of the firm, not its cost. This information is not found
on the balance sheet. In fact, many of the true resources of the firm do not appear on the
balance sheet: good management, proprietary assets, favorable economic conditions, and
so on. Henceforth, whenever we speak of the value of an asset or the value of the firm, we
will normally mean its market value. So, for example, when we say the goal of the finan-
cial manager is to increase the value of the stock, we mean the market value of the stock.
1 Bondholders are investors in the firm’s debt. They are creditors of the firm. In this discussion, the term bondholder means the same thing
as creditor.
2 Confusion often arises because many financial accounting terms have the same meaning. This presents a problem with jargon for the
reader of financial statements. For example, the following terms usually refer to the same thing: assets minus liabilities, net worth, stock-
holders’ equity, owners’ equity, book equity, and equity capitalization.
3 Generally, GAAP requires assets to be carried at the lower of cost or market value. In most instances, cost is lower than market value.
However, in some cases when a fair market value can be readily determined, the assets have their value adjusted to the fair market value.
The home page for the
Financial Accounting
Standards Board (FASB) is
www.fasb.org.
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22
2.2 THE INCOME STATEMENT
The income statement measures performance over a specific period of time, say, a year.
The accounting definition of income is
Revenue – Expenses ≡ Income [2.3]
If the balance sheet is like a snapshot, the income statement is like a video recording of
what the firm did between two snapshots. Table 2.2 gives the income statement for the
U.S. Composite Corporation for 2017.
The income statement usually includes several sections. The operations section reports
the firm’s revenues and expenses from principal operations. One number of particu-
lar importance is earnings before interest and taxes (EBIT), which summarizes earnings
before taxes and financing costs. Among other things, the nonoperating section of the
income statement includes all financing costs, such as interest expense. Usually a second
section reports as a separate item the amount of taxes levied on income. The last item on
the income statement is the bottom line, or net income. Net income is frequently expressed
per share of common stock, that is, earnings per share.
When analyzing an income statement, the financial manager should keep in mind
GAAP, noncash items, time, and costs.
Generally Accepted Accounting Principles
Revenue is recognized on an income statement when the earnings process is virtually com-
pleted and an exchange of goods or services has occurred. Therefore, the unrealized appre-
ciation from owning property will not be recognized as income. This provides a device
for smoothing income by selling appreciated property at convenient times. For example,
if the firm owns a tree farm that has doubled in value, then, in a year when its earn-
ings from other businesses are down, it can raise overall earnings by selling some trees.
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The Cooney Corporation has fixed assets with a book value of $700 and an appraised market value of
about $1,000. Net working capital is $400 on the books, but approximately $600 would be realized if all
the current accounts were liquidated. Cooney has $500 in long-term debt, both book value and market
value. What is the book value of the equity? What is the market value?
We can construct two simplified balance sheets, one in accounting (book value) terms and one in
economic (market value) terms:
COONEY CORPORATION
Balance Sheets
Market Value versus Book Value
Assets Liabilities and Shareholders’ Equity
BOOK MARKET BOOK MARKET
Net working capital
Net fixed assets
$ 400
700
$1,100
$ 600
1,000
$1,600
Long-term debt
Shareholders’ equity
$ 500
600
$1,100
$ 500
1,100
$1,600
In this example, shareholders’ equity is actually worth almost twice as much as what is shown on the
books. The distinction between book and market values is important precisely because book values can
be so different from true economic value.
Market Value versus Book Value
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U. S . COMPOSITE CORPORATION
Income Statement
2017
( in $ mi l l ions)
Total operating revenues
Cost of goods sold
Selling, general, and administrative expenses
Depreciation
Operating income
Other income
Earnings before interest and taxes (EBIT)
Interest expense
Pretax income
Taxes
Current: $71
Deferred: $13
Net income
Addition to retained earnings:
Dividends:
$ 2,262
1,655
327
90
$ 190
29
$ 219
49
$ 170
84
$ 86
$ 43
43
TABLE 2.2
The Income Statement
of the U.S. Composite
Corporation
The matching principle of GAAP dictates that revenues be matched with expenses. Thus,
income is reported when it is earned, or accrued, even though no cash flow has necessar-
ily occurred (for example, when goods are sold for credit, sales and profits are reported).
Noncash Items
The economic value of assets is intimately connected to their future incremental cash flows.
However, cash flow does not appear on an income statement. There are several noncash items
that are expenses against revenues but do not affect cash flow. The most important of these
is depreciation. Depreciation reflects the accountant’s estimate of the cost of equipment used
up in the production process. For example, suppose an asset with a five-year life and no resale
value is purchased for $1,000. According to accountants, the $1,000 cost must be expensed
over the useful life of the asset. If straight-line depreciation is used, there will be five equal
installments and $200 of depreciation expense will be incurred each year. From a finance
perspective, the cost of the asset is the actual negative cash flow incurred when the asset is
acquired (that is, $1,000, not the accountant’s smoothed $200-per-year depreciation expense).
Another noncash expense is deferred taxes. Deferred taxes result from differences
between accounting income and true taxable income.4 Notice that the accounting tax
shown on the income statement for the U.S. Composite Corporation is $84 million. It can
be broken down as current taxes and deferred taxes. The current tax portion is actually sent
to the tax authorities (for example, the Internal Revenue Service). The deferred tax portion
is not. However, the theory is that if taxable income is less than accounting income in the
4 One situation in which taxable income may be lower than accounting income is when the firm uses accelerated depreciation expense
procedures for the IRS but uses straight-line procedures allowed by GAAP for reporting purposes.
Note: There are 29 million shares outstanding. Earnings per share and dividends per share can be calculated as follows:
Earnings per share
=
Net income
____________________
Total shares outstanding
=
$86
____
29
= $2.97 per share
Dividends per share
=
Dividends
____________________
Total shares outstanding
=
$43
____
29
= $1.48 per share
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24
current year, it will be more than accounting income later on. Consequently, the taxes that
are not paid today will have to be paid in the future, and they represent a liability of the
firm. This shows up on the balance sheet as deferred tax liability. From the cash flow per-
spective, though, deferred tax is not a cash outflow.
In practice, the difference between cash flows and accounting income can be quite dra-
matic, so it is important to understand the difference. For example, in January 2016, United
States Steel Corporation reported a loss of $1.5 billion for the 2015 year. That sounds bad,
but U.S. Steel reported a positive cash flow of $359 million for the year! In large part, the
loss was due to charges attributable to restructuring and other strategic actions.
Time and Costs
It is often useful to think of all of future time as having two distinct parts, the short
run and the long run. The short run is that period of time in which certain equipment,
resources, and commitments of the firm are fixed; but the time is long enough for the firm
to vary its output by using more labor and raw materials. The short run is not a precise
period of time that will be the same for all industries. However, all firms making deci-
sions in the short run have some fixed costs, that is, costs that will not change because of
fixed commitments. In real business activity, examples of fixed costs are bond interest,
overhead, and property taxes. Costs that are not fixed are variable. Variable costs change
as the output of the firm changes; some examples are raw materials and wages for laborers
on the production line.
In the long run, all costs are variable. Financial accountants do not distinguish between
variable costs and fixed costs. Instead, accounting costs usually fit into a classification that
distinguishes product costs from period costs. Product costs are the total production costs
incurred during a period—raw materials, direct labor, and manufacturing overhead—and
are reported on the income statement as cost of goods sold. Both variable and fixed costs
are included in product costs. Period costs are costs that are allocated to a time period;
they are called selling, general, and administrative expenses. One period cost would be the
company president’s salary.
2.3 TAXES
Taxes can be one of the largest cash outflows that a firm experiences. For example, for
the fiscal year 2015, Walmart’s earnings before taxes were about $24.8 billion. Its tax bill,
including all taxes paid worldwide, was a whopping $7.99 billion, or about 30.2 percent
of its pretax earnings. The size of the tax bill is determined through the tax code, an often
amended set of rules. In this section, we examine corporate tax rates and how taxes are
calculated.
If the various rules of taxation seem a little bizarre or convoluted to you, keep in mind
that the tax code is the result of political, not economic, forces. As a result, there is no rea-
son why it has to make economic sense.
Corporate Tax Rates
Corporate tax rates in effect for 2016 are shown in Table 2.3. A peculiar feature of taxa-
tion instituted by the Tax Reform Act of 1986 and expanded in the 1993 Omnibus Budget
Reconciliation Act is that corporate tax rates are not strictly increasing. As shown, cor-
porate tax rates rise from 15 percent to 39 percent, but they drop back to 34 percent on
income over $335,000. They then rise to 38 percent and subsequently fall to 35 percent.
According to the originators of the current tax rules, there are only four corporate rates:
15 percent, 25 percent, 34 percent, and 35 percent. The 38 and 39 percent brackets arise
because of “surcharges” applied on top of the 34 and 35 percent rates. A tax is a tax is a
tax, however, so there are really six corporate tax brackets, as we have shown.
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Average versus Marginal Tax Rates
In making financial decisions, it is frequently important to distinguish between average and
marginal tax rates. Your average tax rate is your tax bill divided by your taxable income,
in other words, the percentage of your income that goes to pay taxes. Your marginal tax
rate is the tax you would pay (in percent) if you earned one more dollar. The percentage
tax rates shown in Table 2.3 are all marginal rates. Put another way, the tax rates apply to
the part of income in the indicated range only, not all income.
The difference between average and marginal tax rates can best be illustrated with a
simple example. Suppose our corporation has a taxable income of $200,000. What is the
tax bill? Using Table 2.3, we can figure our tax bill as:
TAXABLE INCOME TAX RATE
$ 0–50,000
50,001–75,000
75,001–100,000
100,001–335,000
335,001–10,000,000
10,000,001–15,000,000
15,000,001–18,333,333
18,333,334+
15%
25
34
39
34
35
38
35
TABLE 2.3
Corporate Tax Rates
.15($ 50,000) = $ 7,500
.25($ 75,000 – 50,000) = 6,250
.34($100,000 – 75,000) = 8,500
.39($200,000 – 100,000) = 39,000
$ 61,250
Our total tax is thus $61,250.
In our example, what is the average tax rate? We had a taxable income of $200,000 and
a tax bill of $61,250, so the average tax rate is $61,250/200,000 = 30.625%. What is the
marginal tax rate? If we made one more dollar, the tax on that dollar would be 39 cents, so
our marginal rate is 39 percent.
The IRS has a great web-
site! (www.irs.gov)
Table 2.4 summarizes some different taxable incomes, marginal tax rates, and average
tax rates for corporations. Notice how the average and marginal tax rates come together at
35 percent.
With a flat-rate tax, there is only one tax rate, so the rate is the same for all income
levels. With such a tax, the marginal tax rate is always the same as the average tax rate. As
Algernon, Inc., has a taxable income of $85,000. What is its tax bill? What is its average tax rate? Its mar-
ginal tax rate?
From Table 2.3, we see that the tax rate applied to the first $50,000 is 15 percent; the rate applied
to the next $25,000 is 25 percent, and the rate applied after that up to $100,000 is 34 percent. So
Algernon must pay .15 × $50,000 + .25 × 25,000 + .34 × (85,000 – 75,000) = $17,150. The average
tax rate is thus $17,150/85,000 = 20.18%. The marginal rate is 34 percent because Algernon’s taxes
would rise by 34 cents if it had another dollar in taxable income.
Deep in the Heart of Taxes
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26
it stands now, corporate taxation in the United States is based on a modified flat-rate tax,
which becomes a true flat rate for the highest incomes.
In looking at Table 2.4, notice that the more a corporation makes, the greater is the per-
centage of taxable income paid in taxes. Put another way, under current tax law, the aver-
age tax rate never goes down, even though the marginal tax rate does. As illustrated, for
corporations, average tax rates begin at 15 percent and rise to a maximum of 35 percent.
It will normally be the marginal tax rate that is relevant for financial decision making.
The reason is that any new cash flows will be taxed at that marginal rate. Because financial
decisions usually involve new cash flows or changes in existing ones, this rate will tell us
the marginal effect of a decision on our tax bill.
There is one last thing to notice about the tax code as it affects corporations. It’s easy
to verify that the corporate tax bill is just a flat 35 percent of taxable income if our taxable
income is more than $18.33 million. Also, for the many midsize corporations with taxable
incomes in the range of $335,000 to $10,000,000, the tax rate is a flat 34 percent. Because
we will normally be talking about large corporations, you can assume that the average and
marginal tax rates are 35 percent unless we explicitly say otherwise. We should note that
the tax rates we have discussed in this section relate to federal taxes only. Overall tax rates
can be higher once state, local, and any other taxes are considered.
With the increasing globalization of business, accounting standards need to be more
globally similar. In recent years, U.S. accounting standards have increasingly become more
closely tied to International Financial Reporting Standards (IFRS). In particular, the Financial
Accounting Standards Board (in charge of U.S. GAAP) and the International Accounting
Standards Board (IASB, the entity in charge of IFRS), had been working toward a conver-
gence of policies, although it appears that the convergence has been tabled, at least for now.
We should note that we have simplified the U.S. tax code in our discussions. In reality, the
tax code is much more complex, and it is riddled with various tax deductions and loopholes
allowed for certain industries. As a result, the average corporate tax rate can be far from
35 percent for many companies. Table 2.5 displays average tax rates for various industries.
(1)
TAXABLE INCOME
(2)
MARGINAL TAX RATE
(3)
TOTAL TAX
(3) / (1)
AVERAGE TAX RATE
$ 45,000
70,000
95,000
250,000
1,000,000
17,500,000
50,000,000
100,000,000
15%
25
34
39
34
38
35
35
$ 6,750
12,500
20,550
80,750
340,000
6,100,000
17,500,000
35,000,000
15.00%
17.86
21.63
32.30
34.00
34.86
35.00
35.00
TABLE 2.4
Corporate Taxes and Tax
Rates
For more information
about IFRS, check out the
website www.ifrs.org.
INDUSTRY NUMBER OF COMPANIES AVERAGE TAX RATE
Electric utilities (Eastern U.S.)
Trucking
Railroad
Securities brokerage
Banking
Medical supplies
Internet
Pharmaceutical
Biotechnology
24
33
15
30
481
264
239
337
121
33.8%
32.7
27.4
20.5
17.5
11.2
5.9
5.6
4.5
TABLE 2.5
Average Tax Rates in
Various Industries
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As you can see, the average tax rate ranges from 33.8 percent for electric utilities to
4.5 percent for biotechnology firms. For a discussion of one of the complexities of the tax
code, see the nearby Finance Matters box.
2.4 NET WORKING CAPITAL
Net working capital is current assets minus current liabilities. Net working capital is posi-
tive when current assets are greater than current liabilities. This means the cash that will
become available over the next 12 months will be greater than the cash that must be paid
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WHAT IS WARREN BUFFETT’S TAX RATE?
In 2011, famed investor Warren Buffett, one of the wealthiest individuals in the world, created a stir when he publicly
stated that his tax rate was lower than the tax rate paid by his secretary. The previous year, Buffett’s gross income was
about $63 million, on which he paid only a 15 percent tax rate. His secretary (with a substantially lower income) had a 31
percent marginal tax rate. Also in 2011, when Republican presidential contender Mitt Romney released his income taxes,
it was revealed that he too only paid an income tax rate of 15 percent on his $21 million annual income.
Why do Buffett’s and Romney’s tax rates appear so low? Currently, under the U.S. tax system, wage income is taxed
at a much higher rate than dividends and long-term capital gains. In fact, in the highest tax bracket, wage income is
taxed at 35 percent, while dividends and long-term capital gains are taxed at 15 percent. Most of Buffett’s and Romney’s
annual income comes from their investments, not wages, hence the 15 percent rates.
So do rich guys get all the (tax) breaks? U.S. President Barack Obama seemed to think so. In his 2012 State of the
Union address, with Buffett’s secretary Debbie Bosanek joining First Lady Michelle Obama in her box as a special guest,
he called for the creation of a “Buffett tax.” As he described it, such a tax would be an extra tax paid by very high-income
individuals. Maybe President Obama was angry about the fact that he and the First Lady paid $1.7 million in federal taxes
on their joint income of $5.5 million in 2009, implying an average tax rate of 31 percent.
Of course, you know that income received from dividends is already taxed. Dividends are paid from corporate
income, which is taxed at 35 percent for larger dividend-paying companies. Effectively, any tax on dividends is double
taxation on that money. The tax code realizes this. The lower tax rate on dividends lowers the double tax rate. The same
thing is true for capital gains; taxes are paid on the money before the investment is made.
In Buffett’s case, most of his wealth stems from his approximately 30 percent ownership of Berkshire Hathaway
Corporation. Based on its 23,000 (no typo!) page tax return, Berkshire’s 2014 corporate tax bill was $7.9 billion on income
of $28.1 billion, a 28 percent average rate. Buffett’s share of Berkshire’s tax bill therefore amounts to something on
the order of $2.37 billion! If we include Berkshire’s corporate taxes, Buffett’s average tax rate is more like 28 + 15 =
43 percent.
To give another example, consider the situation described by N. Gregory Mankiw, the well-known economist and
textbook author. Mankiw considers taking a writing job for $1,000. He figures that if he earns an 8 percent return and
there are no taxes, he would be able to leave his children about $10,000 in 30 years when he passes on. However,
because of federal, state, and Medicare taxes, he would only receive about $523 after taxes today. And because
of corporate taxes and personal income taxes, his return on the same investment would only be about 4 percent,
which will result in a balance of $1,700 in 30 years. When he dies, his account will be taxed using the marginal estate
tax rate, which is as high as 55 percent. As a result, his children will receive only about $1,000, implying a tax rate of
90 percent!
FINANCE MATTERS
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out. The net working capital of the U.S. Composite Corporation is $275 million in 2017
and $252 million in 2016:
Current assets
($millons) −
Current liabilities
($millons) =
Net working capital
($millons)
2017 $761 − $486 = $275
2016 707 − 455 = 252
In addition to investing in fixed assets (i.e., capital spending), a firm can invest in net work-
ing capital. This is called the change in net working capital. The change in net working
capital in 2017 is the difference between the net working capital in 2017 and 2016; that is,
$275 million – 252 million = $23 million. The change in net working capital is usually
positive in a growing firm.5
2.5 CASH FLOW OF THE FIRM
Perhaps the most important item that can be extracted from financial statements is the
actual cash flow of the firm. There is an official accounting statement called the statement
of cash flows. This statement helps to explain the change in accounting cash and equiva-
lents, which for U.S. Composite is $33 million in 2017. (See Section 2.6.) Notice in Table
2.1 that cash and equivalents increase from $157 million in 2016 to $198 million in 2017.
However, we will look at cash flow from a different perspective, the perspective of finance.
In finance, the value of the firm is its ability to generate cash flow. (We will talk more
about cash flow in Chapter 8.)
The first point we should mention is that cash flow is not the same as net working capi-
tal. For example, increasing inventory requires using cash. Because both inventories and
cash are current assets, this does not affect net working capital. In this case, an increase in
a particular net working capital account, such as inventory, is associated with decreasing
cash flow.
Just as we established that the value of a firm’s assets is always equal to the sum of the
value of the liabilities and the value of the equity, the cash flows generated from the firm’s
assets (that is, its operating activities), CF(A), must equal the cash flows it can distribute to
the firm’s creditors, CF(B), and equity investors, CF(S):
CF(A) = CF(B) + CF(S) [2.4]
The first step in determining the cash flow of the firm is to figure out the operating cash
flow. As can be seen in Table 2.6, operating cash flow is the cash flow generated by busi-
ness activities, including sales of goods and services. Operating cash flow reflects tax pay-
ments, but not financing, capital spending, or changes in net working capital.
5 A firm’s current liabilities sometimes include short-term interest-bearing debt usually referred to as notes payable. However, financial ana-
lysts often distinguish between interest-bearing short-term debt and non-interest-bearing short-term debt (such as accounts payable). When
this distinction is made, only non-interest-bearing short-term debt is usually included in the calculation of net working capital. This version of
net working capital is called “operating” net working capital. The interest-bearing short-term debt is not forgotten but instead is included in
cash flow from financing activities, and the interest is considered a return on capital.
IN $ MILLIONS
Earnings before interest and taxes
Depreciation
Current taxes
Operating cash flow
$219
90
–71
$238
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Another important component of cash flow involves changes in fixed assets. For
example, when U.S. Composite sold its power systems subsidiary in 2017, it generated
$25 million in cash flow. The net change in fixed assets equals the acquisition of fixed
assets minus sales of fixed assets. The result is the cash flow used for capital spending:
U.S. COMPOSITE CORPORATION
Cash F low 2017
( in $ mi l l ions)
Distributable Cash Flow of the Firm
Operating cash flow
(Earnings before interest and taxes plus depreciation minus taxes)
Capital spending
(Acquisitions of fixed assets minus sales of fixed assets)
Additions to net working capital
Total
$ 238
−173
−23
$ 42
Cash Flow to Investors in the Firm
Debt
(Interest plus retirement of debt minus long-term debt financing)
Equity
(Dividends plus repurchase of equity minus new equity financing)
Total
$ 36
6
$ 42
TABLE 2.6
Cash Flow of the U.S.
Composite Corporation
Acquisition of fixed assets
Sales of fixed assets
Capital spending
$198
–25
$173 ($149 + 24 = Increase in property,
plant, and equipment + Increase
in intangible assets)
We can also calculate capital spending as
2.5
Capital spending
=
Ending net fixed assets – Beginning net fixed assets
+ Depreciation
= $1,118 – 1,035 + 90
=
$173
Cash flows are also used for making investments in net working capital. In U.S.
Composite Corporation in 2017, additions to net working capital are
Additions to net working capital $23
Note that this $23 is the change in net working capital we previously calculated.
Total cash flows generated by the firm’s assets are the sum of
Operating cash flow
Capital spending
Additions to net working capital
Total distributable cash flow of the firm
$ 238
−173
−23
$ 42
The total outgoing cash flow of the firm can be separated into cash flow distributed
to creditors and cash flow distributed to stockholders. The cash flow distributed to credi-
tors represents a regrouping of the data in Table 2.6 and an explicit recording of interest
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30
expense. Creditors are paid an amount generally referred to as debt service. Debt service is
interest payments plus repayments of principal (that is, retirement of debt).
An important source of cash flow is the sale of new debt. U.S. Composite’s long-term
debt increased by $13 million (the difference between $86 million in new debt and
$73 million in retirement of old debt).6 Thus, an increase in long-term debt is the net effect
of new borrowing and repayment of maturing obligations plus interest expense.
6 New debt and the retirement of old debt are usually found in the “notes” to the balance sheet.
CASH FLOW PAID TO CREDITORS
( in $ mi l l ions)
Interest
Retirement of debt
Debt service
Proceeds from long-term debt sales
Total
$ 49
73
122
−86
$ 36
Cash flow distributed to creditors can also be calculated as
Cash flow paid to creditors = Interest paid – Net new borrowing [2.6]
= Interest paid – (Ending long-term debt
– Beginning long-term debt)
= $49 – (471 – 458)
= $36
CASH FLOW TO STOCKHOLDERS
( in $ mi l l ions)
Dividends
Repurchase of stock
Cash to stockholders
Proceeds from new stock issue
Total
$43
6
49
–43
$ 6
Cash flow of the firm also is distributed to the stockholders. It is the net effect of paying
dividends plus repurchasing outstanding shares of stock and issuing new shares of stock.
In general, cash flow to stockholders can be determined as
Cash flow to stockholders = Dividends paid – Net new equity raised [2.7]
= Dividends paid – ( Stock sold
– Stock repurchased )
To determine stock sold, notice that the common stock and capital surplus accounts went
up by a combined $23 + 20 = $43, which implies that the company sold $43 million worth
of stock. Second, treasury stock went up by $6, indicating that the company bought back
$6 million worth of stock. Net new equity is thus $43 – 6 = $37. Dividends paid were $43,
so the cash flow to stockholders was
Cash flow to stockholders = $43 – 43 – 6 = $6
which is what we previously calculated.
Some important observations can be drawn from our discussion of cash flow:
1. Several types of cash flow are relevant to understanding the financial situation of
the firm. Operating cash flow, defined as earnings before interest and deprecia-
tion minus taxes, measures the cash generated from operations not counting cap-
ital spending or working capital requirements. It is usually positive; a firm is in
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trouble if operating cash flow is negative for a long time because the firm is not
generating enough cash to pay operating costs. Total distributable cash flow of
the firm includes adjustments for capital spending and additions to net working
capital. It will frequently be negative. When a firm is growing at a rapid rate, the
spending on inventory and fixed assets can be higher than cash flow from sales.
2. Net income is not cash flow. The net income of the U.S. Composite Corporation
in 2017 was $86 million, whereas cash flow was $42 million. The two numbers
are not usually the same. In determining the economic and financial condition of
a firm, cash flow is more revealing.
A firm’s total cash flow sometimes goes by a different name, free cash flow. Of course,
there is no such thing as “free” cash (we wish!). Instead, the name refers to cash that the
firm is free to distribute to creditors and stockholders because it is not needed for working
capital or fixed asset investments. We will stick with “total distributable cash flow of the
firm” as our label for this important concept because, in practice, there is some variation
in exactly how free cash flow is computed; different users calculate it in different ways.
Nonetheless, whenever you hear the phrase “free cash flow,” you should understand that
what is being discussed is cash flow from assets after adjusting for capital spending and
changes in net working capital or something quite similar.
2.6 THE ACCOUNTING STATEMENT
OF CASH FLOWS
As previously mentioned, there is an official accounting statement called the statement
of cash flows. This statement helps explain the change in accounting cash, which for U.S.
Composite is $33 million in 2017. It is very useful in understanding financial cash flow.
The first step in determining the change in cash is to figure out cash flow from operating
activities. This is the cash flow that results from the firm’s normal activities producing and
selling goods and services. The second step is to make an adjustment for cash flow from
investing activities. The final step is to make an adjustment for cash flow from financing
activities. Financing activities are the net payments to creditors and owners (excluding
interest expense) made during the year.
The three components of the statement of cash flows are determined below.
Cash Flow from Operating Activities
To calculate cash flow from operating activities we start with net income. Net income can
be found on the income statement and is equal to $86 million. We now need to add back
noncash expenses and adjust for changes in current assets and liabilities (other than cash
and notes payable). The result is cash flow from operating activities.
U.S. COMPOSITE CORPORATION
Cash F low f rom Operat ing Act iv i t ies
2017
( in $ mi l l ions)
Net income
Depreciation
Deferred taxes
Change in current assets and liabilities
Accounts receivable
Inventories
Accounts payable
Cash flow from operating activities
$ 86
90
13
− 24
11
31
$207
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32
Cash Flow from Investing Activities
Cash flow from investing activities involves changes in capital assets: acquisition of
fixed assets and sales of fixed assets (i.e., net capital expenditures). The result for U.S.
Composite is below:
U.S. COMPOSITE CORPORATION
Cash F low f rom Invest ing Act iv i t ies
2017
( in $ mi l l ions)
Acquisition of fixed assets
Sales of fixed assets
Cash flow from investing activities
–$198
25
–$173
Cash Flow from Financing Activities
Cash flows to and from creditors and owners include changes in equity and debt.
U.S. COMPOSITE CORPORATION
Statement of Cash F lows
2017
( in $ mi l l ions)
Operations
Net income
Depreciation
Deferred taxes
Changes in current assets and liabilities
Accounts receivable
Inventories
Accounts payable
Total cash flow from operations
$ 86
90
13
− 24
11
31
$207
Investing activities
Acquisition of fixed assets
Sales of fixed assets
Total cash flow from investing activities
−$198
25
− $173
Financing activities
Retirement of long-term debt
Proceeds from long-term debt sales
Dividends
Repurchase of stock
Proceeds from new stock issue
Total cash flow from financing activities
Change in cash (on the balance sheet)
−$ 73
86
− 43
− 6
43
$ 7
$ 41
TABLE 2.7
Statement of Consolidated
Cash Flows of the U.S.
Composite Corporation
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U.S. COMPOSITE CORPORATION
Cash F low f rom F inancing Act iv i t ies
2017
( in $ mi l l ions)
Retirement of long-term debt
Proceeds from long-term debt sales
Dividends
Repurchase of stock
Proceeds from new stock issue
Cash flow from financing activities
−$73
86
− 43
− 6
43
$ 7
The statement of cash flows is the addition of cash flows from operations, cash flows
from investing activities, and cash flows from financing activities, and is produced in
Table 2.7. When we add all the cash flows together, we get the change in cash on the bal-
ance sheet of $33 million.
There is a close relationship between the official accounting statement called the
statement of cash flows and the total distributable cash flow of the firm used in finance.
Going back to the previous section, you should note a slight conceptual problem here.
Interest paid should really go under financing activities, but unfortunately that is not how
the accounting is handled. The reason is that interest is deducted as an expense when net
income is computed. As a consequence, a primary difference between the accounting cash
flow and the cash flow of the firm (see Table 2.6) is interest expense.
SUMMARY AND CONCLUSIONS
Besides introducing you to corporate accounting, the purpose of this chapter has been to teach you how to
determine cash flow from the accounting statements of a typical company.
1. Cash flow is generated by the firm and paid to creditors and shareholders. It can be classified as
a. Cash flow from operations.
b. Cash flow from changes in fixed assets.
c. Cash flow from changes in working capital.
2. Calculations of cash flow are not difficult, but they require care and particular attention to detail in prop-
erly accounting for noncash expenses such as depreciation and deferred taxes. It is especially important
that you do not confuse cash flow with changes in net working capital and net income.
1. Liquidity What does liquidity measure? Explain the trade-off a firm faces between high liquidity and
low liquidity levels.
2. Accounting and Cash Flows Why is it that the revenue and cost figures shown on a standard income
statement may not be representative of the actual cash inflows and outflows that occurred during the
period?
3. Accounting Statement of Cash Flows Looking at the accounting statement of cash flows, what does
the bottom-line number mean? How useful is this number for analyzing a company?
4. Cash Flows How do financial cash flows and the accounting statement of cash flows differ? Which is
more useful when analyzing a company?
CONCEPT QUESTIONS
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PART 1 Overview34
5. Book Values versus Market Values Under standard accounting rules, it is possible for a company’s
liabilities to exceed its assets. When this occurs, the owners’ equity is negative. Can this happen with
market values? Why or why not?
6. Cash Flow from Assets Suppose a company’s cash flow from assets was negative for a particular
period. Is this necessarily a good sign or a bad sign?
7. Operating Cash Flow Suppose a company’s operating cash flow was negative for several years
running. Is this necessarily a good sign or a bad sign?
8. Net Working Capital and Capital Spending Could a company’s change in net working capital
be negative in a given year? (Hint: Yes.) Explain how this might come about. What about net capital
spending?
9. Cash Flow to Stockholders and Creditors Could a company’s cash flow to stockholders be negative
in a given year? (Hint: Yes.) Explain how this might come about. What about cash flow to creditors?
10. Firm Values Referring back to the Microsoft example used at the beginning of the chapter, note that
we suggested that Microsoft’s stockholders probably didn’t suffer as a result of the reported loss. What
do you think was the basis for our conclusion?
QUESTIONS AND PROBLEMS
1. Building a Balance Sheet Burnett, Inc., has current assets of $6,800, net fixed assets of $29,400,
current liabilities of $5,400, and long-term debt of $13,100. What is the value of the shareholders’
equity account for this firm? How much is net working capital?
2. Building an Income Statement Bradds, Inc., has sales of $528,600, costs of $264,400, depreciation
expense of $41,700, interest expense of $20,700, and a tax rate of 35 percent. What is the net income
for the firm? Suppose the company paid out $27,000 in cash dividends. What is the addition to retained
earnings?
3. Market Values and Book Values Klingon Cruisers, Inc., purchased new cloaking machinery three
years ago for $7 million. The machinery can be sold to the Romulans today for $5.3 million. Klingon’s
current balance sheet shows net fixed assets of $3.9 million, current liabilities of $1.075 million, and
net working capital of $320,000. If all the current accounts were liquidated today, the company would
receive $410,000 cash. What is the book value of Klingon’s total assets today? What is the sum of the
market value of NWC and market value of assets?
4. Calculating Taxes The Alexander Co. had $328,500 in taxable income. Using the rates from Table 2.3
in the chapter, calculate the company’s income taxes. What is the average tax rate? What is the marginal
tax rate?
5. Calculating OCF Timsung, Inc., has sales of $30,700, costs of $11,100, depreciation expense of $2,100,
and interest expense of $1,140. If the tax rate is 40 percent, what is the operating cash flow, or OCF?
6. Calculating Net Capital Spending Busch Driving School’s 2016 balance sheet showed net fixed assets
of $3.75 million, and the 2017 balance sheet showed net fixed assets of $4.45 million. The company’s
2017 income statement showed a depreciation expense of $395,000. What was the company’s net
capital spending for 2017?
7. Building a Balance Sheet The following table presents the long-term liabilities and stockholders’
equity of Information Control Corp. one year ago:
Basic
(Questions 1–10)
Long-term debt
Preferred stock
Common stock ($1 par value)
Capital surplus
Accumulated retained earnings
$37,000,000
2,100,000
8,900,000
41,000,000
75,300,000
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CHAPTER 2 Financial Statements and Cash Flow 35
During the past year, the company issued 4 million shares of new stock at a total price of $26 million,
and issued $9.5 million in new long-term debt. The company generated $15.3 million in net income
and paid $3.1 million in dividends. Construct the current balance sheet reflecting the changes that
occurred on the company’s balance sheet during the year.
8. Cash Flow to Creditors The 2016 balance sheet of Maria’s Tennis Shop, Inc., showed long-term debt
of $2.4 million, and the 2017 balance sheet showed long-term debt of $2.53 million. The 2017 income
statement showed an interest expense of $187,000. What was the firm’s cash flow to creditors during 2017?
9. Cash Flow to Stockholders The 2016 balance sheet of Maria’s Tennis Shop, Inc., showed $540,000 in
the common stock account and $5.6 million in the additional paid-in surplus account. The 2017 balance
sheet showed $595,000 and $6.18 million in the same two accounts, respectively. If the company paid
out $270,000 in cash dividends during 2017, what was the cash flow to stockholders for the year?
10. Calculating Total Cash Flows Given the information for Maria’s Tennis Shop, Inc., in the previous two
problems, suppose you also know that the firm’s net capital spending for 2017 was $640,000, and that
the firm reduced its net working capital investment by $65,000. What was the firm’s 2017 operating
cash flow, or OCF?
11. Cash Flows Ritter Corporation’s accountants prepared the following financial statements for year-ends. Intermediate
(Questions 11–25)
RITTER CORPORATION
Income Statement
2017
Revenue
Expenses
Depreciation
EBT
Tax
Net income
Dividends
$1,068
745
77
$ 246
98
$ 148
$ 40
RITTER CORPORATION
Balance Sheets
December 31
2016 2017
Assets
Cash
Other current assets
Net fixed assets
Total assets
Liabilities and Equity
Accounts payable
Long-term debt
Stockholders’ equity
Total liabilities and equity
$ 81
253
690
$1,024
$ 295
0
729
$1,024
$ 93
265
824
$1,182
$ 301
44
837
$1,182
a. Explain the change in cash during the year 2017.
b. Determine the change in net working capital in 2017.
c. Determine the cash flow generated by the firm’s assets during the year 2017.
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PART 1 Overview36
12. Cash Flow Identity Freeman, Inc., reported the following financial statements for the last two years.
Construct the cash flow identity for the company. Explain what each number means.
FREEMAN, INC.
Balance Sheet as of December 31, 2017
Cash
Accounts receivable
Inventory
Current assets
Net fixed assets
Total assets
$ 18,143
19,527
28,614
$ 66,284
$498,312
$564,596
Accounts payable
Long-term debt
Owners’ equity
Total liabilities and
owners’ equity
$ 32,978
$179,400
$352,218
$564,596
FREEMAN, INC.
2017 Income Statement
Sales
Cost of goods sold
Selling & administrative
Depreciation
EBIT
Interest
EBT
Taxes
Net income
Dividends
Addition to retained earnings
$703,100
329,413
153,405
66,513
$153,769
23,280
$130,489
45,671
$ 84,818
15,200
$ 69,618
FREEMAN, INC.
Balance Sheet as of December 31, 2016
Cash
Accounts receivable
Inventory
Current assets
Net fixed assets
Total assets
$ 16,302
16,849
23,875
57,026
415,289
$472,315
Accounts payable
Long-term debt
Owners’ equity
Total liabilities and
owners’ equity
$ 29,342
165,300
277,673
$472,315
13. Financial Cash Flows The Stancil Corporation provided the following current information:
Proceeds from long-term borrowing
Proceeds from the sale of common stock
Purchases of fixed assets
Purchases of inventories
Payment of dividends
$16,500
2,700
19,200
2,700
7,100
Determine the cash flows from the firm and the cash flows to investors of the firm.
14. Building an Income Statement During the year, the Senbet Discount Tire Company had gross sales
of $757,000. The company’s cost of goods sold and selling expenses were $249,800 and $146,000,
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CHAPTER 2 Financial Statements and Cash Flow 37
respectively. The company also had debt of $675,000, which carried an interest rate of 6 percent.
Depreciation was $87,000. The tax rate was 35 percent.
a. What was the company’s net income?
b. What was the company’s operating cash flow?
15. Calculating Total Cash Flows Schwert Corp. shows the following information on its 2017 income
statement: sales = $225,000; costs = $103,200; other expenses = $6,100; depreciation expense =
$15,300; interest expense = $11,200; taxes = $31,227; dividends = $18,100. In addition, you’re
told that the firm issued $6,000 in new equity during 2017, and redeemed $8,500 in outstanding
long-term debt.
a. What was the 2017 operating cash flow?
b. What was the 2017 cash flow to creditors?
c. What was the 2017 cash flow to stockholders?
d. If net fixed assets increased by $33,000 during the year, what was the addition to net working
capital?
16. Using Income Statements Given the following information for O’Hara Marine Co., calculate the
depreciation expense: sales = $57,900; costs = $28,600; addition to retained earnings = $8,100;
dividends paid = $5,200; interest expense = $2,050; tax rate = 35 percent.
17. Preparing a Balance Sheet Prepare a 2017 balance sheet for Jarrow Corp. based on the following
information: cash = $168,000; patents and copyrights = $827,000; accounts payable = $429,000;
accounts receivable = $237,000; tangible net fixed assets = $3,410,000; inventory = $385,000;
notes payable = $171,000; accumulated retained earnings = $2,084,000; long-term debt =
$1,985,000.
18. Residual Claims Huang, Inc., is obligated to pay its creditors $11,600 very soon.
a. What is the market value of the shareholders’ equity if assets have a market value of $15,100?
b. What if assets equal $9,900?
19. Marginal versus Average Tax Rates (Refer to Table 2.3.) Corporation Growth has $79,500 in taxable
income, and Corporation Income has $7,950,000 in taxable income.
a. What is the tax bill for each firm?
b. Suppose both firms have identified a new project that will increase taxable income by $10,000.
How much in additional taxes will each firm pay? Why is this amount the same?
20. Net Income and OCF During 2017, Raines Umbrella Corp. had sales of $809,000. Cost of goods
sold, administrative and selling expenses, and depreciation expenses were $549,000, $136,000, and
$85,000, respectively. In addition, the company had an interest expense of $67,000 and a tax rate of
35 percent. (Ignore any tax loss carryback or carryforward provisions.)
a. What was the company’s net income for 2017?
b. What was its operating cash flow?
c. Explain your results in (a) and (b).
21. Accounting Values versus Cash Flows In the previous problem, suppose Raines Umbrella Corp. paid
out $75,000 in cash dividends. Is this possible? If net capital spending and the change in net working
capital were both zero, and if no new stock was issued during the year, what was the change in the
firm’s long-term debt account?
22. Calculating Cash Flows Blue Diamond Industries had the following operating results for 2017;
sales = $44,600; cost of goods sold = $27,500; depreciation expense = $4,630; interest expense
= $1,050; dividends paid = $2,275. At the beginning of the year, net fixed assets were $27,510,
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PART 1 Overview38
current assets were $6,840, and current liabilities were $4,580. At the end of the year, net fixed
assets were $35,610, current assets were $7,720, and current liabilities were $4,830. The tax rate
was 40 percent.
a. What was net income for 2017?
b. What was the operating cash flow for 2017?
c. What was the cash flow from assets for 2017? Is this possible? Explain.
d. If no new debt was issued during the year, what was the cash flow to creditors? What was the cash
flow to stockholders? Explain and interpret the positive and negative signs of your answers in (a)
through (d).
23. Calculating Cash Flows Consider the following abbreviated financial statements for Weston
Enterprises:
a. What was owners’ equity for 2016 and 2017?
b. What was the change in net working capital for 2017?
c. In 2017, the company purchased $2,740 in new fixed assets. How much in fixed assets
did the company sell? What was the cash flow from assets for the year? The tax rate is
35 percent.
d. During 2017, the company raised $634 in new long-term debt. How much long-term debt must the
company have paid off during the year? What was the cash flow to creditors?
Use the following information for Ingersoll, Inc., for Problems 24 and 25 (assume the tax rate is
35 percent):
WESTON ENTERPRISES
2017 Income Statement
Sales
Costs
Depreciation
Interest paid
$15,690
3,739
1,339
562
WESTON ENTERPRISES
2016 and 2017 Part ia l Balance Sheets
Assets L iabi l i t ies and Owners’ Equi ty
Current assets
Net fixed assets
2016
$1,066
5,184
2017
$1,145
5,472
Current liabilities
Long-term debt
2016
$ 475
2,880
2017
$ 518
3,090
2016 2017
Sales
Depreciation
Cost of goods sold
Other expenses
Interest
Cash
Accounts receivable
Long-term debt
Net fixed assets
Accounts payable
Inventory
Dividends
$ 40,743
5,853
14,020
3,322
2,098
21,364
28,283
71,550
179,166
27,349
50,287
4,966
$ 43,277
5,858
15,912
2,776
3,142
21,856
31,864
83,476
183,440
25,639
51,675
5,468
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CHAPTER 2 Financial Statements and Cash Flow 39
24. Financial Statements Draw up an income statement and balance sheet for this company for 2016
and 2017.
25. Calculating Cash Flow For 2017, calculate the cash flow from assets, cash flow to creditors, and
cash flow to stockholders.
26. Cash Flows You are researching Time Manufacturing and have found the following accounting
statement of cash flows for the most recent year. You also know that the company paid $185 million in
current taxes and had an interest expense of $96 million. Use the accounting statement of cash flows
to construct the financial statement of cash flows.
Challenge
(Questions 26–28)
TIME MANUFACTURING
Statement of Cash F lows
( in $ mi l l ions)
Operations
Net income
Depreciation
Deferred taxes
Changes in current assets and liabilities
Accounts receivable
Inventories
Accounts payable
Accrued expenses
Other
Total cash flow from operations
Investing activities
Acquisition of fixed assets
Sale of fixed assets
Total cash flow from investing activities
Financing activities
Retirement of long-term debt
Proceeds from long-term debt sales
Dividends
Repurchase of stock
Proceeds from new stock issue
Total cash flow from financing activities
Change in cash (on balance sheet)
$321
177
34
– 52
41
33
– 17
4
$541
–$332
42
–$290
–$195
105
– 158
– 26
50
–$224
$ 27
27. Net Fixed Assets and Depreciation On the balance sheet, the net fixed assets (NFA) account is equal
to the gross fixed assets (FA) account, which records the acquisition cost of fixed assets, minus the
accumulated depreciation (AD) account, which records the total depreciation taken by the firm against
its fixed assets. Using the fact that NFA = FA – AD, show that the expression given in the chapter for
net capital spending, NFAend – NFAbeg + D (where D is the depreciation expense during the year), is
equivalent to FAend – FAbeg.
28. Tax Rates Refer to the corporate marginal tax rate information in Table 2.3.
a. Why do you think the marginal tax rate jumps up from 34 percent to 39 percent at a taxable
income of $100,001, and then falls back to a 34 percent marginal rate at a taxable income of
$335,001?
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PART 1 Overview40
b. Compute the average tax rate for a corporation with exactly $335,001 in taxable income. Does this
confirm your explanation in part (a)? What is the average tax rate for a corporation with income of
exactly $18,333,334? Is the same thing happening here?
c. The 39 percent and 38 percent tax rates both represent what is called a tax “bubble.” Suppose
the government wanted to lower the upper threshold of the 39 percent marginal tax bracket from
$335,000 to $200,000. What would the new 39 percent bubble rate have to be?
WHAT’S ON THE WEB?
1. Change in Net Working Capital Find the most recent abbreviated balance sheets for General
Dynamics at finance.yahoo.com. Enter the ticker symbol “GD” and follow the “Balance Sheet” link. Using
the two most recent balance sheets, calculate the change in net working capital. What does this number
mean?
2. Book Values versus Market Values The home page for The Coca-Cola Company can be found at
www.coca-cola.com. Locate the most recent annual report, which contains a balance sheet for the
company. What is the book value of equity for Coca-Cola? The market value of a company is the number
of shares of stock outstanding times the price per share. This information can be found at finance.yahoo.
com using the ticker symbol for Coca-Cola (KO). What is the market value of equity? Which number is
more relevant for shareholders?
3. Cash Flows to Stockholders and Creditors Cooper Tire and Rubber Company provides financial
information for investors on its website at www.coopertire.com. Follow the “Investors” link and find the
most recent annual report. Using the consolidated statements of cash flows, calculate the cash flow to
stockholders and the cash flow to creditors.
EXCEL MASTER IT ! PROBLEM
Using Excel to find the marginal tax rate can be accomplished with the VLOOKUP function. However, calculat-
ing the total tax bill is a little more difficult. Below we have shown a copy of the IRS tax table for an individual
from a recent year. Often, tax tables are presented in this format.
IF TAXABLE INCOME
IS OVER: BUT NOT OVER: THE TAX IS :
$ 0
9,275
37,650
91,150
190,150
413,350
415,050
$ 9,275
37,650
91,150
190,150
413,350
415,050
10% of the amount over $0
$927.50 plus 15% of the amount over $9,275
$5,183.75 plus 25% of the amount over $37,650
$18,558.75 plus 28% of the amount over $91,150
$46,278.75 plus 33% of the amount over $190,150
$119,934.75 plus 35% of the amount over $413,350
$120,529.75 plus 39.6% of the amount over $415,050
In reading this table, the marginal tax rate for taxable income less than $9,275 is 10 percent. If the taxable
income is between $9,275 and $37,650, the tax bill is $927.50 plus the marginal taxes. The marginal taxes are
calculated as the taxable income minus $9,275 times the marginal tax rate of 15 percent.
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CASH FLOWS AT EAST COAST YACHTS
Because of the dramatic growth at East Coast
Yachts, Larissa decided that the company should
be reorganized as a corporation (see our Chapter
1 Closing Case for more detail). Time has passed
and, today, the company is publicly traded under
the ticker symbol “ECY”.
Dan Ervin was recently hired by East Coast
Yachts to assist the company with its short-term
financial planning and also to evaluate the com-
pany’s financial performance. Dan graduated
from college five years ago with a finance degree,
and he has been employed in the treasury depart-
ment of a Fortune 500 company since then.
The company’s past growth has been some-
what hectic, in part due to poor planning. In antic-
ipation of future growth, Larissa has asked Dan
to analyze the company’s cash flows. The company’s financial statements are prepared by an outside auditor.
Nearby you will find the most recent income statement and the balance sheets for the past two years.
Larissa has also provided the following information. During the year, the company raised $40 million
in new long-term debt and retired $22.6 million in long-term debt. The company also sold $24.2 million in
new stock and repurchased $35.64 million. The company purchased $59.5 million in fixed assets, and sold
$6,718,200 in fixed assets.
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CHAPTER 2 Financial Statements and Cash Flow 41
Below, we have the corporate tax table as shown in Table 2.3.
IF TAXABLE INCOME IS
GREATER THAN OR EQUAL TO: BUT LESS THAN: THE TAX RATE IS :
$ 0
50,001
75,001
100,001
335,001
10,000,001
15,000,001
18,333,334
$ 50,000
75,000
100,000
335,000
10,000,000
15,000,000
18,333,333
15%
25
34
39
34
35
38
35
a. Create a tax table in Excel for corporate taxes similar to the individual tax table shown above. Your
spreadsheet should then calculate the marginal tax rate, the average tax rate, and the tax bill for any
level of taxable income input by a user.
b. For a taxable income of $1,350,000, what is the marginal tax rate?
c. For a taxable income of $1,350,000, what is the total tax bill?
d. For a taxable income of $1,350,000, what is the average tax rate?
CLOSING CASE
EAST COAST YACHTS
2017 Income Statement
Sales
Cost of goods sold
Selling, general, and administrative
Depreciation
EBIT
Interest expense
EBT
Taxes
Net income
Dividends
Retained earnings
$611,582,000
431,006,000
73,085,700
19,958,400
$ 87,531,900
11,000,900
$ 76,531,000
30,612,400
$ 45,918,600
17,374,500
$ 28,544,100
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Larissa has asked Dan to prepare the financial statement of cash flows and the accounting statement of
cash flows. She has also asked you to answer the following questions:
1. How would you describe East Coast Yachts’ cash flows?
2. Which cash flows statement more accurately describes the cash flows at the company?
3. In light of your previous answers, comment on Larissa’s expansion plans.
EAST COAST YACHTS
Balance Sheet
2016 2017 2016 2017
Current assets
Cash and equivalents
Accounts receivable
Inventories
Other
Total current assets
Fixed assets
Property, plant, and equipment
Less accumulated depreciation
Net property, plant, and equipment
Intangible assets and others
Total fixed assets
Total assets
$ 10,644,500
18,924,800
17,090,100
1,097,700
$ 47,757,100
$404,727,800
(93,887,500)
$310,840,300
6,772,000
$317,612,300
$365,369,400
$ 11,119,700
18,681,500
20,149,650
1,172,200
$ 51,123,050
$457,509,600
(113,845,900)
$343,663,700
6,772,000
$350,435,700
$ 401,558,750
Current liabilities
Accounts payable
Accrued expenses
Total current liabilities
Long-term debt
Total long-term liabilities
Stockholders’ equity
Preferred stock
Common stock
Capital surplus
Accumulated retained earnings
Less treasury stock
Total equity
Total liabilities and
shareholders’ equity
$ 43,482,200
5,417,300
$ 48,899,500
$151,860,000
$151,860,000
$ 1,970,000
29,700,000
11,800,000
133,019,900
(11,880,000)
$164,609,900
$365,369,400
$ 44,461,550
6,123,200
$ 50,584,750
$169,260,000
$169,260,000
$ 1,970,000
37,583,700
28,116,300
161,564,000
(47,520,000)
$181,714,000
$401,558,750
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PART 1 Overview42
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CHAPTER 3 Financial Statements Analysis and Financial Models 43
The price of a share of common stock in expensive groceries retailer Whole Foods closed at
about $29 on February 5, 2015. At that price, Whole Foods had a price−earnings (PE) ratio
of 20. That is, investors were willing to pay $20 for every dollar in income earned by Whole
Foods. At the same time, investors were willing to pay $10, $12, and $402 for each dollar
earned by Ford, Cisco Systems, and Amazon.com, respectively. At the other extreme were
General Electric (GE) and Anadarko Petroleum. Each had negative earnings for the previous
year, yet GE was priced at about $29 per share and Anadarko Petroleum at about $41 per
share. Because they had negative earnings, their PE ratios would have been negative, so
they were not reported. At the time, the typical stock in the S&P 500 Index of large-company
stocks was trading at a PE of about 17, or about 17 times earnings, as they say on Wall Street.
Price-to-earnings comparisons are examples of the use of financial ratios. As we will see
in this chapter, there are a wide variety of financial ratios, all designed to summarize spe-
cific aspects of a firm’s financial position. In addition to discussing how to analyze financial
statements and compute financial ratios, we will have quite a bit to say about who uses this
information and why.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
OPENING
CASE
Financial Statements Analysis
and Financial Models
3
3.1 FINANCIAL STATEMENTS ANALYSIS
In Chapter 2, we discussed some of the essential concepts of financial statements and
cash flows. This chapter continues where our earlier discussion left off. Our goal here is
to expand your understanding of the uses (and abuses) of financial statement information.
A good working knowledge of financial statements is desirable because such statements,
and numbers derived from those statements, are the primary means of communicating
financial information both within the firm and outside the firm. In short, much of the lan-
guage of business finance is rooted in the ideas we discuss in this chapter.
Clearly, one important goal of the accountant is to report financial information to the
user in a form useful for decision making. Ironically, the information frequently does not
come to the user in such a form. In other words, financial statements don’t come with a
user’s guide. This chapter is a first step in filling this gap.
Standardizing Statements
One obvious thing we might want to do with a company’s financial statements is to
compare them to those of other, similar companies. We would immediately have a prob-
lem, however. It’s almost impossible to directly compare the financial statements for two
companies because of differences in size.
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44
For example, Tesla and GM are obviously serious rivals in the auto market, but GM
is larger, so it is difficult to compare them directly. For that matter, it’s difficult even to
compare financial statements from different points in time for the same company if the
company’s size has changed. The size problem is compounded if we try to compare GM
and, say, Toyota. If Toyota’s financial statements are denominated in yen, then we have
size and currency differences.
To start making comparisons, one obvious thing we might try to do is to somehow
standardize the financial statements. One common and useful way of doing this is to work
with percentages instead of total dollars. The resulting financial statements are called
common-size statements. We consider these next.
Common-Size Balance Sheets
For easy reference, Prufrock Corporation’s 2016 and 2017 balance sheets are provided in
Table 3.1. Using these, we construct common-size balance sheets by expressing each item
as a percentage of total assets. Prufrock’s 2016 and 2017 common-size balance sheets are
shown in Table 3.2.
Notice that some of the totals don’t check exactly because of rounding errors. Also
notice that the total change has to be zero because the beginning and ending numbers must
add up to 100 percent.
In this form, financial statements are relatively easy to read and compare. For exam-
ple, just looking at the two balance sheets for Prufrock, we see that current assets were
19.7 percent of total assets in 2017, up from 19.0 percent in 2016. Current liabilities
declined from 16.1 percent to 15.1 percent of total liabilities and equity over that same time.
Similarly, total equity rose from 68.2 percent of total liabilities and equity to 72.2 percent.
Overall, Prufrock’s liquidity, as measured by current assets compared to current liabilities,
increased over the year. Simultaneously, Prufrock’s indebtedness diminished as a percentage
of total assets. We might be tempted to conclude that the balance sheet has grown “stronger.”
PRUFROCK CORPORATION
Balance Sheets as of December 31 , 2016 and 2017
($ in mi l l ions)
Assets
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
2016
$ 84
165
393
$ 642
$ 2,731
$ 3,373
2017
$ 98
188
422
$ 708
$ 2,880
$ 3,588
Liabilities and Owners’ Equity
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Retained earnings
Total
Total liabilities and owners’ equity
$ 312
231
$ 543
$ 531
$ 500
1,799
$ 2,299
$ 3,373
$ 344
196
$ 540
$ 457
$ 550
2,041
$ 2,591
$ 3,588
TABLE 3.1
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CHAPTER 3 Financial Statements Analysis and Financial Models 45
ros89907_ch03_043-082.indd 45 12/06/16 06:41 PM
Common-Size Income Statements
Table 3.3 describes some commonly used measures of earnings. A useful way of standard-
izing the income statement shown in Table 3.4 is to express each item as a percentage of
total sales, as illustrated for Prufrock in Table 3.5.
Investors and analysts look closely at the income statement for clues on how well a company has performed during
a particular year. Here are some commonly used measures of earnings (numbers in millions).
Net Income The so-called bottom line, defined as total revenue minus total expenses. Net income for
Prufrock in the latest period is $363 million. Net income reflects differences in a firm’s capital
structure and taxes as well as operating income. Interest expense and taxes are subtracted
from operating income in computing net income. Shareholders look closely at net income
because dividend payout and retained earnings are closely linked to net income.
EPS Net income divided by the number of shares outstanding. It expresses net income on a per-share
basis. For Prufrock, the EPS = (Net income)/(Shares outstanding) = $363/33 = $11.
EBIT Earnings before interest expense and taxes. EBIT is usually called “income from operations”
on the income statement and is income before unusual items, discontinued operations, or
extraordinary items. To calculate EBIT, operating expenses are subtracted from total opera-
tions revenues. Analysts like EBIT because it abstracts from differences in earnings from a
firm’s capital structure (interest expense) and taxes. For Prufrock, EBIT is $691 million.
EBITDA Earnings before interest expense, taxes, depreciation, and amortization. EBITDA = EBIT +
depreciation and amortization. Here amortization refers to a noncash expense similar to depre-
ciation except it applies to an intangible asset (such as a patent), rather than a tangible asset
(such as a machine). The word amortization here does not refer to the payment of debt. There
is no amortization in Prufrock’s income statement. For Prufrock, EBITDA = $691 + 276 = $967
million. Analysts like to use EBITDA because it adds back two noncash items (depreciation and
amortization) to EBIT and thus is a better measure of before-tax operating cash flow.
Sometimes these measures of earnings are preceded by the letters LTM, meaning the last twelve months. For
example, LTM EPS is the last 12 months of EPS and LTM EBITDA is the last 12 months of EBITDA. At other times,
the letters TTM are used, meaning trailing 12 months. Needless to say, LTM is the same as TTM.
TABLE 3.3
Measures of Earnings
PRUFROCK CORPORATION
Common-Size Balance Sheets
December 31, 2016 and 2017
Assets
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
2016
2.5%
4.9
11.7
19.0
81.0
100.0%
2017
2.7%
5.2
11.8
19.7
80.3
100.0%
Change
+ .2%
+ .3
+ .1
+ .7
− .7
.0%
Liabilities and Owners’ Equity
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Retained earnings
Total
Total liabilities and owners’ equity
9.2%
6.8
16.1
15.7
14.8
53.3
68.2
100.0%
9.6%
5.5
15.1
12.7
15.3
56.9
72.2
100.0%
+ .3%
−1.4
−1.0
−3.0
+ .5
+3.5
+4.1
.0%
TABLE 3.2
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46
PRUFROCK CORPORATION
2017 Income Statement
($ in mi l l ions)
Sales
Cost of goods sold
Depreciation
Earnings before interest and taxes
Interest paid
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings
$121
242
$2,311
1,344
276
$ 691
141
$ 550
187
$ 363
TABLE 3.4
PRUFROCK CORPORATION
Common-Size Income Statement 2017
Sales
Cost of goods sold
Depreciation
Earnings before interest and taxes
Interest paid
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings
5.2%
10.5
100.0%
58.2
11.9
29.9
6.1
23.8
8.1
15.7%
TABLE 3.5
This income statement tells us what happens to each dollar in sales. For Prufrock, inter-
est expense eats up $.061 out of every sales dollar, and taxes take another $.081. When all
is said and done, $.157 of each dollar flows through to the bottom line (net income), and
that amount is split into $.105 retained in the business and $.052 paid out in dividends.
These percentages are useful in comparisons. For example, a relevant figure is the cost
percentage. For Prufrock, $.582 of each $1.00 in sales goes to pay for goods sold. It would
be interesting to compute the same percentage for Prufrock’s main competitors to see how
Prufrock stacks up in terms of cost control.
3.2 RATIO ANALYSIS
Another way of avoiding the problems involved in comparing companies of different sizes
is to calculate and compare financial ratios. Such ratios are ways of comparing and inves-
tigating the relationships between different pieces of financial information. We cover some
of the more common ratios next (there are many others we don’t discuss here).
One problem with ratios is that different people and different sources frequently don’t
compute them in exactly the same way, and this leads to much confusion. The specific
definitions we use here may or may not be the same as ones you have seen or will see else-
where. If you are using ratios as tools for analysis, you should be careful to document how
you calculate each one; and, if you are comparing your numbers to those of another source,
be sure you know how their numbers are computed.
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CHAPTER 3 Financial Statements Analysis and Financial Models 47
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We will defer much of our discussion of how ratios are used and some problems that
come up with using them until later in the chapter. For now, for each ratio we discuss, sev-
eral questions come to mind:
1. How is it computed?
2. What is it intended to measure, and why might we be interested?
3. What is the unit of measurement?
4. What might a high or low value be telling us? How might such values be
misleading?
5. How could this measure be improved?
Financial ratios are traditionally grouped into the following categories:
1. Short-term solvency, or liquidity, ratios.
2. Long-term solvency, or financial leverage, ratios.
3. Asset management, or turnover, ratios.
4. Profitability ratios.
5. Market value ratios.
We will consider each of these in turn. In calculating these numbers for Prufrock, we will
use the ending balance sheet (2017) figures unless we explicitly say otherwise.
Short-Term Solvency or Liquidity Measures
As the name suggests, short-term solvency ratios as a group are intended to provide infor-
mation about a firm’s liquidity, and these ratios are sometimes called liquidity measures.
The primary concern is the firm’s ability to pay its bills over the short run without undue
stress. Consequently, these ratios focus on current assets and current liabilities.
For obvious reasons, liquidity ratios are particularly interesting to short-term creditors.
Because financial managers are constantly working with banks and other short-term lend-
ers, an understanding of these ratios is essential.
One advantage of looking at current assets and liabilities is that their book values and
market values are likely to be similar. Often (though not always), these assets and liabilities
just don’t live long enough for the two to get seriously out of step. On the other hand, like
any type of near-cash, current assets and liabilities can and do change fairly rapidly, so
today’s amounts may not be a reliable guide to the future.
CURRENT RATIO One of the best-known and most widely used ratios is the current ratio.
As you might guess, the current ratio is defined as
Current ratio = Current assets _______________
Current liabilities
[3.1]
For Prufrock, the 2017 current ratio is
Current ratio = $708 _____
$540
= 1.31 times
Because current assets and liabilities are, in principle, converted to cash over the follow-
ing 12 months, the current ratio is a measure of short-term liquidity. The unit of measurement
is either dollars or times. So, we could say Prufrock has $1.31 in current assets for every $1 in
current liabilities, or we could say Prufrock has its current liabilities covered 1.31 times over.
To a creditor, particularly a short-term creditor such as a supplier, the higher the cur-
rent ratio, the better. To the firm, a high current ratio indicates liquidity, but it also may
indicate an inefficient use of cash and other short-term assets. Absent some extraordinary
Go to www.reuters.com/
finance/stocks and find
the “Financials” link to
examine comparative
ratios for a huge number
of companies.
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48
circumstances, we would expect to see a current ratio of at least 1; a current ratio of less
than 1 would mean that net working capital (current assets less current liabilities) is nega-
tive. This would be unusual in a healthy firm, at least for most types of businesses.
The current ratio, like any ratio, is affected by various types of transactions. For exam-
ple, suppose the firm borrows over the long term to raise money. The short-run effect
would be an increase in cash from the issue proceeds and an increase in long-term debt.
Current liabilities would not be affected, so the current ratio would rise.
E
X
A
M
P
L
E
3
.1
Suppose a firm were to pay off some of its suppliers and short-term creditors. What would happen to the
current ratio? Suppose a firm buys some inventory. What happens in this case? What happens if a firm
sells some merchandise?
The first case is a trick question. What happens is that the current ratio moves away from 1. If it is
greater than 1 (the usual case), it will get bigger, but if it is less than 1, it will get smaller. To see this,
suppose the firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. If we use
$1 in cash to reduce current liabilities, the new current ratio is ($4 − 1)/($2 − 1) = 3. If we reverse the
original situation to $2 in current assets and $4 in current liabilities, the change will cause the current
ratio to fall to 1/3 from 1/2.
The second case is not quite as tricky. Nothing happens to the current ratio because cash goes down
while inventory goes up—total current assets are unaffected.
In the third case, the current ratio would usually rise because inventory is normally shown at cost and
the sale would normally be at something greater than cost (the difference is the markup). The increase
in either cash or receivables is therefore greater than the decrease in inventory. This increases current
assets, and the current ratio rises.
Current Events
Finally, note that an apparently low current ratio may not be a bad sign for a company
with a large reserve of untapped borrowing power.
QUICK (OR ACID-TEST) RATIO Inventory is often the least liquid current asset. It’s also the
one for which the book values are least reliable as measures of market value because the
quality of the inventory isn’t considered. Some of the inventory may later turn out to be
damaged, obsolete, or lost.
More to the point, relatively large inventories are often a sign of short-term trouble. The
firm may have overestimated sales and overbought or overproduced as a result. In this case,
the firm may have a substantial portion of its liquidity tied up in slow-moving inventory.
To further evaluate liquidity, the quick, or acid-test, ratio is computed just like the cur-
rent ratio, except inventory is omitted:
Quick ratio = Current assets − Inventory _____________________
Current liabilities
[3.2]
Notice that using cash to buy inventory does not affect the current ratio, but it reduces the
quick ratio. Again, the idea is that inventory is relatively illiquid compared to cash. For
Prufrock, this ratio in 2017 was
Quick ratio = $708 − 422 _________
$540
= .53 times
The quick ratio here tells a somewhat different story than the current ratio because inven-
tory accounts for more than half of Prufrock’s current assets. To exaggerate the point, if
this inventory consisted of, say, unsold nuclear power plants, then this would be a cause
for concern.
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CHAPTER 3 Financial Statements Analysis and Financial Models 49
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To give an example of current versus quick ratios, based on recent financial statements,
Walmart and Manpower, Inc., had current ratios of .93 and 1.47, respectively. However,
Manpower carries no inventory to speak of, whereas Walmart’s current assets are virtually
all inventory. As a result, Walmart’s quick ratio was only .20, and Manpower’s was 1.47,
the same as its current ratio.
CASH RATIO A very short-term creditor might be interested in the cash ratio:
Cash ratio = Cash _______________
Current liabilities
[3.3]
You can verify that this works out to be .18 times for Prufrock.
Long-Term Solvency Measures
Long-term solvency ratios are intended to address the firm’s long-run ability to meet its
obligations or, more generally, its financial leverage. These ratios are sometimes called
financial leverage ratios or just leverage ratios. We consider three commonly used mea-
sures and some variations.
TOTAL DEBT RATIO The total debt ratio takes into account all debts of all maturities to all
creditors. It can be defined in several ways, the easiest of which is this:
Total debt ratio = Total assets − Total equity ______________________
Total assets
[3.4]
= $3,588 − 2,591 _____________
$3,588
= .28 times
In this case, an analyst might say that Prufrock uses 28 percent debt.1 Whether this is high
or low or whether it even makes any difference depends on whether capital structure mat-
ters, a subject we discuss in a later chapter.
Prufrock has $.28 in debt for every $1 in assets. Therefore, there is $.72 in equity
(= $1 − .28) for every $.28 in debt. With this in mind, we can define two useful variations
on the total debt ratio, the debt−equity ratio and the equity multiplier:
Debt–equity ratio = Total debt∕Total equity [3.5]
= $28∕$.72 = .39 times
Equity multiplier = Total assets∕Total equity [3.6]
= $1∕$.72 = 1.39 times
The fact that the equity multiplier is 1 plus the debt−equity ratio is not a coincidence:
Equity multiplier = Total assets/Total equity = $1/$.72 = 1.39 times
= (Total equity + Total debt)/Total equity
= 1 + Debt–equity ratio = 1.39 times
The thing to notice here is that given any one of these three ratios, you can immediately
calculate the other two, so they all say exactly the same thing.
The online Women’s
Business Center has
more information about
financial statements,
ratios, and small busi-
ness topics at www.sba.
gov/content/womens-
business-resources.
1 Total equity here includes preferred stock, if there is any. An equivalent numerator in this ratio would be (Current liabilities + Long-term debt).
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50
TIMES INTEREST EARNED Another common measure of long-term solvency is the times
interest earned (TIE) ratio. Once again, there are several possible (and common) defini-
tions, but we’ll stick with the most traditional:
Times interest earned ratio = EBIT _______
Interest
[3.7]
= $691 _____
$141
= 4.90 times
As the name suggests, this ratio measures how well a company has its interest obligations
covered, and it is often called the interest coverage ratio. For Prufrock, the interest bill is
covered 4.9 times over.
CASH COVERAGE A problem with the TIE ratio is that it is based on EBIT, which is not
really a measure of cash available to pay interest. The reason is that depreciation and amor-
tization, noncash expenses, have been deducted out. Because interest is most definitely a
cash outflow (to creditors), one way to define the cash coverage ratio is
Cash coverage ratio = EBIT + (Depreciation and amortization) _______________________________
Interest
[3.8]
= $691 + 276 ___________
$141
= $967 _____
$141
= 6.86 times
The numerator here, EBIT plus depreciation and amortization, is often abbreviated EBITDA
(earnings before interest, taxes, depreciation, and amortization). It is a basic measure of the
firm’s ability to generate cash from operations, and it is frequently used as a measure of
cash flow available to meet financial obligations.
More recently another long-term solvency measure is increasingly seen in financial state-
ment analysis and in debt covenants. It uses EBITDA and interest bearing debt. Specifically,
for Prufrock:
Interest bearing debt _________________
EBITDA
= $196 million + 457 million _______________________
$967 million
= .68 times
Here we include notes payable (most likely notes payable is bank debt) and long-term debt in
the numerator and EBITDA in the denominator. Values below 1 on this ratio are considered
very strong and values above 5 are considered weak. However, a careful comparison with
other comparable firms is necessary to properly interpret the ratio.
Asset Management or Turnover Measures
We next turn our attention to the efficiency with which Prufrock uses its assets. The mea-
sures in this section are sometimes called asset management or utilization ratios. The spe-
cific ratios we discuss can all be interpreted as measures of turnover. What they are intended
to describe is how efficiently, or intensively, a firm uses its assets to generate sales. We first
look at two important current assets: inventory and receivables.
INVENTORY TURNOVER AND DAYS’ SALES IN INVENTORY During the year, Prufrock had a
cost of goods sold of $1,344. Inventory at the end of the year was $422. With these num-
bers, inventory turnover can be calculated as
Inventory turnover = Cost of goods sold ________________
Inventory
[3.9]
= $1,344 _______
$422
= 3.18 times
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In a sense, we sold off, or turned over, the entire inventory 3.18 times during the year. As
long as we are not running out of stock and thereby forgoing sales, the higher this ratio is,
the more efficiently we are managing inventory.
If we know that we turned our inventory over 3.18 times during the year, we can imme-
diately figure out how long it took us to turn it over on average. The result is the average
days’ sales in inventory:
Days’ sales in inventory = 365 days ________________
Inventory turnover
[3.10]
= 365 _____
3.18
= 114.61 days
This tells us that, roughly speaking, inventory sits about 115 days on average before it is
sold. Alternatively, assuming we used the most recent inventory and cost figures, it will
take about 115 days to work off our current inventory.
For example, in December 2015, General Motors had an 82-day supply of vehicles
in inventory, more than the 60-day supply considered normal. This figure means that at
the then-current rate of sales, it would have taken General Motors 82 days to deplete the
available supply, or, equivalently, that General Motors had 82 days of sales in inventory.
At the same time, Ford had a 59-day inventory supply and Toyota’s inventory level stood
at 45 days. Of course, we could also examine these numbers on a per-segment basis. For
example, there was only a 26-day inventory for compact trucks and an inventory period of
44 days for midrange luxury SUVs. At the other end, van and large car inventory levels
stood at 93 days and 98 days, respectively.
RECEIVABLES TURNOVER AND DAYS’ SALES IN RECEIVABLES Our inventory measures
give some indication of how fast we can sell products. We now look at how fast we col-
lect on those sales. The receivables turnover is defined in the same way as inventory
turnover:
Receivables turnover = Sales _________________
Accounts receivable
[3.11]
= $2,311 _______
$188
= 12.29 times
Loosely speaking, we collected our outstanding credit accounts and lent the money again
12.29 times during the year.2
This ratio makes more sense if we convert it to days, so the days’ sales in receivables is
Days’ sales in receivables = 365 days __________________
Receivables turnover
[3.12]
= 365 ______
12.29
= 29.69 days
Therefore, on average, we collect on our credit sales in about 30 days. For obvious reasons,
this ratio is frequently called the average collection period (ACP). Also note that if we are
using the most recent figures, we can also say that we have 30 days’ worth of sales currently
uncollected.
2 Here we have implicitly assumed that all sales are credit sales. If they were not, we would use total credit sales in these calculations, not
total sales. Also, in making this calculation, we use the value of accounts receivable at the end of the accounting period. A common alterna-
tive is to use the average value of accounts receivable over the accounting period. The important point is to be consistent in your method of
calculation over time and across firms.
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52
TOTAL ASSET TURNOVER Moving away from specific accounts like inventory or receiv-
ables, we can consider an important “big picture” ratio, the total asset turnover ratio. As
the name suggests, total asset turnover is
Total asset turnover = Sales __________
Total assets
[3.13]
= $2,311 _______
$3,588
= .64 times
In other words, for every dollar in assets, we generated $.64 in sales.
Profitability Measures
The three types of measures we discuss in this section are probably the best-known and most
widely used of all financial ratios. In one form or another, they are intended to measure how
efficiently the firm uses its assets and how efficiently the firm manages its operations.
PROFIT MARGIN Companies pay a great deal of attention to their profit margin:
Profit margin = Net income __________
Sales
[3.14]
= $363 ______
$2,311
= .157, or 15.7%
This tells us that Prufrock, in an accounting sense, generates a little less than 16 cents in
net income for every dollar in sales.
Here is a variation on the receivables collection period. How long, on average, does it take for Prufrock
Corporation to pay its bills? To answer, we need to calculate the accounts payable turnover rate using
cost of goods sold. We will assume that Prufrock purchases everything on credit.
The cost of goods sold is $1,344, and accounts payable are $344. The turnover is therefore
$1,344/$344 = 3.91 times. So, payables turned over about every 365/3.91 = 93.42 days. On
average, then, Prufrock takes about 93 days to pay. As a potential creditor, we might take note of
this fact.
Payables Turnover
E
X
A
M
P
L
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3
.2
Suppose you find that a particular company generates $.40 in annual sales for every dollar in total
assets. How often does this company turn over its total assets?
The total asset turnover here is .40 times per year. It takes 1/.40 = 2.5 years to turn assets over
completely. The 2.5 number is frequently referred to as the firm’s capital intensity.
More Turnover
E
X
A
M
P
L
E
3
.3
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EBITDA MARGIN Another commonly used measure of profitability is the EBITDA
margin. As mentioned, EBITDA is a measure of before-tax operating cash flow. It adds
back noncash expenses and does not include taxes or interest expense. As a consequence,
EBITDA margin looks more directly at operating cash flows than does net income and
does not include the effect of capital structure or taxes. For Prufrock, EBITDA margin is
EBITDA ______
Sales
= $967 million _____________
$2,311 million
= .418, or 41.8%
All other things being equal, a relatively high margin is obviously desirable. This situation
corresponds to low expense ratios relative to sales. However, we hasten to add that other
things are often not equal.
For example, lowering our sales price will usually increase unit volume but will nor-
mally cause margins to shrink. Total profit (or, more importantly, operating cash flow)
may go up or down, so the fact that margins are smaller isn’t necessarily bad. After all, isn’t
it possible that, as the saying goes, “Our prices are so low that we lose money on every-
thing we sell, but we make it up in volume”?3
Margins are very different for different industries. Grocery stores have a notoriously
low profit margin, generally around 2 percent. In contrast, the profit margin for the phar-
maceutical industry is about 18 percent. So, for example, it is not surprising that recent
profit margins for Kroger and Pfizer were about 1.6 percent and 17.6 percent, respectively.
RETURN ON ASSETS Return on assets (ROA) is a measure of profit per dollar of assets. It
can be defined several ways,4 but the most common is
Return on assets = Net income __________
Total assets
[3.15]
= $363 ______
$3,588
= .101, or 10.1%
RETURN ON EQUITY Return on equity (ROE) is a measure of how the stockholders fared
during the year. Because benefiting shareholders is our goal, ROE is, in an accounting
sense, the true bottom-line measure of performance. ROE is usually measured as
Return on equity = Net income __________
Total equity
[3.16]
= $363 ______
$2,591
= .140, or 14.0%
Therefore, for every dollar in equity, Prufrock generated 14 cents in profit; but, again, this
is correct only in accounting terms.
Because ROA and ROE are such commonly cited numbers, we stress that it is important
to remember they are accounting rates of return. For this reason, these measures should
properly be called return on book assets and return on book equity.
The fact that ROE exceeds ROA reflects Prufrock’s use of financial leverage. We will
examine the relationship between these two measures in the next section.
3 No, it’s not.
4 For example, we might want a return on assets measure that is neutral with respect to capital structure (interest expense) and taxes. Such
a measure for Prufrock would be:
EBIT ___________
Total assets
= $691 _______
$3,588
= 19.3%
This measure has a very natural interpretation. If 19.3 percent exceeds Prufrock’s borrowing rate, Prufrock will earn more money on its
investments than it will pay out to its creditors. The surplus will be available to Prufrock’s shareholders after adjusting for taxes.
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54
Market Value Measures
Our final group of measures is based, in part, on information not necessarily contained in
financial statements—the market price per share of the stock. Obviously, these measures
can be calculated directly only for publicly traded companies.
We assume that Prufrock has 33 million shares outstanding and the stock sold for $88 per
share at the end of the year. If we recall that Prufrock’s net income was $363 million, then
we can calculate that its earnings per share (EPS) was
EPS = Net income ________________
Shares outstanding
= $363 _____
33
[3.17]
PRICE–EARNINGS RATIO The first of our market value measures, the price−earnings or
PE ratio (or multiple), is defined as
PE ratio = Price per share ________________
Earnings per share
[3.18]
= $88 ____
$11
= 8 times
In the vernacular, we would say that Prufrock shares sell for eight times earnings, or we
might say that Prufrock shares have, or “carry,” a PE multiple of 8.
Because the PE ratio measures how much investors are willing to pay per dollar of cur-
rent earnings, higher PEs are often taken to mean that the firm has significant prospects for
future growth. Of course, if a firm had no or almost no earnings, its PE would probably be
quite large; so, as always, care is needed in interpreting this ratio.
MARKET-TO-BOOK RATIO A second commonly quoted measure is the market-to-book ratio:
Market-to-book ratio = Market value per share ___________________
Book value per share
[3.19]
= $88 _________
$2,591/33
= $88 ______
$78.5
= 1.12 times
Notice that book value per share is total equity (not just common stock) divided by the
number of shares outstanding.
Book value per share is an accounting number that reflects historical costs. In a loose
sense, the market-to-book ratio therefore compares the market value of the firm’s invest-
ments to their cost. A value less than 1 could mean that the firm has not been successful
overall in creating value for its stockholders.
MARKET CAPITALIZATION The market capitalization of a public firm is equal to the firm’s
stock market price per share multiplied by the number of shares outstanding. For Prufrock,
this is:
Price per share × Shares outstanding = $88 × 33 million = $2,904 million
This is a useful number for potential buyers of Prufrock. A prospective buyer of all of the
outstanding shares of Prufrock (in a merger or acquisition) would need to come up with at
least $2,904 million plus a premium.
ENTERPRISE VALUE Enterprise value (EV) is a measure of firm value that is very closely
related to market capitalization. Instead of focusing on only the market value of outstanding
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shares of stock, it measures the market value of outstanding shares of stock plus the market
value of outstanding interest bearing debt less cash on hand. We know the market capital-
ization of Prufrock but we do not know the market value of its outstanding interest bearing
debt. In this situation, the common practice is to use the book value of outstanding inter-
est bearing debt less cash on hand as an approximation. For Prufrock, enterprise value is
(in millions)
EV
=
Market capitalization + Market value of interest bearing debt − Cash
=
$2,904 + ( $196 + 457 ) − $98 = $3,459 million
[3.20]
The purpose of the EV measure is to better estimate how much it would take to buy all of
the outstanding stock of a firm and also to pay off the debt. The adjustment for cash is to
recognize that if we were a buyer the cash could be used immediately to buy back debt or
pay a dividend.
ENTERPRISE VALUE MULTIPLES Financial analysts use valuation multiples based upon a
firm’s enterprise value when the goal is to estimate the value of the firm’s total business
rather than just focusing on the value of its equity. To form an appropriate multiple, enter-
prise value is divided by EBITDA. For Prufrock, the enterprise value multiple is
EV ________
EBITDA
= $3,459 ___________
$967 million
= 3.58 times
The multiple is especially useful because it allows comparison of one firm with another
when there are differences in capital structure (interest expense), taxes, or capital spend-
ing. The multiple is not directly affected by these differences.
Similar to PE ratios, we would expect a firm with high growth opportunities to have
high EV multiples.
This completes our definition of some common ratios. We could tell you about more of
them, but these are enough for now. We’ll leave it here and go on to discuss some ways of
using these ratios instead of just how to calculate them. Table 3.6 summarizes some of the
ratios we’ve discussed.
TABLE 3.6
Common Financial Ratios
I. Short-Term Solvency, or Liquidity, Ratios
Current ratio = Current assets _______________
Current liabilities
Days’ sales in receivables = 365 days __________________
Receivables turnover
Quick ratio = Current assets − Inventory _____________________
Current liabilities
Total asset turnover = Sales __________
Total assets
Cash ratio = Cash _______________
Current liabilities
Capital intensity = Total assets __________
Sales
II. Long-Term Solvency, or Financial Leverage, Ratios IV. Profitability Ratios
Total debt ratio = Total assets − Total equity _____________________
Total assets
Profit margin = Net income __________
Sales
Debt–equity ratio = Total debt _________
Total equity
Return on assets (ROA) = Net income __________
Total assets
Equity multiplier = Total assets __________
Total equity
Return on equity (ROE) = Net income __________
Total equity
Times interest earned ratio = EBIT _______
Interest
ROE = Net income __________
Sales
× Sales ______
Assets
× Assets ______
Equity
Cash coverage ratio = EBITDA ________
Interest
(continued )
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56
III. Asset Utilization, or Turnover, Ratios V. Market Value Ratios
Inventory turnover = Cost of goods sold ________________
Inventory
Price–earnings ratio = Price per share ________________
Earnings per share
Days’ sales in inventory = 365 days ________________
Inventory turnover
Market-to-book ratio = Market value per share ___________________
Book value per share
Receivables turnover = Sales _________________
Accounts receivable
EV multiple = Enterprise value ______________
EBITDA
TABLE 3.6
(continued)
E
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M
P
L
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Consider the following 2017 data for Atlantic’s Companies and Pacific Depot (billions except for price and
earnings per share):
ATLANTIC’S COMPANIES, INC. PACIFIC DEPOT, INC.
Sales $48.3 $77.3
EBIT $ 4.8 $ 7.3
Net income $ 2.8 $ 4.4
Cash $ .5 $ .5
Depreciation $ 1.5 $ 1.9
Interest bearing debt $ 6.7 $13.4
Total assets $30.9 $44.3
Price per share $24 $27
Shares outstanding 1.5 1.7
Shareholder equity $16.1 $17.7
Earnings per share $ 1.87 $ 2.6
1. Determine the profit margin, ROE, market capitalization, enterprise value, PE multiple, and EV
multiple for both Atlantic’s and Pacific Depot.
ATLANTIC’S COMPANIES, INC. PACIFIC DEPOT, INC.
Equity multiplier 30.9/16.1 = 1.9 44.3/17.7 = 2.5
Asset turnover 48.3/30.9 = 1.6 77.3/44.3 = 1.7
Profit margin 2.8/48.3 = 5.8% 4.4/77.3 = 5.7%
ROE 2.8/16.1 = 17.4% 4.4/17.7 = 24.9%
Market capitalization 1.5 × 24 = $36 billion 1.7 × 27 = $45.9 billion
Enterprise value (1.5 × 24) + 6.7 − .5 = $42.2 billion (1.7 × 27) + 13.4 − .5 = $58.8 billion
PE multiple 24/1.87 = 12.8 27/2.6 = 10.4
EBITDA 4.8 + 1.5 = $6.3 7.3 + 1.9 = $9.2
EV multiple 42.2/6.3 = 6.7 58.8/9.2 = 6.4
2. How would you describe these two companies from a financial point of view? These are simi-
larly situated companies. In 2017, Pacific Depot had a higher ROE (partially because of using
more debt and higher turnover), but Atlantic’s had slightly higher PE and EV multiples. Both
companies’ multiples were somewhat below the general market, raising questions about future
growth prospects.
Atlantic and Pacific
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3.3 THE DUPONT IDENTITY
As we mentioned in discussing ROA and ROE, the difference between these two prof-
itability measures reflects the use of debt financing or financial leverage. We illustrate
the relationship between these measures in this section by investigating a famous way of
decomposing ROE into its component parts.
A Closer Look at ROE
To begin, let’s recall the definition of ROE:
Return on equity = Net income __________
Total equity
If we were so inclined, we could multiply this ratio by Assets/Assets without changing
anything:
Return on equity = Net income __________
Total equity
= Net income __________
Total equity
× Assets ______
Assets
= Net income __________
Assets
× Assets __________
Total equity
Notice that we have expressed the ROE as the product of two other ratios—ROA and the
equity multiplier:
ROE = ROA × Equity multiplier = ROA × ( 1 + Debt–equity ratio )
Looking back at Prufrock, for example, we see that the debt–equity ratio was .39 and ROA
was 10.1 percent. Our work here implies that Prufrock’s ROE, as we previously calcu-
lated, is
ROE = 10.1% × 1.39 = 14.0%
The difference between ROE and ROA can be substantial, particularly for certain busi-
nesses. For example, based on recent financial statements, Wells Fargo has an ROA of only
1.29 percent, which is actually fairly typical for a bank. However, banks tend to borrow
a lot of money, and, as a result, have relatively large equity multipliers. For Wells Fargo,
ROE is about 11.83 percent, implying an equity multiplier of 9.17.
We can further decompose ROE by multiplying the top and bottom by total sales:
ROE = Sales _____
Sales
× Net income __________
Assets
× Assets __________
Total equity
If we rearrange things a bit, ROE is
ROE = Net income __________
Sales
× Sales ______
Assets
× Assets __________
Total equity
[3.21]
= Profit margin × Total asset turnover × Equity multiplier
Return on assets
ExcelMaster
coverage online
www.mhhe.com/RossCore5e
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58
What we have now done is to partition ROA into its two component parts, profit margin
and total asset turnover. The last expression of the preceding equation is called the DuPont
identity after the DuPont Corporation, which popularized its use.
We can check this relationship for Prufrock by noting that the profit margin was
15.7 percent and the total asset turnover was .64. ROE should thus be
ROE
= Profit margin
× Total asset turnover
× Equity multiplier
= .157 × .64 × 1.39
= .140, or 14.0%
This 14.0 percent ROE is exactly what we had before (aside from a small rounding error).
The DuPont identity tells us that ROE is affected by three things:
1. Operating efficiency (as measured by profit margin).
2. Asset use efficiency (as measured by total asset turnover).
3. Financial leverage (as measured by the equity multiplier).
Weakness in either operating or asset use efficiency (or both) will show up in a diminished
return on assets, which will translate into a lower ROE.
Considering the DuPont identity, it appears that the ROE could be leveraged up by
increasing the amount of debt in the firm. However, notice that increasing debt also
increases interest expense, which reduces profit margins, which acts to reduce ROE. So,
ROE could go up or down, depending. More important, the use of debt financing has a
number of other effects, and, as we discuss at some length in later chapters, the amount of
leverage a firm uses is governed by its capital structure policy.
The decomposition of ROE we’ve discussed in this section is a convenient way of sys-
tematically approaching financial statement analysis. If ROE is unsatisfactory by some
measure, then the DuPont identity tells you where to start looking for the reasons.
Yahoo! and Alphabet (formerly Google) are among the most important Internet com-
panies in the world. They may be good examples of how DuPont analysis can be useful in
helping to ask the right questions about a firm’s financial performance. The DuPont break-
downs for Yahoo! and Alphabet are summarized in Table 3.7.
As can be seen, in 2015, Yahoo! had an ROE of .001 percent (excluding non-
recurring charges), down from its ROE in 2013 of 12.6 percent. In 2015, Alphabet
Yahoo!
TWELVE MONTHS ENDING ROE = PROFIT MARGIN × TOTAL ASSET TURNOVER × EQUITY MULTIPLIER
12/15 .001% = .01% × .110 × 1.56
12/14 .4% = 3.1% × .075 × 1.60
12/13 4.5% = 12.6% × .279 × 1.29
Alphabet
TWELVE MONTHS ENDING ROE = PROFIT MARGIN × TOTAL ASSET TURNOVER × EQUITY MULTIPLIER
12/15 12.3% = 22.9% × .430 × 1.24
12/14 13.8% = 21.9% × .503 × 1.25
12/13 15.3% = 24.0% × .501 × 1.27
TABLE 3.7 The DuPont Breakdown for Yahoo! and Alphabet
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had an ROE of 12.3 percent, down from its ROE in 2013 of 15.3 percent. Given this
information, how is it possible that Alphabet’s ROE could be so much higher than
the ROE of Yahoo! during this period of time, and what accounts for the decline in
Yahoo!’s ROE?
On close inspection of the DuPont breakdown, we see that Yahoo!’s profit margin in
2015 was .01 percent. Meanwhile Alphabet’s profit margin was 22.9 percent in 2015. Yet
Yahoo! and Alphabet have similar financial leverage. What can account for Alphabet’s
advantage over Yahoo! in ROE? Clearly, it is profit margin and asset utilization. Asset
utilization can come from higher volumes, higher prices, and/or lower costs. It is clear that
the big difference in ROE between the two firms can be attributed to the difference in these
two ratios.
Problems with Financial Statement Analysis
We continue our chapter by discussing some additional problems that can arise in using
financial statements. In one way or another, the basic problem with financial statement
analysis is that there is no underlying theory to help us identify which quantities to look at
and to guide us in establishing benchmarks.
As we discuss in other chapters, there are many cases in which financial theory and eco-
nomic logic provide guidance in making judgments about value and risk. Little such help
exists with financial statements. This is why we can’t say which ratios matter the most and
what a high or low value might be.
One particularly severe problem is that many firms are conglomerates, owning more or
less unrelated lines of business. GE is a well-known example. The consolidated financial
statements for such firms don’t really fit any neat industry category. More generally, the
kind of peer group analysis we have been describing is going to work best when the firms
are strictly in the same line of business, the industry is competitive, and there is only one
way of operating.
Another problem that is becoming increasingly common is that major competitors and
natural peer group members in an industry may be scattered around the globe. The auto-
mobile industry is an obvious example. The problem here is that financial statements
from outside the United States do not necessarily conform to GAAP. The existence of dif-
ferent standards and procedures makes it difficult to compare financial statements across
national borders.
Even companies that are clearly in the same line of business may not be comparable.
For example, electric utilities engaged primarily in power generation are all classified in
the same group. This group is often thought to be relatively homogeneous. However, most
utilities operate as regulated monopolies, so they don’t compete much with each other, at
least not historically. Many have stockholders, and many are organized as cooperatives
with no stockholders. There are several different ways of generating power, ranging from
hydroelectric to nuclear, so the operating activities of these utilities can differ quite a bit.
Finally, profitability is strongly affected by the regulatory environment, so utilities in dif-
ferent locations can be similar but show different profits.
Several other general problems frequently crop up. First, different firms use different
accounting procedures—for inventory, for example. This makes it difficult to compare
statements. Second, different firms end their fiscal years at different times. For firms
in seasonal businesses (such as a retailer with a large Christmas season), this can lead
to difficulties in comparing balance sheets because of fluctuations in accounts during
the year. Finally, for any particular firm, unusual or transient events, such as a one-time
profit from an asset sale, may affect financial performance. Such events can give mis-
leading signals as we compare firms. The nearby Finance Matters box discusses some
issues along these lines.
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WHAT’S IN A RATIO?
Abraham Briloff, a well-known financial commentator, famously remarked that “financial statements are like fine per-
fume; to be sniffed but not swallowed.” As you have probably figured out by now, his point is that information gleaned
from financial statements—and ratios and growth rates computed from that information—should be taken with a grain
of salt.
For example, in early 2016, shares in network and logistics technology company Descartes Systems Group had a
PE ratio of about 67 times earnings. You would expect that this stock would have a high growth rate, and indeed ana-
lysts thought so. The estimated earnings growth rate for Descartes for the next year was 33 percent. At the same time,
Churchill Downs, Inc., owner of, among other things, the Kentucky Derby, had a PE ratio of about 50, but analysts esti-
mated an earnings growth rate of only 7 percent for the next year. Why is the PE so high? The answer is that Churchill
Downs had low earnings the previous year. So, caution is warranted when looking at PE ratios.
AK Steel Holdings illustrates another issue. If you calculated its ROE in 2014, you would get about 22 percent, which
is quite good. What’s strange is the company reported a loss of about $96.9 million dollars during 2014! What’s going on
is that AK Steel had a book value of equity balance of negative $492 million. In this situation, the more AK Steel loses, the
higher the ROE becomes. Of course, AK Steel’s market-to-book and PE ratios are also both negative. How do you inter-
pret a negative PE? We’re not really sure, either. Whenever a company has a negative book value of equity, it means that
losses have been so large that book equity has been wiped out. In such cases, the ROE, PE ratio, and market-to-book
ratio are often not reported because they are meaningless.
Even if a company’s book equity is positive, you still have to be careful. For example, consider The Clorox Company,
which had a market-to-book ratio of about 125 in early 2016. Since the market-to-book ratio measures the value cre-
ated by the company for shareholders, this would seem to be a good sign. But a closer look shows that Clorox’s book
value of equity per share was negative $1.04 in 2012 and had only risen to $.92 in 2016. This decline had to do with
accounting for stock repurchases made by the company, not gains or losses, but it nonetheless dramatically increased
the market-to-book ratio.
Financial ratios are important tools used in evaluating companies of all types, but you cannot take a number as given.
Instead, before doing any analysis, the first step is to ask whether the number actually makes sense.
FINANCE MATTERS
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60
3.4 FINANCIAL MODELS
Financial planning is another important use of financial statements. Most financial plan-
ning models output pro forma financial statements, where pro forma means “as a matter of
form.” In our case, this means that financial statements are the form we use to summarize
the projected future financial status of a company.
A Simple Financial Planning Model
We can begin our discussion of financial planning models with a relatively simple exam-
ple. The Computerfield Corporation’s financial statements from the most recent year are
shown below.
Unless otherwise stated, the financial planners at Computerfield assume that all vari-
ables are tied directly to sales and current relationships are optimal. This means that all
items will grow at exactly the same rate as sales. This is obviously oversimplified; we use
this assumption only to make a point.
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Suppose sales increase by 20 percent, rising from $1,000 to $1,200. Planners would
then also forecast a 20 percent increase in costs, from $800 to $800 × 1.2 = $960. The pro
forma income statement would thus look like this:
COMPUTERFIELD CORPORATION
F inancia l Statements
Income Statement Balance Sheet
Sales
Costs
Net income
$1,000
800
$ 200
Assets
Total
$500
$500
Debt
Equity
Total
$250
250
$500
Pro Forma Income Statement
Sales
Costs
Net income
$1,200
960
$ 240
Pro Forma Balance Sheet
Assets
Total
$600 (+100)
$600 (+100)
Debt
Equity
Total
$300 (+50)
300 (+50)
$600 (+100)
PRO FORMA BALANCE SHEET
Assets
Total
$600 (+100)
$600 (+100)
Debt
Equity
Total
$110 (−140)
490 (+240)
$600 (+100)
The assumption that all variables will grow by 20 percent lets us easily construct the pro
forma balance sheet as well:
Notice we have increased every item by 20 percent. The numbers in parentheses are the
dollar changes for the different items.
Now we have to reconcile these two pro forma statements. How, for example, can net
income be equal to $240 and equity increase by only $50? The answer is that Computerfield
must have paid out the difference of $240 − 50 = $190, possibly as a cash dividend. In this
case dividends are the “plug” variable.
Suppose Computerfield does not pay out the $190. In this case, the addition to retained
earnings is the full $240. Computerfield’s equity will thus grow to $250 (the starting
amount) plus $240 (net income), or $490, and debt must be retired to keep total assets
equal to $600.
With $600 in total assets and $490 in equity, debt will have to be $600 − 490 = $110.
Because we started with $250 in debt, Computerfield will have to retire $250 − 110 = $140
in debt. The resulting pro forma balance sheet would look like this:
Planware provides insight
into cash flow forecasting
at www.planware.org.
In this case, debt is the plug variable used to balance projected total assets and liabilities.
This example shows the interaction between sales growth and financial policy. As sales
increase, so do total assets. This occurs because the firm must invest in net working capital
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62
and fixed assets to support higher sales levels. Because assets are growing, total liabilities
and equity, the right side of the balance sheet, will grow as well.
The thing to notice from our simple example is that the way the liabilities and owners’
equity change depends on the firm’s financing policy and its dividend policy. The growth
in assets requires that the firm decide on how to finance that growth. This is strictly a man-
agerial decision. Note that in our example the firm needed no outside funds. This won’t
usually be the case, so we explore a more detailed situation in the next section.
The Percentage of Sales Approach
In the previous section, we described a simple planning model in which every item increased
at the same rate as sales. This may be a reasonable assumption for some elements. For oth-
ers, such as long-term borrowing, it probably is not: The amount of long-term borrowing is
set by management, and it does not necessarily relate directly to the level of sales.
In this section, we describe an extended version of our simple model. The basic idea is
to separate the income statement and balance sheet accounts into two groups, those that
vary directly with sales and those that do not. Given a sales forecast, we will then be able
to calculate how much financing the firm will need to support the predicted sales level.
The financial planning model we describe next is based on the percentage of sales
approach. Our goal here is to develop a quick and practical way of generating pro forma
statements. We defer discussion of some “bells and whistles” to a later section.
THE INCOME STATEMENT We start out with the most recent income statement for the
Rosengarten Corporation, as shown in Table 3.8. Notice that we have still simplified things
by including costs, depreciation, and interest in a single cost figure.
Rosengarten has projected a 25 percent increase in sales for the coming year, so we are
anticipating sales of $1,000 × 1.25 = $1,250. To generate a pro forma income statement, we
assume that total costs will continue to run at $800/1,000 = 80 percent of sales. With this
assumption, Rosengarten’s pro forma income statement is as shown in Table 3.9. The effect
here of assuming that costs are a constant percentage of sales is to assume that the profit mar-
gin is constant. To check this, notice that the profit margin was $132/1,000 = 13.2 percent. In
our pro forma statement, the profit margin is $165/1,250 = 13.2 percent; so it is unchanged.
Next, we need to project the dividend payment. This amount is up to Rosengarten’s
management. We will assume Rosengarten has a policy of paying out a constant fraction of
ROSENGARTEN CORPORATION
Pro Forma Income Statement
Sales (projected)
Costs (80% of sales)
Taxable income
Taxes (34%)
Net income
$1,250
1,000
$ 250
85
$ 165
TABLE 3.9
ROSENGARTEN CORPORATION
Income Statement
Sales
Costs
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings
$44
88
$1,000
800
$ 200
68
$ 132
TABLE 3.8
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net income in the form of a cash dividend. For the most recent year, the dividend payout
ratio was
Dividend payout ratio
=
Cash dividends / Net income
=
$44 /132 = 33 1 / 3%
[3.22]
We can also calculate the ratio of the addition to retained earnings to net income:
Addition to retained earnings/Net income = $88 / 132 = 66 2 / 3%
This ratio is called the retention ratio or plowback ratio, and it is equal to 1 minus
the dividend payout ratio because everything not paid out is retained. Assuming that the
payout ratio is constant, the projected dividends and addition to retained earnings will be
Projected dividends paid to shareholders = $165 × 1/3 = $ 55
Projected addition to retained earnings = $165 × 2/3 = 110
$165
THE BALANCE SHEET To generate a pro forma balance sheet, we start with the most
recent statement, as shown in Table 3.10.
On our balance sheet, we assume that some items vary directly with sales and others
do not. For those items that vary with sales, we express each as a percentage of sales for
the year just completed. When an item does not vary directly with sales, we write “n/a” for
“not applicable.”
For example, on the asset side, inventory is equal to 60 percent of sales (=$600/1,000)
for the year just ended. We assume this percentage applies to the coming year, so for each
$1 increase in sales, inventory will rise by $.60. More generally, the ratio of total assets to
sales for the year just ended is $3,000/1,000 = 3, or 300 percent.
This ratio of total assets to sales is sometimes called the capital intensity ratio. It tells
us the amount of assets needed to generate $1 in sales; the higher the ratio is, the more
capital intensive is the firm. Notice also that this ratio is just the reciprocal of the total asset
turnover ratio we defined previously.
ROSENGARTEN CORPORATION
Balance Sheet
Assets Liabilities and Owners’ Equity
$
PERCENTAGE
OF SALES $
PERCENTAGE
OF SALES
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
$ 160
440
600
$1,200
$1,800
$3,000
16%
44
60
120
180
300%
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Retained earnings
Total
Total liabilities and owners’ equity
$ 300
100
$ 400
$ 800
$ 800
1,000
$1,800
$3,000
30%
n/a
n/a
n/a
n/a
n/a
n/a
n/a
TABLE 3.10
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64
For Rosengarten, assuming that this ratio is constant, it takes $3 in total assets to gen-
erate $1 in sales (apparently Rosengarten is in a relatively capital-intensive business).
Therefore, if sales are to increase by $100, Rosengarten will have to increase total assets by
three times this amount, or $300.
On the liability side of the balance sheet, we show accounts payable varying with sales.
The reason is that we expect to place more orders with our suppliers as sales volume
increases, so payables will change “spontaneously” with sales. Notes payable, on the other
hand, represents short-term debt such as bank borrowing. This will not vary unless we take
specific actions to change the amount, so we mark this item as “n/a.”
Similarly, we use “n/a” for long-term debt because it won’t automatically change with
sales. The same is true for common stock and paid-in surplus. The last item on the right
side, retained earnings, will vary with sales, but it won’t be a simple percentage of sales.
Instead, we will explicitly calculate the change in retained earnings based on our projected
net income and dividends.
We can now construct a partial pro forma balance sheet for Rosengarten. We do this by
using the percentages we have just calculated wherever possible to calculate the projected
amounts. For example, net fixed assets are 180 percent of sales; so, with a new sales level
of $1,250, the net fixed asset amount will be 1.80 × $1,250 = $2,250, representing an
increase of $2,250 − 1,800 = $450 in plant and equipment. It is important to note that for
items that don’t vary directly with sales, we initially assume no change and write in the
original amounts. The result is shown in Table 3.11. Notice that the change in retained
earnings is equal to the $110 addition to retained earnings we calculated earlier.
Inspecting our pro forma balance sheet, we notice that assets are projected to increase
by $750. However, without additional financing, liabilities and equity will increase by only
$185, leaving a shortfall of $750 − 185 = $565. We label this amount external financing
needed (EFN).
Rather than create pro forma statements, if we were so inclined, we could calculate EFN
directly as follows:
EFN
= Assets ______
Sales
× ΔSales − Spontaneous liabilities ___________________
Sales
× ΔSales − PM
× Projected sales × (1 − d)
[3.23]
ROSENGARTEN CORPORATION
Part ia l Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
NEXT
YEAR
CHANGE FROM
CURRENT YEAR
NEXT
YEAR
CHANGE FROM
CURRENT YEAR
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
$ 200
550
750
$1,500
$2,250
$3,750
$ 40
110
150
$300
$450
$750
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Retained earnings
Total
Total liabilities and owners’ equity
External financing needed
$ 375
100
$ 475
$ 800
$ 800
1,110
$1,910
$3,185
$ 565
$ 75
0
$ 75
$ 0
$ 0
110
$110
$185
$565
TABLE 3.11
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In this expression, “ΔSales” is the projected change in sales (in dollars). In our example
projected sales for next year are $1,250, an increase of $250 over the previous year, so
ΔSales = $250. By “Spontaneous liabilities,” we mean liabilities that naturally move up
and down with sales. For Rosengarten, the spontaneous liabilities are the $300 in accounts
payable. Finally, PM and d are the profit margin and dividend payout ratios, which we pre-
viously calculated as 13.2 percent and 33 1/3 percent, respectively. Total assets and sales
are $3,000 and $1,000, respectively, so we have
EFN = $3,000 ______
1,000
× $250 − $300 _____
1,000
× $250 − .132 × $1,250 × ( 1 −
1 _
3
) = $565
In this calculation, notice that there are three parts. The first part is the projected increase
in assets, which is calculated using the capital intensity ratio. The second is the spontane-
ous increase in liabilities. The third part is the product of profit margin and projected sales,
which is projected net income, multiplied by the retention ratio. Thus, the third part is the
projected addition to retained earnings.
A PARTICULAR SCENARIO Our financial planning model now reminds us of one of those
good news–bad news jokes. The good news is we’re projecting a 25 percent increase in
sales. The bad news is this isn’t going to happen unless Rosengarten can somehow raise
$565 in new financing.
This is a good example of how the planning process can point out problems and poten-
tial conflicts. If, for example, Rosengarten has a goal of not borrowing any additional funds
and not selling any new equity, then a 25 percent increase in sales is probably not feasible.
If we take the need for $565 in new financing as given, we know that Rosengarten has
three possible sources: short-term borrowing, long-term borrowing, and new equity. The
choice of some combination among these three is up to management; we will illustrate
only one of the many possibilities.
Suppose Rosengarten decides to borrow the needed funds. In this case, the firm might
choose to borrow some over the short term and some over the long term. For example, cur-
rent assets increased by $300 whereas current liabilities rose by only $75. Rosengarten could
borrow $300 − 75 = $225 in short-term notes payable and leave total net working capital
unchanged. With $565 needed, the remaining $565 − 225 = $340 would have to come from
long-term debt. Table 3.12 shows the completed pro forma balance sheet for Rosengarten.
We have used a combination of short- and long-term debt as the plug here, but we
emphasize that this is just one possible strategy; it is not necessarily the best one by any
means. We could (and should) investigate many other scenarios. The various ratios we dis-
cussed earlier come in handy here. For example, with the scenario we have just examined,
we would surely want to examine the current ratio and the total debt ratio to see if we were
comfortable with the new projected debt levels.
AN ALTERNATIVE SCENARIO The assumption that assets are a fixed percentage of sales is
convenient, but it may not be suitable in many cases. In particular, note that we effectively
assumed that Rosengarten was using its fixed assets at 100 percent of capacity because any
increase in sales led to an increase in fixed assets. For most businesses, there would be some
slack or excess capacity, and production could be increased by perhaps running an extra shift.
According to the Federal Reserve, the overall capacity utilization for U.S. manufacturing com-
panies in December 2015 was 76.5 percent, up from a recent low of 64.4 percent in June 2009.
If we assume that Rosengarten is operating at only 70 percent of capacity, then the need
for external funds will be quite different. When we say “70 percent of capacity,” we mean
that the current sales level is 70 percent of the full-capacity sales level:
Current sales = $1,000 = .70 × Full-capacity sales
Full-capacity sales = $1,000 / .70 = $1,429
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66
ROSENGARTEN CORPORATION
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
NEXT
YEAR
CHANGE FROM
CURRENT YEAR
NEXT
YEAR
CHANGE FROM
CURRENT YEAR
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
$ 200
550
750
$1,500
$2,250
$3,750
$ 40
110
150
$300
$450
$750
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in
surplus
Retained earnings
Total
Total liabilities and owners’ equity
$ 375
325
$ 700
$1,140
$ 800
1,110
$1,910
$3,750
$ 75
225
$300
$340
$ 0
110
$110
$750
TABLE 3.12
E
X
A
M
P
L
E
3
.5
Suppose Rosengarten is operating at 90 percent capacity. What would sales be at full capacity? What is
the capital intensity ratio at full capacity? What is EFN in this case?
Full-capacity sales would be $1,000/.90 = $1,111. From Table 3.10, we know that fixed assets are
$1,800. At full capacity, the ratio of fixed assets to sales is thus:
Fixed assets ________________
Full-capacity sales
= $1,800 ______
1,111
= 1.62
So, Rosengarten needs $1.62 in fixed assets for every $1 in sales once it reaches full capacity. At the
projected sales level of $1,250, then, it needs $1,250 × 1.62 = $2,025 in fixed assets. Compared to the
$2,250 we originally projected, this is $225 less, so EFN is $565 − 225 = $340.
Current assets would still be $1,500, so total assets would be $1,500 + 2,025 = $3,525. The capital
intensity ratio would thus be $3,525/1,250 = 2.82, which is less than our original value of 3 because of
the excess capacity.
The Capital Intensity Ratio
This tells us that sales could increase by almost 43 percent—from $1,000 to $1,429—
before any new fixed assets would be needed.
In our previous scenario, we assumed it would be necessary to add $450 in net fixed
assets. In the current scenario, no spending on net fixed assets is needed because sales are
projected to rise only to $1,250, which is substantially less than the $1,429 full-capacity level.
As a result, our original estimate of $565 in external funds needed is too high. We
estimated that $450 in net new fixed assets would be needed. Instead, no spending on new
net fixed assets is necessary. Thus, if we are currently operating at 70 percent capacity, we
need only $565 − 450 = $115 in external funds. The excess capacity thus makes a consid-
erable difference in our projections.
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3.5 EXTERNAL FINANCING AND GROWTH
Growth and the need for external financing are obviously related. All other things staying
the same, the higher the rate of growth in sales or assets, the greater will be the need for
external financing. In the previous section, we took a growth rate as given, and then we
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determined the amount of external financing needed to support that growth. In this sec-
tion, we turn things around a bit. We will take the firm’s financial policy as given and then
examine the relationship between that financial policy and the firm’s ability to finance new
investments and thereby grow.
We emphasize that we are focusing on growth not because growth is an appropriate goal;
instead, for our purposes, growth is a convenient means of examining the interactions between
investment and financing decisions. In effect, we assume that the use of growth as a basis for
planning is just a reflection of the very high level of aggregation used in the planning process.
EFN and Growth
The first thing we need to do is establish the relationship between EFN and growth. To
do this, we introduce the simplified income statement and balance sheet for the Hoffman
Company in Table 3.13. Notice that we have simplified the balance sheet by combining
short-term and long-term debt into a single total debt figure. Effectively, we are assuming
that none of the current liabilities vary spontaneously with sales. This assumption isn’t as
restrictive as it sounds. If any current liabilities (such as accounts payable) vary with sales,
we can assume that any such accounts have been netted out in current assets. Also, we con-
tinue to combine depreciation, interest, and costs on the income statement.
Suppose the Hoffman Company is forecasting next year’s sales level at $600, a $100
increase. Notice that the percentage increase in sales is $100/500 = 20 percent. Using
the percentage of sales approach and the figures in Table 3.13, we can prepare a pro
forma income statement and balance sheet as in Table 3.14. As Table 3.14 illustrates, at
a 20 percent growth rate, Hoffman needs $100 in new assets. The projected addition to
retained earnings is $52.8, so the external financing needed, EFN, is $100 − 52.8 = $47.2.
Notice that the debt−equity ratio for Hoffman was originally (from Table 3.13) equal
to $250/250 = 1.0. We will assume that the Hoffman Company does not wish to sell
new equity. In this case, the $47.2 in EFN will have to be borrowed. What will the new
debt−equity ratio be? From Table 3.14, we know that total owners’ equity is projected at
$302.8. The new total debt will be the original $250 plus $47.2 in new borrowing, or $297.2
total. The debt−equity ratio thus falls slightly from 1.0 to $297.2/302.8 = .98.
HOFFMAN COMPANY
Income Statement and Balance Sheet
INCOME STATEMENT
Sales
Costs
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings
$22
44
$500
400
$100
34
$ 66
BALANCE SHEET
Assets Liabilities and Owners’ Equity
$ PERCENTAGE OF SALES $ PERCENTAGE OF SALES
Current assets
Net fixed assets
Total assets
$200
300
$500
40%
60
100%
Total debt
Owners’ equity
Total liabilities and owners’ equity
$250
250
$500
n/a
n/a
n/a
TABLE 3.13
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68
Table 3.15 shows EFN for several different growth rates. The projected addition to
retained earnings and the projected debt−equity ratio for each scenario are also given (you
should probably calculate a few of these for practice). In determining the debt−equity
ratios, we assumed that any needed funds were borrowed, and we also assumed any sur-
plus funds were used to pay off debt. Thus, for the zero growth case the debt falls by $44,
from $250 to $206. In Table 3.15, notice that the increase in assets required is equal to the
original assets of $500 multiplied by the growth rate. Similarly, the addition to retained
earnings is equal to the original $44 plus $44 times the growth rate.
Table 3.15 shows that for relatively low growth rates, Hoffman will run a surplus, and
its debt−equity ratio will decline. Once the growth rate increases to about 10 percent, how-
ever, the surplus becomes a deficit. Furthermore, as the growth rate exceeds approximately
20 percent, the debt−equity ratio passes its original value of 1.0.
Figure 3.1 illustrates the connection between growth in sales and external financing
needed in more detail by plotting asset needs and additions to retained earnings from
Table 3.15 against the growth rates. As shown, the need for new assets grows at a much
faster rate than the addition to retained earnings, so the internal financing provided by the
addition to retained earnings rapidly disappears.
PROJECTED
SALES
GROWTH
INCREASE
IN ASSETS
REQUIRED
ADDITION TO
RETAINED
EARNINGS
EXTERNAL
F INANCING
NEEDED, EFN
PROJECTED
DEBT–EQUITY
RATIO
0%
5
10
15
20
25
$ 0
25
50
75
100
125
$44.0
46.2
48.4
50.6
52.8
55.0
–$44.0
–21.2
1.6
24.4
47.2
70.0
.70
.77
.84
.91
.98
1.05
TABLE 3.15
Growth and Projected EFN
for the Hoffman Company
TABLE 3.14
HOFFMAN COMPANY
Pro Forma Income Statement and Balance Sheet
INCOME STATEMENT
Sales (projected)
Costs (80% of sales)
Taxable income
Taxes (34%)
Net income
Dividends
Addition to retained earnings
$26.4
52.8
$600.0
480.0
$120.0
40.8
$ 79.2
BALANCE SHEET
Assets Liabilities and Owners’ Equity
$ PERCENTAGE
OF SALES
$ PERCENTAGE
OF SALES
Current assets
Net fixed assets
Total assets
$240.0
360.0
$600.0
40%
60
100%
Total debt
Owners’ equity
Total liabilities and owners’ equity
External financing needed
$250.0
302.8
$552.8
$ 47.2
n/a
n/a
n/a
n/a
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As this discussion shows, whether a firm runs a cash surplus or deficit depends on
growth. Microsoft is a good example. Its revenue growth in the 1990s was amazing,
averaging well over 30 percent per year for the decade. Growth slowed down noticeably
over the 2000–2015 period, but, nonetheless, Microsoft’s combination of growth and sub-
stantial profit margins led to enormous cash surpluses. In part because Microsoft paid
relatively low dividends, the cash really piled up; in 2016, Microsoft’s cash and short-term
investment hoard exceeded $102 billion.
Financial Policy and Growth
Based on our discussion just preceding, we see that there is a direct link between growth
and external financing. In this section, we discuss two growth rates that are particularly
useful in long-range planning.
THE INTERNAL GROWTH RATE The first growth rate of interest is the maximum growth
rate that can be achieved with no external financing of any kind. We will call this the
internal growth rate because this is the rate the firm can maintain with internal financ-
ing only. In Figure 3.1, this internal growth rate is represented by the point where the two
lines cross. At this point, the required increase in assets is exactly equal to the addition to
retained earnings, and EFN is therefore zero. We have seen that this happens when the
growth rate is slightly less than 10 percent. With a little algebra (see Problem 28 at the end
of the chapter), we can define this growth rate more precisely as
Internal growth rate = ROA × b __________
1 − ROA × b
[3.24]
where ROA is the return on assets we discussed earlier, and b is the plowback, or retention,
ratio also defined earlier in this chapter.
For the Hoffman Company, net income was $66 and total assets were $500. ROA is thus
$66/500 = 13.2 percent. Of the $66 net income, $44 was retained, so the plowback ratio, b,
is $44/66 = 2/3. With these numbers, we can calculate the internal growth rate as
Internal growth rate
=
ROA × b __________
1 − ROA × b
=
.132 × (2 / 3) _______________
1 − .132 × (2 / 3)
= 9.65%
FIGURE 3.1
Growth and Related
Financing Needed for the
Hoffman Company
5 10
Increase
in assets
required
Projected
addition
to retained
earnings
EFN < 0
(surplus)
Projected growth in sales (%)
As
se
t n
ee
ds
a
nd
re
ta
in
ed
e
ar
ni
ng
s
($
)
25
50
44
75
100
125
15 20 25
EFN > 0
(deficit)
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70
Thus, the Hoffman Company can expand at a maximum rate of 9.65 percent per year with-
out external financing.
THE SUSTAINABLE GROWTH RATE We have seen that if the Hoffman Company wishes
to grow more rapidly than at a rate of 9.65 percent per year, external financing must be
arranged. The second growth rate of interest is the maximum growth rate a firm can
achieve with no external equity financing while it maintains a constant debt−equity ratio.
This rate is commonly called the sustainable growth rate because it is the maximum rate
of growth a firm can maintain without increasing its financial leverage.
There are various reasons why a firm might wish to avoid equity sales. For example,
new equity sales can be expensive because of the substantial fees that may be involved.
Alternatively, the current owners may not wish to bring in new owners or contribute
additional equity. Why a firm might view a particular debt−equity ratio as optimal is dis-
cussed in later chapters; for now, we will take it as given.
Based on Table 3.15, the sustainable growth rate for Hoffman is approximately
20 percent because the debt−equity ratio is near 1.0 at that growth rate. The precise value
can be calculated as follows (see Problem 28 at the end of the chapter):
Sustainable growth rate = ROE × b ___________
1 − ROE × b
[3.25]
This is identical to the internal growth rate except that ROE, return on equity, is used
instead of ROA.
For the Hoffman Company, net income was $66 and total equity was $250; ROE is thus
$66/250 = 26.4 percent. The plowback ratio, b, is still 2/3, so we can calculate the sustain-
able growth rate as
Sustainable growth rate
= ROE × b ____________
1 − ROE × b
= .264 × (2 / 3) _______________
1 − .264 × (2 / 3)
= 21.36%
Thus, the Hoffman Company can expand at a maximum rate of 21.36 percent per year
without external equity financing.
E
X
A
M
P
L
E
3
.6
Suppose Hoffman grows at exactly the sustainable growth rate of 21.36 percent. What will the pro forma
statements look like?
At a 21.36 percent growth rate, sales will rise from $500 to $606.8. The pro forma income statement
will look like this:
HOFFMAN COMPANY
Pro Forma Income Statement
Sales (projected) $606.8
Costs (80% of sales) 485.4
Taxable income $121.4
Taxes (34%) 41.3
Net income $ 80.1
Dividends $26.7
Addition to retained earnings 53.4
Sustainable Growth
(continued )
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DETERMINANTS OF GROWTH Earlier in this chapter, we saw that the return on equity, ROE,
could be decomposed into its various components using the DuPont identity. Because ROE
appears so prominently in the determination of the sustainable growth rate, it is obvious that
the factors important in determining ROE are also important determinants of growth.
From our previous discussions, we know that ROE can be written as the product of
three factors:
ROE = Profit margin × Total asset turnover × Equity multiplier
If we examine our expression for the sustainable growth rate, we see that anything that
increases ROE will increase the sustainable growth rate by making the top bigger and the
bottom smaller. Increasing the plowback ratio will have the same effect.
Putting it all together, what we have is that a firm’s ability to sustain growth depends
explicitly on the following four factors:
1. Profit margin: An increase in profit margin will increase the firm’s ability to
generate funds internally and thereby increase its sustainable growth.
2. Dividend policy: A decrease in the percentage of net income paid out as divi-
dends will increase the retention ratio. This increases internally generated equity
and thus increases sustainable growth.
3. Financial policy: An increase in the debt−equity ratio increases the firm’s finan-
cial leverage. Because this makes additional debt financing available, it increases
the sustainable growth rate.
4. Total asset turnover: An increase in the firm’s total asset turnover increases the
sales generated for each dollar in assets. This decreases the firm’s need for new
assets as sales grow and thereby increases the sustainable growth rate. Notice that
increasing total asset turnover is the same thing as decreasing capital intensity.
The sustainable growth rate is a very useful planning number. What it illustrates is the
explicit relationship between the firm’s four major areas of concern: its operating effi-
ciency as measured by profit margin, its asset use efficiency as measured by total asset
turnover, its dividend policy as measured by the retention ratio, and its financial policy as
measured by the debt−equity ratio.
We construct the balance sheet just as we did before. Notice, in this case, that owners’ equity will rise
from $250 to $303.4 because the addition to retained earnings is $53.4.
HOFFMAN COMPANY
Pro Forma Balance Sheet
Assets Liabilities and Owners’ Equity
$
PERCENTAGE
OF SALES $
PERCENTAGE
OF SALES
Current assets $242.7 40% Total debt $250.0 n/a
Net fixed assets 364.1 60 Owners’ equity 303.4 n/a
Total assets $606.8 100% Total liabilities and
owners’ equity
$553.4 n/a
External financing
needed
$ 53.4 n/a
As illustrated, EFN is $53.4. If Hoffman borrows this amount, then total debt will rise to $303.4, and the
debt−equity ratio will be exactly 1.0, which verifies our earlier calculation. At any other growth rate,
something would have to change.
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72
If a firm does not wish to sell new equity and its profit margin, dividend policy, financial pol-
icy, and total asset turnover (or capital intensity) are all fixed, then there is only one possible
growth rate.
I. Internal Growth Rate
Internal growth rate = ROA × b ____________
1 − ROA × b
where
ROA = Return on assets = Net income/Total assets
b = Plowback (retention) ratio
b = Addition to retained earnings/Net income
The internal growth rate is the maximum growth rate that can be achieved with no external financing of any kind.
II. Sustainable Growth Rate
Sustainable growth rate = ROE × b ____________
1 − ROE × b
where
ROE = Return on equity = Net income/Total equity
b = Plowback (retention) ratio
b = Addition to retained earnings/Net income
The sustainable growth rate is the maximum growth rate that can be achieved with no external equity financing while
maintaining a constant debt–equity ratio.
TABLE 3.16
Summary of Internal and
Sustainable Growth Rates
E
X
A
M
P
L
E
3
.7
The Sandar Co. has a debt–equity ratio of .5, a profit margin of 3 percent, a dividend payout ratio of
40 percent, and a capital intensity ratio of 1. What is its sustainable growth rate? If Sandar desired a
10 percent sustainable growth rate and planned to achieve this goal by improving profit margins, what
would you think?
ROE is .03 × 1 × 1.5 = 4.5 percent. The retention ratio is 1 − .40 = .60 Sustainable growth is thus
.045(.60)/[1 − .045(.60)] = 2.77 percent.
For the company to achieve a 10 percent growth rate, the profit margin will have to rise. To see this,
assume that sustainable growth is equal to 10 percent and then solve for profit margin, PM:
.10 = PM (1.5) (.6) / [ 1 − PM (1.5) (.6) ]
PM = .1/.99 = 10.1%
For the plan to succeed, the necessary increase in profit margin is substantial, from below 3 percent to
about 10 percent. This may not be feasible.
Profit Margins and Sustainable Growth
Given values for all four of these, there is only one growth rate that can be achieved.
This is an important point, so it bears restating:
One of the primary benefits of financial planning is that it ensures internal consistency
among the firm’s various goals. The concept of the sustainable growth rate captures this
element nicely. Also, we now see how a financial planning model can be used to test
the feasibility of a planned growth rate. If sales are to grow at a rate higher than the sus-
tainable growth rate, the firm must increase profit margins, increase total asset turnover,
increase financial leverage, increase earnings retention, or sell new shares.
The two growth rates, internal and sustainable, are summarized in Table 3.16.
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A Note about Sustainable Growth Rate Calculations
Very commonly, the sustainable growth rate is calculated using just the numerator in
our expression, ROE × b. This causes some confusion, which we can clear up here. The
issue has to do with how ROE is computed. Recall that ROE is calculated as net income
divided by total equity. If total equity is taken from an ending balance sheet (as we have
done consistently, and is commonly done in practice), then our formula is the right one.
However, if total equity is from the beginning of the period, then the simpler formula is
the correct one.
In principle, you’ll get exactly the same sustainable growth rate regardless of which
way you calculate it (as long as you match up the ROE calculation with the right formula).
In reality, you may see some differences because of accounting-related complications. By
the way, if you use the average of beginning and ending equity (as some advocate), yet
another formula is needed. Also, all of our comments here apply to the internal growth
rate as well.
3.6 SOME CAVEATS REGARDING FINANCIAL
PLANNING MODELS
Financial planning models do not always ask the right questions. A primary reason is that
they tend to rely on accounting relationships and not financial relationships. In particular,
the three basic elements of firm value tend to get left out—namely, cash flow size, risk,
and timing.
Because of this, financial planning models sometimes do not produce output that gives
the user many meaningful clues about what strategies will lead to increases in value.
Instead, they divert the user’s attention to questions concerning the association of, say, the
debt−equity ratio and firm growth.
The financial model we used for the Hoffman Company was simple—in fact, too
simple. Our model, like many in use today, is really an accounting statement generator at
heart. Such models are useful for pointing out inconsistencies and reminding us of finan-
cial needs, but they offer little guidance concerning what to do about these problems.
In closing our discussion, we should add that financial planning is an iterative process.
Plans are created, examined, and modified over and over. The final plan will be a result
negotiated between all the different parties to the process. In fact, long-term financial plan-
ning in most corporations relies on what might be called the Procrustes approach.5 Upper-
level management has a goal in mind, and it is up to the planning staff to rework and to
ultimately deliver a feasible plan that meets that goal.
The final plan will therefore implicitly contain different goals in different areas and
also satisfy many constraints. For this reason, such a plan need not be a dispassionate
assessment of what we think the future will bring; it may instead be a means of recon-
ciling the planned activities of different groups and a way of setting common goals for
the future.
However it is done, the important thing to remember is that financial planning
should not become a purely mechanical exercise. If it does, it will probably focus on
the wrong things. Nevertheless, the alternative to planning is stumbling into the future.
Perhaps the immortal Yogi Berra (the baseball catcher, not the cartoon character), said
it best: “Ya gotta watch out if you don’t know where you’re goin’. You just might not
get there.”6
5 In Greek mythology, Procrustes is a giant who seizes travelers and ties them to an iron bed. He stretches them or cuts off their legs as
needed to make them fit the bed.
6 Were not exactly sure what this means, either, but we like the sound of it.
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PART 1 Overview74
This chapter focuses on working with information contained in financial statements. Specifically, we studied
standardized financial statements, ratio analysis, and long-term financial planning.
1. We explained that differences in firm size make it difficult to compare financial statements, and we dis-
cussed how to form common-size statements to make comparisons easier and more meaningful.
2. Evaluating ratios of accounting numbers is another way of comparing financial statement information.
We defined a number of the most commonly used ratios, and we discussed the famous DuPont identity.
3. We showed how pro forma financial statements can be generated and used to plan for future financing needs.
After you have studied this chapter, we hope that you have some perspective on the uses and abuses of
financial statement information. You should also find that your vocabulary of business and financial terms has
grown substantially.
SUMMARY AND CONCLUSIONS
1. Financial Ratio Analysis A financial ratio by itself tells us little about a company since financial ratios
vary a great deal across industries. There are two basic methods for analyzing financial ratios for a
company: time trend analysis and peer group analysis. Why might each of these analysis methods be
useful? What does each tell you about the company’s financial health?
2. Industry-Specific Ratios So-called “same-store sales” are a very important measure for companies as
diverse as McDonald’s and Sears. As the name suggests, examining same-store sales means comparing
revenues from the same stores or restaurants at two different points in time. Why might companies
focus on same-store sales rather than total sales?
3. Sales Forecast Why do you think most long-term financial planning begins with sales forecasts? Put
differently, why are future sales the key input?
4. Sustainable Growth In the chapter, we used Rosengarten Corporation to demonstrate how to
calculate EFN. The ROE for Rosengarten is about 7.3 percent, and the plowback ratio is about 67
percent. If you calculate the sustainable growth rate for Rosengarten, you will find it is only 5.14 percent.
In our calculation for EFN, we used a growth rate of 25 percent. Is this possible? (Hint: Yes. How?)
5. EFN and Growth Rate Broslofski Co. maintains a positive retention ratio and keeps its debt–equity
ratio constant every year. When sales grow by 20 percent, the firm has a negative projected EFN. What
does this tell you about the firm’s sustainable growth rate? Do you know, with certainty, if the internal
growth rate is greater than or less than 20 percent? Why? What happens to the projected EFN if the
retention ratio is increased? What if the retention ratio is decreased? What if the retention ratio is zero?
6. Common-Size Financials One tool of financial analysis is common-size financial statements. Why
do you think common-size income statements and balance sheets are used? Note that the accounting
statement of cash flows is not converted into a common-size statement. Why do you think this is?
7. Asset Utilization and EFN One of the implicit assumptions we made in calculating the external funds
needed was that the company was operating at full capacity. If the company is operating at less than full
capacity, how will this affect the external funds needed?
Use the following information to answer the next five questions: A small business called The
Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit,
and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company
leased more space and expanded capacity, but it still could not keep up with demand. Equipment failed
from overuse and quality suffered. Working capital was drained to expand production, and, at the same
time, payments from customers were often delayed until the product was shipped. Unable to deliver on
orders, the company became so strapped for cash that employee paychecks began to bounce. Finally,
out of cash, the company ceased operations entirely three years later.
CONCEPT QUESTIONS
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CHAPTER 3 Financial Statements Analysis and Financial Models 75
8. Product Sales Do you think the company would have suffered the same fate if its product had been
less popular? Why or why not?
9. Cash Flow The Grandmother Calendar Company clearly had a cash flow problem. In the context of
the cash flow analysis we developed in Chapter 2, what was the impact of customers not paying until
orders were shipped?
10. Corporate Borrowing If the firm was so successful at selling, why wouldn’t a bank or some other
lender step in and provide it with the cash it needed to continue?
11. Cash Flow Which is the biggest culprit here: too many orders, too little cash, or too little production
capacity?
12. Cash Flow What are some of the actions that a small company like The Grandmother Calendar
Company can take (besides expansion of capacity) if it finds itself in a situation in which growth in sales
outstrips production?
13. Comparing ROE and ROA Both ROE and ROA measure profitability. Which one is more useful for
comparing two companies? Why?
14. Ratio Analysis Consider the ratio EBITDA/Assets. What does this ratio tell us? Why might it be more
useful than ROA in comparing two companies?
QUESTIONS AND PROBLEMS
1. DuPont Identity If Harley, Inc., has an equity multiplier of 1.35, total asset turnover of 2.15, and a
profit margin of 6.08 percent, what is its ROE?
2. Equity Multiplier and Return on Equity Quinn Company has a debt–equity ratio of .75. Return on
assets is 8.6 percent, and total equity is $975,000. What is the equity multiplier? Return on equity?
Net income?
3. Using the DuPont Identity Y3K, Inc., has sales of $6,180, total assets of $3,680, and a debt–equity
ratio of .45. If its return on equity is 15 percent, what is its net income?
4. EFN The most recent financial statements for Cornell, Inc., are shown here:
INCOME STATEMENT BALANCE SHEET
Sales
Costs
Taxable income
Taxes (34%)
Net income
$43,000
30,200
$12,800
4,352
$ 8,448
Assets
Total
$104,500
$104,500
Debt
Equity
Total
$ 28,200
76,300
$104,500
Assets and costs are proportional to sales. Debt and equity are not. A dividend of $2,600 was paid, and
the company wishes to maintain a constant payout ratio. Next year’s sales are projected to be $50,310.
What is the external financing needed?
5. Sales and Growth The most recent financial statements for Weyland Co. are shown here:
INCOME STATEMENT BALANCE SHEET
Sales
Costs
Taxable income
Taxes (34%)
Net income
$67,400
39,600
$27,800
9,452
$18,348
Current assets
Fixed assets
Total
$ 19,000
141,000
$160,000
Long term debt
Equity
Total
$ 51,000
109,000
$160,000
Basic
(Questions 1–10)
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PART 1 Overview76
Assets and costs are proportional to sales. The company maintains a constant 30 percent dividend
payout ratio and a constant debt–equity ratio. What is the maximum increase in sales that can be
sustained assuming no new equity is issued?
6. Sustainable Growth If the SGS Corp. has an ROE of 14.5 percent and a payout ratio of 25 percent,
what is its sustainable growth rate?
7. Sustainable Growth Assuming the following ratios are constant, what is the sustainable growth rate?
Total asset turnover
Profit margin
Equity multiplier
Payout ratio
= 3.20
= 7.4%
= 1.45
= 60%
8. Calculating EFN The most recent financial statements for Incredible Edibles, Inc., are shown here
(assuming no income taxes):
INCOME STATEMENT BALANCE SHEET
Sales
Costs
Net income
$12,100
8,760
$ 3,340
Assets
Total
$28,300
$28,300
Debt
Equity
Total
$ 7,400
20,900
$28,300
Assets and costs are proportional to sales. Debt and equity are not. No d ividends are paid. Next year’s
sales are projected to be $14,399. What is the external financing needed?
9. External Funds Needed Cheryl Colby, CFO of Charming Florist Ltd., has created the firm’s pro forma
balance sheet for the next fiscal year. Sales are projected to grow by 15 percent to $211.6 million.
Current assets, fixed assets, and short-term debt are 20 percent, 90 percent, and 15 percent of sales,
respectively. The company pays out 40 percent of its net income in dividends. The company currently
has $32 million of long-term debt, and $16 million in common stock par value. The profit margin is
10 percent.
a. Construct the current balance sheet for the firm using the projected sales figure.
b. Based on the sales growth forecast, how much does the company need in external funds for the
upcoming fiscal year?
c. Construct the firm’s pro forma balance sheet for the next fiscal year and confirm the external funds
needed that you calculated in part (b).
10. Sustainable Growth Rate The Dent Company has an ROE of 13.15 percent and a payout ratio of
30 percent.
a. What is the company’s sustainable growth rate?
b. Can the company’s actual growth rate be different from its sustainable growth rate? Why or why not?
c. How can the company increase its sustainable growth rate?
11. Return on Equity Firm A and Firm B have debt/total asset ratios of 35 percent and 30 percent and
returns on total assets of 8 percent and 9 percent, respectively. Which firm has a greater return on equity?
12. Ratios and Foreign Companies Prince Albert Canning PLC had a net loss of £17,218 on sales of
£153,875. What was the company’s profit margin? Does the fact that these figures are quoted in a
foreign currency make any difference? Why? In dollars, sales were $223,180. What was the net loss in
dollars?
13. External Funds Needed The Optical Scam Company has forecast a sales growth rate of 18 percent
for next year. The current financial statements are shown below. Current assets, fixed assets, and
short-term debt are proportional to sales.
Intermediate
(Questions 11–23)
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CHAPTER 3 Financial Statements Analysis and Financial Models 77
INCOME STATEMENT
Sales
Costs
Taxable income
Taxes
Net income
Dividends
Addition to retained earnings
$1,450,000
3,067,500
$ 31,600,000
24,650,000
$ 6,950,000
2,432,500
$ 4,517,500
BALANCE SHEET
Assets Liabilities and Equity
Current assets
Fixed assets
Total assets
$10,750,000
32,100,000
$42,850,000
Short-term debt
Long-term debt
Common stock
Accumulated retained earnings
Total equity
Total liabilities and equity
$ 5,150,000
$ 7,700,000
$ 3,100,000
26,900,000
$30,000,000
$42,850,000
a. Using the equation from the chapter, calculate the external funds needed for next year.
b. Construct the firm’s pro forma balance sheet for next year and confirm the external funds needed
you calculated in part (a).
c. Calculate the sustainable growth rate for the company.
d. Can the company eliminate the need for external funds by changing its dividend policy? What other
options are available to the company to meet its growth objectives?
14. Days’ Sales in Receivables A company has net income of $263,000, a profit margin of 7.4 percent,
and an accounts receivable balance of $165,700. Assuming 80 percent of sales are on credit, what is
the company’s days’ sales in receivables?
15. Ratios and Fixed Assets The Arkham Company has a ratio of long-term debt to long-term debt
plus equity of .45 and a current ratio of 1.25. Current liabilities are $1,215, sales are $9,360,
profit margin is 7.5 percent, and ROE is 15.3 percent. What is the amount of the firm’s net
fixed assets?
16. Calculating the Cash Coverage Ratio PVA Inc.’s net income for the most recent year was $21,460.
The tax rate was 34 percent. The firm paid $7,340 in total interest expense and deducted $8,720 in
depreciation expense. What was the cash coverage ratio for the year?
17. Cost of Goods Sold Sexton Corp. has current liabilities of $263,000, a quick ratio of .75,
inventory turnover of 10.35, and a current ratio of 1.25. What is the cost of goods sold for the
company?
18. Common-Size and Common-Base-Year Financial Statements In addition to common-size financial
statements, common-base-year financial statements are often used. Common-base-year financial
statements are constructed by dividing the current-year account value by the base-year account value.
Thus, the result shows the growth rate in the account. Using the financial statements below, construct
the common-size balance sheet and common-base-year balance sheet for the company. Use 2016
as the base year.
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PART 1 Overview78
JARROW CORPORATION
2016 and 2017 Balance Sheets
ASSETS LIABILITIES AND OWNERS’ EQUITY
2016 2017 2013 2014
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and
equipment
Total assets
$ 17,928
28,565
48,607
$ 95,100
$422,852
$517,952
$ 22,608
32,170
57,173
$111,951
$488,184
$600,135
Current liabilities
Accounts receivable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and
paid-in surplus
Accumulated retained
earnings
Total
Total liabilities and owners’ equity
$ 25,192
32,379
$ 57,571
$ 46,200
$ 55,000
359,181
$414,181
$517,952
$ 32,198
39,476
$ 71,674
$ 70,000
$ 55,000
403,461
$458,461
$600,135
19. Full-Capacity Sales Breyfolge Mfg., Inc., is currently operating at only 92 percent of fixed asset
capacity. Current sales are $905,000. How fast can sales grow before any new fixed assets
are needed?
20. Fixed Assets and Capacity Usage For the company in the previous problem, suppose fixed
assets are currently $895,000 and sales are projected to grow to $997,000. How much in new
fixed assets is required to support this growth in sales? Assume the company operates at full
capacity.
21. Calculating EFN The most recent financial statements for Retro Machine, Inc., follow. Sales for 2017
are projected to grow by 20 percent. Interest expense will remain constant; the tax rate and
the dividend payout rate will also remain constant. Costs, other expenses, current assets, fixed
assets, and accounts payable increase spontaneously with sales. If the firm is operating at full capacity
and no new debt or equity are issued, what is the external financing needed to support the
20 percent growth rate in sales?
RETRO MACHINE INC
2016 Income Statement
Sales
Costs
Other expenses
Earnings before interest and taxes
Interest paid
Taxable income
Taxes (35%)
Net income
Dividends
Addition to retained earnings
$594,600
462,700
12,200
$119,700
8,960
$110,740
38,759
$ 71,981
$ 28,792
43,189
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CHAPTER 3 Financial Statements Analysis and Financial Models 79
RETRO MACHINE, INC
Balance Sheet as of December 31 , 2016
ASSETS LIABILITIES AND OWNERS’ EQUITY
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and equipment
Total assets
$ 17,070
24,560
58,650
$100,280
$278,780
$379,060
Current liabilities
Accounts payable
Notes payable
Total
Long-term debt
Owners’ equity
Common stock and paid-in surplus
Accumulated retained earnings
Total
Total liabilities and owners’ equity
$ 45,900
11,480
$ 57,380
$106,000
$ 95,000
120,680
$215,680
$379,060
22. Capacity Usage and Growth In the previous problem, suppose the firm was operating at only
85 percent capacity in 2016. What is EFN now?
23. Calculating EFN In Problem 21, suppose the firm wishes to keep its debt–equity ratio constant. What
is EFN now?
24. EFN and Internal Growth Redo Problem 21 using sales growth rates of 15 and 25 percent in addition
to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and use this
graph to determine the relationship between them.
25. EFN and Sustainable Growth Redo Problem 23 using sales growth rates of 30 and 35 percent in
addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and
use this graph to determine the relationship between them.
26. Constraints on Growth Dahlia, Inc., wishes to maintain a growth rate of 9 percent per year and
a debt–equity ratio of .40. The profit margin is 7.2 percent, and the ratio of total assets to sales is
constant at 2.25. Is this growth rate possible? To answer, determine what the dividend payout ratio
must be. How do you interpret the result?
27. EFN Define the following:
S = Previous year’s sales
A = Total assets
E = Total equity
g = Projected growth in sales
PM = Profit margin
b = Retention (plowback) ratio
Assuming that all debt is constant, show that EFN can be written as
EFN = −PM(S)b + [A − PM(S)b] × g
Hint: Asset needs will equal A × g. The addition to retained earnings will equal PM(S)b × (1 + g).
28. Sustainable Growth Rate Based on the results in Problem 27, show that the internal and sustainable
growth rates can be calculated as shown in equations 3.24 and 3.25. Hint: For the internal growth rate,
set EFN equal to zero and solve for g.
29. Sustainable Growth Rate In the chapter, we discussed one calculation of the sustainable growth rate as
Sustainable growth rate = ROE × b __________
1 − ROE × b
Challenge
(Questions 24–30)
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PART 1 Overview80
In practice, probably the most commonly used calculation of the sustainable growth rate is ROE × b.
This equation is identical to the two sustainable growth rate equations presented in the chapter if
the ROE is calculated using the beginning of period equity. Derive this equation from the equation
presented in the chapter.
30. Sustainable Growth Rate Use the sustainable growth rate equations from the previous problem to
answer the following questions. Grendl, Inc., had total assets of $410,000 and equity of $265,000 at
the beginning of the year. At the end of the year, the company had total assets of $460,000. During
the year the company sold no new equity. Net income for the year was $75,000 and dividends
were $32,000. What is the approximate sustainable growth rate for the company? What is the exact
sustainable growth rate? What is the approximate sustainable growth rate if you calculate ROE based
on the beginning of period equity? Is this number too high or too low? Why?
RATIOS AND FINANCIAL PLANNING AT EAST
COAST YACHTS
After Dan’s analysis of East Coast Yachts’ cash flow (at the end of our previous chapter), Larissa approached
Dan about the company’s performance and future growth plans. First, Larissa wants to find out how East Coast
Yachts is performing relative to its peers. Additionally, she wants to find out the future financing necessary to
fund the company’s growth. In the past, East Coast Yachts experienced difficulty in financing its growth plan,
in large part because of poor planning. In fact, the company had to turn down several large jobs because its
facilities were unable to handle the additional demand. Larissa hoped that Dan would be able to estimate the
amount of capital the company would have to raise next year so that East Coast Yachts would be better pre-
pared to fund its expansion plans.
To get Dan started with his analyses, Larissa provided the following financial statements. Dan then gath-
ered the industry ratios for the yacht manufacturing industry.
WHAT’S ON THE WEB?
1. DuPont Identity You can find financial statements for Walt Disney Company at Disney’s home page,
disney.com. For the three most recent years, calculate the DuPont identity for Disney. How has ROE
changed over this period? How have changes in each component of the DuPont identity affected ROE
over this period?
2. Ratio Analysis You want to examine the financial ratios for Starwood Hotels & Resorts. Go to www.
reuters.com and type in the ticker symbol for the company (HOT). Now find financial ratios for Starwood
and the industry and sector averages for each ratio.
a. What do TTM and MRQ mean?
b. How do Starwood’s recent profitability ratios compare to their values over the past five years? To the
industry averages? To the sector averages? Which is the better comparison group for Starwood: the
industry or sector averages? Why?
c. In what areas does Starwood seem to outperform its competitors based on the financial ratios?
Where does Starwood seem to lag behind its competitors?
3. Applying Percentage of Sales Locate the most recent annual financial statements for DuPont at
www.dupont.com under the “Investors” link. Locate the annual report. Using the growth in sales for the
most recent year as the projected sales growth for next year, construct a pro forma income statement
and balance sheet. Based on these projections, what are the external funds needed?
4. Growth Rates You can find the home page for Caterpillar, Inc., at www.cat.com. Go to the web page
and find the most recent annual report. Using the information from the financial statements, what is the
sustainable growth rate?
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CHAPTER 3 Financial Statements Analysis and Financial Models 81
EAST COAST YACHTS
2017 Income Statement
Sales
Cost of goods sold
Selling, general, and administrative
Depreciation
EBIT
Interest expense
EBT
Taxes
Net income
Dividends
Retained earnings
$611,582,000
431,006,000
73,085,700
19,958,400
$ 87,531,900
11,000,900
$ 76,531,000
30,612,400
$ 45,918,600
$ 17,374,500
$ 28,544,100
EAST COAST YACHTS
2017 Balance Sheet
Current assets
Cash and equivalents
Accounts receivable
Inventory
Other
Total current assets
Fixed assets
Property, plant, and equipment
Less accumulated depreciation
Net property, plant, and equipment
Intangible assets and others
Total fixed assets
Total assets
$ 11,119,700
18,681,500
20,149,650
1,172,200
$ 51,123,050
$457,509,600
(113,845,900)
$343,663,700
6,772,000
$350,435,700
$401,558,750
Current liabilities
Accounts payable
Accrued expenses
Total current liabilities
Long-term debt
Total long-term liabilities
Stockholders’ equity
Preferred stock
Common stock
Capital surplus
Accumulated retained earnings
Less treasury stock
Total equity
Total liabilities and shareholders’ equity
$ 44,461,550
6,123,200
$ 50,584,750
$169,260,000
$169,260,000
$ 1,970,000
37,583,700
28,116,300
161,564,000
(47,520,000)
$181,714,000
$401,558,750
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PART 1 Overview82
1. East Coast Yachts uses a small percentage of preferred stock as a source of financing. In calculating the
ratios for the company, should preferred stock be included as part of the company’s total equity?
2. Calculate all of the ratios listed in the industry table for East Coast Yachts.
3. Compare the performance of East Coast Yachts to the industry as a whole. For each ratio, comment on
why it might be viewed as positive or negative relative to the industry. Suppose you create an inventory
ratio calculated as inventory divided by current liabilities. How would you interpret this ratio? How does
East Coast Yachts compare to the industry average for this ratio?
4. Calculate the sustainable growth rate for East Coast Yachts. Calculate external funds needed (EFN)
and prepare pro forma income statements and balance sheets assuming growth at precisely this rate.
Recalculate the ratios in the previous question. What do you observe?
5. As a practical matter, East Coast Yachts is unlikely to be willing to raise external equity capital, in part
because the shareholders don’t want to dilute their existing ownership and control positions. However,
East Coast Yachts is planning for a growth rate of 20 percent next year. What are your conclusions and
recommendations about the feasibility of East Coast’s expansion plans?
6. Most assets can be increased as a percentage of sales. For instance, cash can be increased by any
amount. However, fixed assets often must be increased in specific amounts since it is impossible, as
a practical matter, to buy part of a new plant or machine. In this case, a company has a “staircase” or
“lumpy” fixed cost structure. Assume that East Coast Yachts is currently producing at 100 percent of
capacity and sales are expected to grow at 20 percent. As a result, to expand production, the company
must set up an entirely new line at a cost of $95,000,000. Prepare the pro forma income statement
and balance sheet. What is the new EFN with these assumptions? What does this imply about capacity
utilization for East Coast Yachts next year?
Yacht Industry Rat ios
LOWER QUARTILE MEDIAN UPPER QUARTILE
Current ratio .86 1.51 1.97
Quick ratio .43 .75 1.01
Total asset turnover 1.10 1.27 1.46
Inventory turnover 12.18 14.38 16.43
Receivables turnover 10.25 17.65 22.43
Debt ratio .32 .56 .61
Debt–equity ratio .83 1.13 1.44
Equity multiplier 1.83 2.13 2.44
Interest coverage 5.72 8.21 10.83
Profit margin 5.02% 7.48% 9.05%
Return on assets 7.05% 10.67% 14.16%
Return on equity 14.06% 19.32% 26.41%
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CHAPTER 4 Discounted Cash Flow Valuation 83
The signing of big-name athletes is often accompanied by great fanfare, but the numbers are often
misleading. For example, in late 2015, catcher Matt Weiters reached a one-year deal with the Baltimore
Orioles, signing a contract with a reported value of $15.8 million. Not bad, especially for someone who
makes a living using the “tools of ignorance” (jock jargon for a catcher’s equipment). Another example
is the contract signed by David Price of the Boston Red Sox, which had a stated value of $217 million.
It looks like Matt and David did pretty well, but the Orioles weren’t done as they signed
first baseman Chris Davis to a contract that has a stated value of $161 million, but this amount
was actually payable over several years. The contract called for $17 million per year for the
first six years, plus $42 million in future salary to be paid in the years 2023 through 2037.
David Price’s payments were similarly spread over time, although his payments were only
for seven years. Because two of the three contracts called for payments that are made at
future dates, we must consider the time value of money, which means none of these players
received the quoted amounts. How much did they really get? This chapter gives you the “tools
of knowledge” to answer this question.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
OPENING
CASE
Discounted Cash Flow Valuation 4
PART TWO: VALUATION AND CAPITAL BUDGETING
4.1 VALUATION: THE ONE-PERIOD CASE
Keith Vaughan is trying to sell a piece of raw land in Alaska. Yesterday, he was offered
$10,000 for the property. He was about ready to accept the offer when another indi-
vidual offered him $11,424. However, the second offer was to be paid a year from now.
Keith has satisfied himself that both buyers are honest and financially solvent, so he has
no fear that the offer he selects will fall through. These two offers are pictured as cash
flows in Figure 4.1. Which offer should Mr. Vaughan choose?
Jim Ellis, Keith’s financial adviser, points out that if Keith takes the first offer, he could invest
the $10,000 in a bank at an insured rate of 12 percent.1 At the end of one year, he would have:
$10,000 + (.12 × $10,000) = $10,000 × 1.12 = $11,200
Return of Interest
principal
Because this is less than the $11,424 Keith could receive from the second offer, Mr. Ellis
recommends that he take the latter. This analysis uses the concept of future value, or
compound value, which is the value of a sum after investing over one or more periods.
The compound, or future value, of $10,000 at 12 percent is $11,200.
An alternative method employs the concept of present value. One can determine
present value by asking the following question: How much money must Keith put in
1 At this point, the savvy reader could ask where one could actually find guaranteed debt yielding 12%. One example is Puerto Rico’s recent
constitutionally guaranteed debt yielding a similar rate. However, in general, we concede that government guaranteed debt yielding double
digit is very unusual and we should point out that Puerto Rico defaulted on its debt in July 2016.
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84
the bank today at 12 percent so that he will have $11,424 next year? We can write this
algebraically as:
PV × 1.12 = $11,424
We want to solve for present value (PV), the amount of money that yields $11,424 if
invested at 12 percent today. Solving for PV, we have:
PV = $11,424 _______
1.12
= $10,200
The formula for PV can be written as:
Present Value of Investment:
PV = C 1 ______
1 + r
[4.1]
where C1 is cash flow at Date 1 and r is the rate of return that Keith Vaughan requires on
his land sale. It is sometimes referred to as the discount rate.
Present value analysis tells us that a payment of $11,424 to be received next year has a
present value of $10,200 today. In other words, at a 12 percent interest rate, Mr. Vaughan
is indifferent between $10,200 today or $11,424 next year. If you gave him $10,200 today,
he could put it in the bank and receive $11,424 next year.
Because the second offer has a present value of $10,200, whereas the first offer is for only
$10,000, present value analysis also indicates that Mr. Vaughan should take the second offer. In
other words, both future value analysis and present value analysis lead to the same decision. As it
turns out, present value analysis and future value analysis must always lead to the same decision.
As simple as this example is, it contains the basic principles that we will be working
with over the next few chapters. We now use another example to develop the concept of
net present value.
0 1
$10,000 $11,424Alternative
sale prices
Year
FIGURE 4.1
Cash Flow for Mr. Vaughan’s
Sale
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Diane Badame, a financial analyst at Kaufman & Broad, a leading real estate firm, is thinking about rec-
ommending that Kaufman & Broad invest in a piece of land that costs $85,000. She is certain that next
year the land will be worth $91,000, a sure $6,000 gain. Given that the guaranteed interest rate in the
bank is 10 percent, should Kaufman & Broad undertake the investment in land? Ms. Badame’s choice is
described in Figure 4.2 with the cash flow time chart.
Present Value
FIGURE 4.2 Cash Flows for Land Investment
0 1
-$85,000
$91,000Cash inflow
Time
Cash outflow
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A moment’s thought should be all it takes to convince her that this is not an attractive business deal.
By investing $85,000 in the land, she will have $91,000 available next year. Suppose, instead, that
Kaufman & Broad puts the same $85,000 into the bank. At the interest rate of 10 percent, this $85,000
would grow to:
(1 + .10) × $85,000 = $93,500
next year.
It would be foolish to buy the land when investing the same $85,000 in the financial market would
produce an extra $2,500 (that is, $93,500 from the bank minus $91,000 from the land investment).
This is a future value calculation.
Alternatively, she could calculate the present value of the sale price next year as:
Present value = $91,000 _______
1.10
= $82,727.27
Because the present value of next year’s sales price is less than this year’s purchase price of $85,000,
present value analysis also indicates that she should not recommend purchasing the property.
Frequently, business people want to determine the exact cost or benefit of a decision.
The decision to buy this year and sell next year can be evaluated as
Net Present Value of Investment:
–$2,273 = –$85,000 + $91,000 ________
1.10
Cost of land
today
Present value of
next year’s sales price
The formula for NPV can be written as:
NPV = –Cost + PV [4.2]
Equation 4.2 says that the value of the investment is –$2,273, after stating all the benefits
and all the costs as of Date 0. We say that –$2,273 is the net present value (NPV) of
the investment. That is, NPV is the present value of future cash flows minus the
present value of the cost of the investment. Because the net present value is negative,
Diane Badame should not recommend purchasing the land.
Both the Vaughan and the Badame examples deal with perfect certainty. That is, Keith
Vaughan knows with perfect certainty that he could sell his land for $11,424 next year.
Similarly, Diane Badame knows with perfect certainty that Kaufman & Broad could
receive $91,000 for selling its land. Unfortunately, business people frequently do not know
future cash flows. This uncertainty is treated in the next example.
Professional Artworks, Inc., is a firm that speculates in modern paintings. The manager is thinking of buying
an original Picasso for $400,000 with the intention of selling it at the end of one year. The manager expects
that the painting will be worth $480,000 in one year. The relevant cash flows are depicted in Figure 4.3.
Of course, this is only an expectation—the painting could be worth more or less than $480,000.
Suppose the guaranteed interest rate granted by banks is 10 percent. Should the firm purchase the
piece of art?
Our first thought might be to discount at the interest rate, yielding:
$480,000
_________
1.10
= $436,364
Uncertainty and Valuation
(continued )
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Because $436,364 is greater than $400,000, it looks at first glance as if the painting should be
purchased. However, 10 percent is the return we have assumed one can earn on a riskless investment.
Because the painting is quite risky, a higher discount rate is called for. The manager chooses a rate of
25 percent to reflect this risk. In other words, he argues that a 25 percent expected return is fair
compensation for an investment as risky as this painting.
The present value of the painting becomes:
$480,000
_________
1.25
= $384,000
Thus, the manager believes that the painting is currently overpriced at $400,000 and does not make the
purchase.
FIGURE 4.3 Cash Flows for Investment in Painting
0 1
-$400,000
$480,000Expected cash inflow
Time
Cash outflow
The preceding analysis is typical of decision making in today’s corporations, though
real-world examples are, of course, much more complex. Unfortunately, any example with
risk poses a problem not faced by a riskless example. In an example with riskless cash
flows, the appropriate required return (i.e., discount rate) can be determined by checking
the current returns on U.S. Treasury securities. Conceptually, the correct discount rate for
a risky expected cash flow is the expected return available in the market on other invest-
ments of the same risks. This is the correct discount rate to apply because it represents the
economic opportunity cost to investors. It is the expected return they will require before
committing funding to an investment. However, the actual selection of the discount rate for
a risky investment is quite a difficult task. We don’t know at this point whether the discount
rate on the painting should be 11 percent, 25 percent, 52 percent, or some other percentage.
Because the choice of a discount rate is so difficult, we merely wanted to broach the
subject here. We must wait until the specific material on risk and return is covered in later
chapters before a risk-adjusted analysis can be presented.
4.2 THE MULTIPERIOD CASE
The previous section presented the calculation of future value and present value for one
period only. We will now perform the calculations for the multiperiod case.
Future Value and Compounding
Suppose an individual were to make a loan of $1. At the end of the first year, the borrower
would owe the lender the principal amount of $1 plus the interest on the loan at the interest rate
of r. For the specific case where the interest rate is, say, 9 percent, the borrower owes the lender:
$1 × (1 + r ) = $1 × 1.09 = $1.09
At the end of the year, though, the lender has two choices. She can either take the $1.09—
or, more generally, (1 + r)—out of the financial market, or she can leave it in and lend
it again for a second year. The process of leaving the money in the financial market and
lending it for another year is called compounding.
ExcelMaster
coverage online
www.mhhe.com/RossCore5e
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Suppose that the lender decides to compound her loan for another year. She does this
by taking the proceeds from her first one-year loan, $1.09, and lending this amount for the
next year. At the end of next year, then, the borrower will owe her:
$1 × (1 + r) × (1 + r) = $1 × (1 + r)2 = 1 + 2r + r2
$1 × (1.09) × (1.09) = $1 × (1.09)2 = $1 + $.18 + $.0081 = $1.1881
This is the total she will receive two years from now by compounding the loan.
In other words, by providing a ready opportunity for lending, the capital market enables
the investor to transform $1 today into $1.1881 at the end of two years. At the end of three
years, the total cash will be $1 × (1.09)3 = $1.2950.
The most important point to notice is that the total amount that the lender receives is not
just the $1 that she lent out plus two years’ worth of interest on $1:
2 × r = 2 × $.09 = $.18
The lender also gets back an amount r2, which is the interest in the second year on the
interest that was earned in the first year. The term, 2 × r, represents simple interest over
the two years, and the term, r2, is referred to as the interest on interest. In our example this
latter amount is exactly:
r2 = $.092 = $.0081
When cash is invested at compound interest, each interest payment is reinvested. With
simple interest, the interest is not reinvested. Benjamin Franklin’s statement, “Money
makes money and the money that money makes makes more money,” is a colorful way
of explaining compound interest. The difference between compound interest and simple
interest is illustrated in Figure 4.4. In this example, the difference does not amount to
much because the loan is for $1. If the loan were for $1 million, the lender would receive
$1,188,100 in two years’ time. Of this amount, $8,100 is interest on interest. The lesson
is that those small numbers beyond the decimal point can add up to big dollar amounts
when the transactions are for big amounts. In addition, the longer-lasting the loan, the more
important interest on interest becomes.
The general formula for an investment over many periods can be written as:
Future Value of an Investment:
FV = C0 × (1 + r )T [4.3]
FIGURE 4.4
Simple and Compound
Interest
$1.295
$1.270
$1.188
$1.180
$1.09
$1
1 year 2 years 3 years
The purple-shaded area represents the initial investment.
The green-shaded area represents the simple interest.
The blue-shaded area represents interest on interest.
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where C0 is the cash to be invested at Date 0 (i.e., today), r is the interest rate per period,
and T is the number of periods over which the cash is invested.
Suh-Pyng Ku has put $500 in a savings account at the First National Bank of Kent. The account earns
7 percent, compounded annually. How much will Ms. Ku have at the end of three years?
$500 × 1.07 × 1.07 × 1.07 = $500 × (1.07)3 = $612.52
Figure 4.5 illustrates the growth of Ms. Ku’s account.
Interest on Interest
FIGURE 4.5 Suh-Pyng Ku’s Savings Account
0 01 12 23 3
$612.52
$500D
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la
rs
Time Time
$612.52
-$500
Jay Ritter invested $1,000 in the stock of the SDH Company. The company pays a current dividend of
$2, which is expected to grow by 20 percent per year for the next two years. What will the dividend
of the SDH Company be after two years?
$2 × (1.20)2 = $2.88
Figure 4.6 illustrates the increasing value of SDH’s dividends.
Compound Growth
FIGURE 4.6 The Growth of the SDH Dividends
0 21
$2.00
D
ol
la
rs
Time Time
0 1 2
$2.88
$2.40
$2.88
$2.40
$2.00
Cash inflows
The two previous examples can be calculated in any one of four ways. The computa-
tions could be done by hand, by calculator, by spreadsheet, or with the help of a table.
The appropriate table is Table A.3, which appears in the back of the text. This table
presents future value of $1 at the end of T periods. The table is used by locating the
appropriate interest rate on the horizontal axis and the appropriate number of periods on
the vertical axis.
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For example, Suh-Pyng Ku would look at the following portion of Table A.3:
INTEREST RATE
PERIOD 6% 7% 8%
1 1.0600 1.0700 1.0800
2 1.1236 1.1449 1.1664
3 1.1910 1.2250 1.2597
4 1.2625 1.3108 1.3605
She could calculate the future value of her $500 as:
$500 × 1.2250 = $612.50
Initial investment Future value of $1
In the example concerning Suh-Pyng Ku, we gave you both the initial investment and
the interest rate and then asked you to calculate the future value. Alternatively, the interest
rate could have been unknown, as shown in the following example:
Gareth James, who recently won $10,000 in the lottery, wants to buy a car in five years. Gareth
estimates that the car will cost $16,105 at that time. His cash flows are displayed in Figure 4.7.
What interest rate must he earn to be able to afford the car?
Finding the Rate
The ratio of purchase price to initial cash is:
$16,105
________
$10,000
= 1.6105
Thus, he must earn an interest rate that allows $1 to become $1.6105 in five years. Table A.3 tells us that
an interest rate of 10 percent will allow him to purchase the car.
One can express the problem algebraically as:
$10,000 × (1 × r )5 = $16,105
where r is the interest rate needed to purchase the car. Because $16,105/$10,000 = 1.6105, we have
(1 + r )5 = 1.6105
Either the table or a calculator solves for r.
FIGURE 4.7 Cash Flows for Purchase of Gareth James’ Car
0
5
-$16,105
Cash inflow
Time
Cash outflow
$10,000
The Power of Compounding: A Digression
Most people who have had any experience with compounding are impressed with its
power over long periods of time. In fact, compound interest has been described as the
“eighth wonder of the world” and “the most powerful force in the universe.”2 Take the
2 These quotes are often attributed to Albert Einstein (particularly the second one), but whether he really said either is not known. The first
quote is also often attributed to Baron Rothschild, John Maynard Keynes, Benjamin Franklin, and others.
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stock market, for example. Ibbotson and Sinquefield have calculated what the stock market
returned as a whole from 1926 through 2015.3 They find that one dollar placed in these
stocks at the beginning of 1926 would have been worth $5,384.08 at the end of 2015.
This is 10.02 percent compounded annually for 90 years, i.e., ($1.1002)90 = $5,384.08,
ignoring a small rounding error.
The example illustrates the great difference between compound and simple interest.
At 10.02 percent, simple interest on $1 is .1002 cents a year (i.e., $.1002). Simple interest
over 90 years is $9.01 (90 × $.1002). That is, an individual withdrawing .1002 cents every
year would have withdrawn $9.01 (90 × $.1002) over 90 years. This is quite a bit below the
$5,384.08 that was obtained by reinvestment of all principal and interest.
The results are more impressive over even longer periods of time. A person with no
experience in compounding might think that the value of $1 at the end of 180 years would
be twice the value of $1 at the end of 90 years, if the yearly rate of return stayed the same.
Actually the value of $1 at the end of 180 years would be the square of the value of $1 at
the end of 90 years. That is, if the annual rate of return remained the same, a $1 investment
in common stocks should be worth $28,988,317.45 [$1 × (5,384.08 × 5,384.08)].
A few years ago, an archaeologist unearthed a relic stating that Julius Caesar lent
the Roman equivalent of one penny to someone. Since there was no record of the penny
ever being repaid, the archaeologist wondered what the interest and principal would be
if a descendant of Caesar tried to collect from a descendant of the borrower in the 20th
century. The archaeologist felt that a rate of 6 percent might be appropriate. To his sur-
prise, the principal and interest due after more than 2,000 years was vastly greater than
the entire wealth on earth.
The power of compounding can explain why the parents of well-to-do families fre-
quently bequeath wealth to their grandchildren rather than to their children. That is, they
skip a generation. The parents would rather make the grandchildren very rich than make
the children moderately rich. We have found that in these families the grandchildren have a
more positive view of the power of compounding than do the children.
3 Stocks, Bonds, Bills, and Inflation [SBBI]. 2016 Yearbook, Ibbotson Associates, Chicago, 2016.
Present Value and Discounting
We now know that an annual interest rate of 9 percent enables the investor to transform
$1 today into $1.1881 two years from now. In addition, we would like to know:
How much would an investor need to lend today so that she could receive $1 two years from
today?
Some people have said that it was the best real estate deal in history. Peter Minuit, director-general of
New Netherlands, the Dutch West India Company’s colony in North America, in 1626 allegedly bought
Manhattan Island from native Americans for 60 guilders’ worth of trinkets. This sounds cheap, but did
the Dutch really get the better end of the deal? It is reported that 60 guilders was worth about $24 at
the prevailing exchange rate. If the native Americans had sold the trinkets at a fair market value and
invested the $24 at 5 percent (tax-free), it would now, about 390 years later, be worth about $4.4 billion.
Today, Manhattan is undoubtedly worth more than $4.4 billion, and so, at a 5 percent rate of return, the
native Americans got the worst of the deal. However, if invested at 10 percent, the amount of money
they received would be worth about:
$24(1 + r )T = 24 × 1.1390 = $330.7 quadrillion
This is a lot of money. In fact, $330.7 quadrillion is more than all the real estate in the world is worth
today. Note that no one in the history of the world has ever been able to find an investment yielding 10
percent every year for 390 years.
How Much for That Island?
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Algebraically, we can write this as:
PV × (1.09)2 = $1
In the preceding equation, PV stands for present value, the amount of money we must lend
today in order to receive $1 in two years’ time.
Solving for PV in this equation, we have:
PV = $1 _______
1.1881
= $.84
This process of calculating the present value of a future cash flow is called discounting.
It is the opposite of compounding. The difference between compounding and discounting
is illustrated in Figure 4.8.
To be certain that $.84 is in fact the present value of $1 to be received in two years, we
must check whether or not, if we loaned out $.84 and rolled over the loan for two years,
we would get exactly $1 back. If this were the case, the capital markets would be saying
that $1 received in two years’ time is equivalent to having $.84 today. Checking the exact
numbers, we get:
$.84168 × 1.09 × 1.09 = $1
In other words, when we have capital markets with a sure interest rate of 9 percent, we
are indifferent between receiving $.84 today or $1 in two years. We have no reason to treat
these two choices differently from each other, because if we had $.84 today and loaned
it out for two years, it would return $1 to us at the end of that time. The value [1/(1.09)2]
is called the present value factor. It is the factor used to calculate the present value of a
future cash flow.
In the multiperiod case, the formula for PV can be written as:
Present Value of Investment:
PV = CT ______
(1 + r)T
[4.4]
where CT is cash flow at Date T and r is the appropriate discount rate.
FIGURE 4.8
Compounding and
Discounting
D
ol
la
rs
Future years
$1,000
101
Compounding
at 9%
$2,367.36
Compound interest
Discounting at
9%
$422.41
$1,900
Simple interest
$1,000
2 3 4 5 6 7 8 9
The top line shows the growth of $1,000 at compound interest with the funds
invested at 9 percent: $1,000 × (1.09)10 = $2,367.36. Simple interest is shown on
the next line. It is $1,000 + [10 × ($1,000 × .09)] = $1,900. The bottom line shows
the discounted value of $1,000 if the interest rate is 9 percent.
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92
In the preceding example, we gave both the interest rate and the future cash flow.
Alternatively, the interest rate could have been unknown.
Harry DeAngelo will receive $10,000 three years from now. Harry can earn 8 percent on his
investments, so the appropriate discount rate is 8 percent. What is the present value of his future
cash flow?
PV = $10,000 × (
1
_____
1.08
)
3
= $10,000 × .7938
= $7,938
Figure 4.9 illustrates the application of the present value factor to Harry’s investment.
When his investments grow at an 8 percent rate of interest, Harry DeAngelo is equally inclined
toward receiving $7,938 now and receiving $10,000 in three years’ time. After all, he could convert
the $7,938 he receives today into $10,000 in three years by lending it at an interest rate of
8 percent.
Harry DeAngelo could have reached his present value calculation in one of three ways.
The computation could have been done by hand, by calculator, or with the help of Table A.1,
which appears in the back of the text. This table presents present value of $1 to be received
after T periods. The table is used by locating the appropriate interest rate on the horizontal and
the appropriate number of periods on the vertical. For example, Harry De Angelo would look at
the following portion of Table A.1:
INTEREST RATE
PERIOD 7% 8% 9%
1 .9346 .9259 .9174
2 .8734 .8573 .8417
3 .8163 .7938 .7722
4 .7629 .7350 .7084
The appropriate present value factor is .7938.
Multiperiod Discounting
FIGURE 4.9 Discounting Harry DeAngelo’s Opportunity
0 1 2
$7,938D
ol
la
rs
Time
0 3
$10,000
$10,000
Cash inflows
1 2
3 Time
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A customer of the Beatty Corp. wants to buy a tugboat today. Rather than paying immediately, he
will pay $50,000 in three years. It will cost the Beatty Corp. $38,610 to build the tugboat immediately.
The relevant cash flows to Beatty Corp. are displayed in Figure 4.10. By charging what interest rate
would the Beatty Corp. neither gain nor lose on the sale?
Finding the Rate
FIGURE 4.10 Cash Flows for Tugboat
0
-$38,610
$50,000Cash inflows
Time
Cash outflows
3
The ratio of construction cost to sale price is:
$38,610
________
$50,000
= .7722
We must determine the interest rate that allows $1 to be received in three years to have a present value
of $.7722. Table A.1 tells us that 9 percent is that interest rate.
Dennis Draper has won the Kentucky state lottery and will receive the following set of cash flows over
the next two years:
YEAR CASH FLOW
1 $2,000
2 5,000
Mr. Draper can currently earn 6 percent in his money market account, so, the appropriate discount rate
is 6 percent. The present value of the cash flows is:
YEAR CASH FLOW × PRESENT VALUE FACTOR = PRESENT VALUE
1 $2,000 × 1 _____
1.06
= $2,000 × .943 = $1,887
2 $5,000 × (
1
_____
1.06
)
2
= $5,000 × .890 = 4,450
Total $6,337
In other words, Mr. Draper is equally inclined toward receiving $6,337 today and receiving $2,000 and
$5,000 over the next two years.
Cash Flow Valuation
Frequently, an investor or a business will receive more than one cash flow. The present
value of the set of cash flows is the sum of the present values of the individual cash flows.
This is illustrated in the following examples:
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94
Finance.com has an opportunity to invest in a new high-speed computer that costs $50,000. The com-
puter will generate cash flows (from cost savings) of $25,000 one year from now, $20,000 two years
from now, and $15,000 three years from now. The computer will be worthless after three years, and
no additional cash flows will occur. Finance.com has determined that the appropriate discount rate is
7 percent for this investment. Should Finance.com make this investment in a new high-speed computer?
What is the present value of the investment?
The cash flows and present value factors of the proposed computer are as follows:
CASH FLOWS PRESENT VALUE FACTOR
Year 0 –$50,000 1 = 1
1 25,000
1
____
1.07
= .9346
2 20,000 (
1
_____
1.07
)
2
= .8734
3 15,000 (
1
_____
1.07
)
3
= .8163
The present values of the cash flows are:
Cash flows × Present value factor = Present value
Year 0 –$50,000 × 1 = –$50,000.00
1 $25,000 × .9346 = 23,364.49
2 $20,000 × .8734 = 17,468.77
3 $15,000 × .8163 = 12,244.47
Total $ 3,077.73
Finance.com should invest in a new high-speed computer because the present value of its future cash
flows is greater than its cost. The NPV is $3,077.73.
NPV
The Algebraic Formula
To derive an algebraic formula for the net present value of a cash flow, recall that the PV
of receiving a cash flow one year from now is:
PV = C1/(1 + r)
and the PV of receiving a cash flow two years from now is:
PV = C2 /(1 + r )2
We can write the NPV of a T-period project as:
NPV = −C0 +
C1 _____
1 + r
+ C2 ______
(1 + r)2
+ . . . + CT ______
(1 + r)T
= −C0 + ∑
t =1
T
Ci ______
(1 + r)T
[4.5]
The initial flow, −C0, is assumed to be negative because it represents an investment.
The Σ is shorthand for the sum of the series.
We will close this section by answering the question we posed at the beginning of the
chapter concerning baseball player Chris Davis’ contract. The terms of the contract called
for $17 million per year for 2016 through 2022, $3.5 million per year for 2023 through
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2032, and $1.4 million per year for 2033 through 2037. If 12 percent is the appropriate
interest rate, what kind of deal did the Oriole’s first baseman snag?
To answer, we can calculate the present value by discounting each year’s salary back to
the present as follows (notice we assume that all the payments are made at year-end and
that 12 percent is the appropriate discount rate):
Year 1 (2016): $17,000,000 × 1/1.121 = $15,178,571.43
Year 2 (2017): $17,000,000 × 1/1.122 = $13,552,295.92
Year 3 (2018): $17,000,000 × 1/1.123 = $12,100,264.21
. . . .
Year 8 (2023): $ 3,500,000 × 1/1.128 = $ 1,413,591.30
. . . .
Year 22 (2037): $ 1,400,000 × 1/1.1222 = $ 115,699.51
If you fill in the missing rows and then add (do it for practice), you will see that Chris’
contract had a present value of about $87.3 million, or only about 54 percent of the stated
$161 million value (but still pretty good).
As you have probably noticed, doing extensive present value calculations can get to
be pretty tedious, so a nearby Spreadsheet Techniques box shows how we recommend
doing them. As an application, we take a look at lottery payouts in a nearby Finance
Matters box.
We can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows.
Notice that we have calculated the present values one at a time and added them up:
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 1
2 2
A B C D E
What is the present value of $200 in one year, $400 the next year, $600 the next year, and
$800 the last year if the discount rate is 12 percent?
Rate: .12
Year Cash flows Present values Formula used
1 $200 $178.57 =PV($B$7,A10,0,-B10)
2 $400 $318.88 =PV($B$7,A11,0,-B11)
3 $600 $427.07 =PV($B$7,A12,0,-B12)
4 $800 $508.41 =PV($B$7,A13,0,-B13)
Total PV: $1,432.93 =SUM(C10:C13)
Notice the negative signs inserted in the PV formulas. These just make the present values have
positive signs. Also, the discount rate in cell B7 is entered as $B$7 (an “absolute” reference)
because it is used over and over. We could have just entered “.12” instead, but our approach is more
flexible.
Using a spreadsheet to value multiple future cash flows
How to Calculate Present Values
wi th Mult ip le Future Cash F lows
Using a Spreadsheet
SPREADSHEET TECHNIQUES
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96
JACKPOT!
If you or someone you know is a regular lottery player, you probably already understand that you are 1,300 times more
likely to get struck by lightning than you are to win a big lottery jackpot. What are your odds of winning? Below you will
find a table with your chances of winning the Mega Millions Lottery compared to other events.
Odds of winning a Mega Millions jackpot 1:175,711,536*
Odds of being killed in a fireworks discharge 1:652,046
Odds of being killed by a dog 1:144,899
Odds of being killed by lightning 1:134,906
Odds of being killed in an earthquake 1:97,807
Odds of being killed by bees 1:79,842
Odds of being killed by air transport 1:7,178
Odds of being killed by or in a car 1:368
*Source: Mega Millions Lottery website. All other odds from the National Safety Council.
Sweepstakes may have different odds than lotteries, but these odds may not be much better. At one time, the larg-
est advertised potential grand prize ever was Pepsi’s “Play for a Billion,” which, you guessed it, had a $1 billion (billion!)
prize. Not bad for a day’s work, but you still have to read the fine print. It turns out that the winner would be paid $5
million per year for the next 20 years, $10 million per year for years 21 through 39, and a lump sum $710 million in 40
years. From what you have learned, you know the value of the sweepstakes wasn’t even close to $1 billion. In fact, at an
interest rate of 10 percent, the present value is about $70.7 million.
In January 2016, three winners split the record $1.584 billion Powerball jackpot. Each winner was given the option of
receiving the jackpot as $328 million immediately or $7.9 million per year for the next 30 years, with the first payment to
be made immediately. In a unique twist, the payments will increase at 5 percent pear year. So, what discount rate does
this imply? After you learn about growing annuities in the next section, see if you don’t agree that the interest rate is
about 2.79 percent.
Some lotteries make your decision a little tougher. The Ontario Lottery will pay you either $2,000 a week for the
rest of your life or $1.3 million now. (That’s in Canadian dollars, or “loonies,” by the way.) Of course, there is the chance
you might die in the near future, so the lottery guarantees that your heirs will collect the $2,000 weekly payments
until the 20th anniversary of the first payment, or until you would have turned 91, whichever comes first. This payout
scheme complicates your decision quite a bit. If you live for only the 20-year minimum, the break-even interest rate
between the two options is about 5.13 percent per year, compounded weekly. If you expect to live longer than the
20-year minimum, you might be better off accepting $2,000 per week for life. Of course, if you manage to invest the
$1.3 million lump sum at a rate of return of about 8 percent per year (compounded weekly), you can have your cake
and eat it too because the investment will return $2,000 at the end of each week forever! Taxes complicate the deci-
sion in this case because the lottery payments are all on an after-tax basis. Thus, the rates of return in this example
would have to be after-tax as well.
FINANCE MATTERS
4.3 COMPOUNDING PERIODS
So far we have assumed that compounding and discounting occur yearly. Sometimes
compounding may occur more frequently than just once a year. For example, imagine
that a bank pays a 10 percent interest rate “compounded semiannually.” This means that a
$1,000 deposit in the bank would be worth $1,000 × 1.05 = $1,050 after six months, and
$1,050 × 1.05 = $1,102.50 at the end of the year.
ExcelMaster
coverage online
www.mhhe.com/RossCore5e
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4 By law, lenders are required to report the APR on all loans. In this text, we compute the APR as the interest rate per period multiplied by the
number of periods in a year. According to federal law, the APR is a measure of the cost of consumer credit expressed as a yearly rate and it
includes interest and certain noninterest charges and fees. In practice, the APR can be much higher than the interest rate on the loan if the
lender charges substantial fees that must be included in the federally mandated APR calculation.
The end-of-the-year wealth can be written as:
$1,000 (1 +
.10 ___
2
)
2
= $1,000 × (1.05)2 = $1,102.50
Of course, a $1,000 deposit would be worth $1,100 (= $1,000 × 1.10) with yearly
compounding. Note that the future value at the end of one year is greater with semian-
nual compounding than with yearly compounding. With yearly compounding, the original
$1,000 remains the investment base for the full year. The original $1,000 is the investment
base only for the first six months with semiannual compounding. The base over the second
six months is $1,050. Hence, one gets interest on interest with semiannual compounding.
Because $1,000 × 1.1025 = $1,102.50, 10 percent compounded semiannually is the
same as 10.25 percent compounded annually. In other words, a rational investor could not
care less whether she is quoted a rate of 10 percent compounded semiannually or a rate of
10.25 percent compounded annually.
Quarterly compounding at 10 percent yields wealth at the end of one year of:
$1,000 (1 +
.10 ___
4
)
4
= $1,103.81
More generally, compounding an investment m times a year provides end-of-year
wealth of:
C0 (1 +
r
__
m
)
m
[4.6]
where C0 is one’s initial investment and r is the annual percentage rate (APR). The
APR is the annual interest rate without consideration of compounding. Banks and other
financial institutions may use other names for the APR.4
What is the end-of-year wealth if Fernando Zapatero receives an annual percentage rate of 24 percent
compounded monthly on a $1 investment?
Using Equation 4.6, his wealth is:
$1 (1 +
.24
____
12
)
12
= $1 × (1.02)12
= $1.2682
The annual rate of return is 26.82 percent. This annual rate of return is either called the effective
annual rate (EAR) or the effective annual yield (EAY). Due to compounding, the effective annual
interest rate is greater than the annual percentage rate of 24 percent. Algebraically, we can rewrite the
effective annual interest rate as:
Effective Annual Rate:
(1 +
r
__
m
)
m
− 1 [4.7]
Students are often bothered by the subtraction of 1 in Equation 4.7. Note that end-of-year wealth is
composed of both the interest earned over the year and the original principal. We remove the original
principal by subtracting 1 in Equation 4.7.
EARs
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Distinction between Annual Percentage
Rate and Effective Annual Rate
The distinction between the annual percentage rate (APR) and the effective annual rate
(EAR) is frequently quite troubling to students. One can reduce the confusion by noting
that the APR becomes meaningful only if the compounding interval is given. For example,
for an APR of 10 percent, the future value at the end of one year with semiannual
compounding is [1 + (.10/2)]2 = 1.1025. The future value with quarterly compounding is
[1 + (.10/4)]4 = 1.1038. If the APR is 10 percent but no compounding interval is given,
one cannot calculate future value. In other words, one does not know whether to compound
semiannually, quarterly, or over some other interval.
By contrast, the EAR is meaningful without a compounding interval. For example,
an EAR of 10.25 percent means that a $1 investment will be worth $1.1025 in one year.
One can think of this as an APR of 10 percent with semiannual compounding or an APR
of 10.25 percent with annual compounding, or some other possibility.
There can be a big difference between an APR and an EAR when interest rates are
high. For example, consider “payday loans.” Payday loans are short-term loans made
to consumers, often for less than two weeks. They are offered by companies such as
Check Into Cash and AmeriCash Platinum. The loans work like this: You write a check
today that is postdated. When the check date arrives, you go to the store and either pay
the cash for the check or the company cashes the check. For example, in one particular
state, Check Into Cash allows you to write a check for $115 dated 14 days in the future,
for which they give you $100 today. So what are the APR and EAR of this arrange-
ment? First, we need to find the interest rate, which we can find by the FV equation
as follows:
FV = PV × (1 + r)1
$115 = $100 × (1 + r)1
1.15 = (1 + r)
r = .15, or 15%
If an annual percentage rate of 8 percent is compounded quarterly, what is the effective annual rate?
Using Equation 4.7, we have:
(1 +
r
__
m
)
m
− 1 = (1 +
.08
____
4
)
4
− 1 = .0824 = 8.24%
Referring back to our earlier example where C0 = $1,000 and r = 10%, we can generate the
following table:
C 0
COMPOUNDING
FREQUENCY (m ) C 1
EFFECTIVE ANNUAL
RATE = (1 +
r
__
m
)
m
− 1
$1,000 Yearly (m = 1) $1,100.00 .10
1,000 Semiannually (m = 2) 1,102.50 .1025
1,000 Quarterly (m = 4) 1,103.81 .10381
1,000 Daily (m = 365) 1,105.16 .10516
Compounding Frequencies
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That doesn’t seem too bad until you remember this is the interest rate for 14 days!
The APR of the loan is:
APR = .15 × 365/14
APR = 3.9107, or 391.07%
And the EAR for this loan is:
EAR = (1 + Quoted rate/m)m − 1
EAR = (1 + .15)365/14 − 1
EAR = 37.2366, or 3,723.66%
Now that’s an interest rate! Just to see what a difference a small variation in fees can
make, AmeriCash Platinum will make you write a check for $117.50 for the same amount
today. Check for yourself that the APR of this arrangement is 456.25 percent and the EAR
is 6,598.65 percent. Definitely not a loan we would like to take out!
By law, lenders are required to report the APR on all loans. In this text, we compute
the APR as the interest rate per period multiplied by the number of periods in a year.
According to federal law, the APR is a measure of the cost of consumer credit expressed as
a yearly rate, and it includes interest and certain noninterest charges and fees. In practice,
the APR can be much higher than the interest rate on the loan if the lender charges substan-
tial fees that must be included in the federally mandated APR calculation.
Compounding over Many Years
Formula 4.6 applies for an investment over one year. For an investment over one or more
(T) years, the formula becomes:
Future Value with Compounding:
FV = C0 (1 +
r
__
m
)
mT
[4.8]
Continuous Compounding
The previous discussion shows that one can compound much more frequently than once a
year. One could compound semiannually, quarterly, monthly, daily, hourly, each minute, or
even more often. The limiting case would be to compound every infinitesimal instant, which
is commonly called continuous compounding. Surprisingly, banks and other financial
institutions sometimes quote continuously compounded rates, which is why we study them.
Though the idea of compounding this rapidly may boggle the mind, a simple formula
is involved. With continuous compounding, the value at the end of T years is expressed as:
C0 × erT [4.9]
Harry DeAngelo is investing $5,000 at an annual percentage rate of 12 percent per year, compounded
quarterly, for five years. What is his wealth at the end of five years?
Using Equation 4.8, his wealth is:
$5,000 × (1 + .
12
___
4
)
4 ×5
= $5,000 × (1.03)20 = $5,000 × 1.8061 = $9,030.50
Multiyear Compounding
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100
where C0 is the initial investment, r is the annual percentage rate, and T is the number of
years over which the investment runs. The number e is a constant and is approximately
equal to 2.718. It is not an unknown like C0, r, and T.
Linda DeFond invested $1,000 at a continuously compounded rate of 10 percent for one year. What is
the value of her wealth at the end of one year?
From Equation 4.9, we have:
$1,000 × e.10 = $1,000 × 1.1052 = $1,105.20
This number can easily be read from our Table A.5. One merely sets r, the value on the horizontal
dimension, to 10 percent and T, the value on the vertical dimension, to 1. For this problem, the relevant
portion of the table is:
PERIOD
(T )
CONTINUOUSLY COMPOUNDED RATE ( r )
9% 10% 11%
1 1.0942 1.1052 1.1163
2 1.1972 1.2214 1.2461
3 1.3100 1.3499 1.3910
Note that a continuously compounded rate of 10 percent is equivalent to an annually compounded
rate of 10.52 percent. In other words, Linda DeFond would not care whether her bank quoted a
continuously compounded rate of 10 percent or a 10.52 percent rate, compounded annually.
Continuous Compounding
Linda DeFond’s brother, Mark, invested $1,000 at a continuously compounded rate of 10 percent for two
years.
The appropriate equation here is:
$1,000 × e.10×2 = $1,000 × e.20 = $1,221.40
Using the portion of the table of continuously compounded rates reproduced above, we find the value to
be 1.2214.
Continuous Compounding, Continued
The Michigan state lottery is going to pay you $1,000 at the end of four years. If the annual continuously
compounded rate of interest is 8 percent, what is the present value of this payment?
$1,000 × 1 _____
e.08×4
= $1,000 × 1 _______
1.3771
= $726.15
Present Value with Continuous Compounding
Figure 4.11 illustrates the relationship among annual, semiannual, and continuous
compounding. Semiannual compounding gives rise to both a smoother curve and a higher
ending value than does annual compounding. Continuous compounding has both the
smoothest curve and the highest ending value of all.
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FIGURE 4.11
Annual, Semiannual, and
Continuous Compounding
0 1 5
1
D
ol
la
rs
D
ol
la
rs
D
ol
la
rs
2
3
2 3 4
4
Interest
earned
Annual compounding
1
2
3
4
Interest
earned
Years
Semiannual compounding
1
2
3
4
Interest
earned
Continuous compounding
0 1 52 3 4
Years
0 1 52 3 4
Years
4.4 SIMPLIFICATIONS
The first part of this chapter has examined the concepts of future value and present value.
Although these concepts allow one to answer a host of problems concerning the time value
of money, the human effort involved can frequently be excessive. For example, consider a
bank calculating the present value on a 20-year monthly mortgage. Because this mortgage
has 240 (= 20 × 12) payments, a lot of time is needed to perform a conceptually simple task.
Because many basic finance problems are potentially so time-consuming, we search out
simplifications in this section. We provide simplifying formulas for four classes of cash
flow streams:
1. Perpetuity
2. Growing perpetuity
3. Annuity
4. Growing annuity
Perpetuity
A perpetuity is a constant stream of cash flows without end. If you are thinking that
perpetuities have no relevance to reality, it will surprise you that there is a well-known case
of an unending cash flow stream: the British bonds called consols. An investor purchasing
a consol is entitled to receive yearly interest from the British government forever.
How can the price of a consol be determined? Consider a consol that pays a coupon
of C dollars each year and will do so forever. Applying the PV formula gives us:
PV = C _____
1 + r
+ C ______
(1 + r)2
+ C ______
(1 + r)3
+ . . .
where the dots at the end of the formula stand for the infinite string of terms that continues
the formula. Series like the preceding one are called geometric series. It is well known
that even though they have an infinite number of terms, the whole series has a finite sum
because each term is only a fraction of the preceding term. Before turning to our calculus
books, though, it is worth going back to our original principles to see if a bit of financial
intuition can help us find the PV.
The present value of the consol is the present value of all of its future coupons. In other
words, it is an amount of money that, if an investor had it today, would enable him to
achieve the same pattern of expenditures that the consol and its coupons would. Suppose
that an investor wanted to spend exactly C dollars each year. If he had the consol, he could
do this. How much money must he have today to spend the same amount? Clearly he
would need exactly enough so that the interest on the money would be C dollars per year.
If he had any more, he could spend more than C dollars each year. If he had any less,
he would eventually run out of money spending C dollars per year.
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The amount that will give the investor C dollars each year, and therefore the present
value of the consol, is:
PV = C __
r
[4.10]
To confirm that this is the right answer, notice that if we lend the amount C/r, the interest
it earns each year will be:
Interest = C __
r
× r = C
which is exactly the consol payment. To sum up, we have shown that for a consol:
Formula for Present Value of Perpetuity:
PV = C _____
1 + r
+ C ______
(1 + r)2
+ C ______
(1 + r)3
+ . . . [4.11]
= C __
r
It is comforting to know how easily we can use a bit of financial intuition to solve this
mathematical problem.
Growing Perpetuity
Imagine an apartment building where cash flows to the landlord after expenses will
be $100,000 next year. These cash flows are expected to rise at 5 percent per year.
Assuming that this rise will continue indefinitely, the cash flow stream is termed a
growing perpetuity. The relevant interest rate is 11 percent. Therefore, the appropriate
discount rate is 11 percent and the present value of the cash flows can be represented as:
PV = $100,000 _________
1.11
+ $100,000(1.05) ______________
(1.11)2
+ $100,000(1.05)
2
______________
(1.11)3
+ . . .
+ $100,000(1.05)
N −1
________________
(1.11)N
+ . . .
Algebraically, we can write the formula as:
PV = C _____
1 + r
+ C × (1 + g) _________
(1 + r)2
+ C × (1 + g)
2
__________
(1 + r)3
+ . . . + C × (1 + g)
N−1
____________
(1 + r)N
+ . . .
where C is the cash flow to be received one period hence, g is the rate of growth per
period, expressed as a percentage, and r is the appropriate discount rate.
Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value of
the consol?
Using Equation 4.10, we have:
PV = $100 _____
.08
= $1,250
Now suppose that interest rates fall to 6 percent. Using [4.10], the value of the perpetuity is:
PV = $100 _____
.06
= $1,666.67
Note that the value of the perpetuity rises with a drop in the interest rate. Conversely, the value of the
perpetuity falls with a rise in the interest rate.
Perpetuities
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Fortunately, this formula reduces to the following simplification:
Formula for Present Value of Growing Perpetuity:
PV = C _____
r − g
[4.12]
From Formula 4.12, the present value of the cash flows from the apartment building is:
$100,000 _________
.11 − .05
= $1,666,667
There are three important points concerning the growing perpetuity formula:
1. The Numerator. The numerator in Formula 4.12 is the cash flow one period
hence, not at Date 0. Consider the following example:
Rothstein Corporation is just about to pay a dividend of $3.00 per share. Investors anticipate that the
annual dividend will rise by 6 percent a year forever. The applicable discount rate is 11 percent. What is
the price of the stock today?
The numerator in Formula 4.12 is the cash flow to be received next period. Since the growth rate is
6 percent, the dividend next year is $3.18 (= $3.00 × 1.06). The price of the stock today is:
$66. = $3.00
Imminent
dividend
+ $3.18 ________
.11 − .06
Present value of all
dividends beginning
a year from now
The price of $66.60 includes both the dividend to be received immediately and the present value of all
dividends beginning a year from now. Formula 4.12 only makes it possible to calculate the present value
of all dividends beginning a year from now. Be sure you understand this example; test questions on this
subject always seem to trip up a few of our students.
Paying Dividends
2. The Discount Rate and the Growth Rate. The discount rate r must be greater
than the growth rate g for the growing perpetuity formula to work. Consider the
case in which the growth rate approaches the discount rate in magnitude. Then
the denominator in the growing perpetuity formula gets infinitesimally small and
the present value grows infinitely large. The present value is in fact undefined
when r is less than g.
3. The Timing Assumption. Cash generally flows into and out of real-world firms
both randomly and nearly continuously. However, Formula 4.12 assumes that
cash flows are received and disbursed at regular and discrete points in time. In the
example of the apartment, we assumed that the net cash flows of $100,000 only
occurred once a year. In reality, rent checks are commonly received every month.
Payments for maintenance and other expenses may occur anytime within the year.
The growing perpetuity formula [4.12] can be applied only by assuming a
regular and discrete pattern of cash flow. Although this assumption is sensible
because the formula saves so much time, the user should never forget that it is an
assumption. This point will be mentioned again in the chapters ahead.
A few words should be said about terminology. Authors of financial textbooks generally
use one of two conventions to refer to time. A minority of financial writers treat cash flows as
being received on exact dates, for example Date 0, Date 1, and so forth. Under this convention,
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104
Date 0 represents the present time. However, because a year is an interval, not a specific
moment in time, the great majority of authors refer to cash flows that occur at the end of a year
(or alternatively, the end of a period). Under this end-of-the-year convention, the end of Year 0
is the present, the end of Year 1 occurs one period hence, and so on. (The beginning of Year 0
has already passed and is not generally referred to.)5
The interchangeability of the two conventions can be seen from the following chart:
Date 0 Date 1 Date 2 Date 3
Now
End of Year 0 End of Year 1 End of Year 2 End of Year 3
Now
We strongly believe that the dates convention reduces ambiguity. However, we use both
conventions because you are likely to see the end-of-year convention in later courses.
In fact, both conventions may appear in the same example for the sake of practice.
Annuity
An annuity is a level stream of regular payments that lasts for a fixed number of periods.
Not surprisingly, annuities are among the most common kinds of financial instruments.
The pensions that people receive when they retire are often in the form of an annuity.
Leases and mortgages are also often annuities.
To figure out the present value of an annuity we need to evaluate the following equation:
C
_____
1 + r
+ C ______
(1 + r)2
+ C ______
(1 + r)3
+ . . . + C ______
(1 + r)T
The present value of only receiving the coupons for T periods must be less than the
present value of a consol, but how much less? To answer this we have to look at consols
a bit more closely.
Consider the following time chart:
woN
Date (or end of year) 0 1 2 3 T (T 1) (T 2)
Consol 1 C C C . . . C C C . . .
Consol 2 C C . . .
Annuity C C C . . . C
Consol 1 is a normal consol with its first payment at Date 1. The first payment of
Consol 2 occurs at Date T + 1.
The present value of having a cash flow of C at each of T dates is equal to the present value
of Consol 1 minus the present value of Consol 2. The present value of Consol 1 is given by:
PV = C __
r
[4.13]
Consol 2 is just a consol with its first payment at Date T + 1. From the perpetuity formula,
this consol will be worth C/r at Date T.6 However, we do not want the value at Date T.
5 Sometimes financial writers merely speak of a cash flow in Year x. Although this terminology is ambiguous, such writers generally mean
the end of Year x.
6 Students frequently think that C/r is the present value at Date T + 1 because the consol’s first payment is at Date T + 1. However, the
formula values the annuity as of one period prior to the first payment.
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The term we use to compute the present value of the stream of level payments, C, for
T years is called an annuity factor. The annuity factor in the current example is 9.8181.
Because the annuity factor is used so often in PV calculations, we have included it in
Table A.2 in the back of this book. The table gives the values of these factors for a range of
interest rates, r, and maturity dates, T.
The annuity factor as expressed in the brackets of Formula 4.15 is a complex formula.
For simplification, we may from time to time refer to the present value annuity factor as:
PVIFAr,T
That is, the above expression stands for the present value of $1 a year for T years at an
interest rate of r.
We want the value now; in other words, the present value at Date 0. We must discount C/r
back by T periods. Therefore, the present value of Consol 2 is:
PV = C __
r
[
1 ______
(1 + r)T
] [4.14]
The present value of having cash flows for T years is the present value of a consol with its
first payment at Date 1 minus the present value of a consol with its first payment at Date
T + 1. Thus, the present value of an annuity is Formula 4.13 minus Formula 4.14. This can
be written as:
C
__
r
− C __
r
[
1 ______
(1 + r)T
]
This simplifies to:
Formula for Present Value of Annuity:
PV = C [
1 __
r
− 1 _______
r (1 + r)T
] [4.15]
This can also be written as:
PV = C
⎡
⎢ ⎣
1 − 1 ______
(1 + r)T
__________
r
⎤
⎥ ⎦
Mark Young has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his first
payment a year from now. The state advertises this as the Million Dollar Lottery because $1,000,000 =
$50,000 × 20. If the interest rate is 8 percent, what is the true value of the lottery?
Equation 4.15 yields:
Present value of
Million Dollar Lottery = $50,000 ×
⎡
⎢ ⎣
1 − 1 _______
(1.08)20
____________
.08
⎤
⎥ ⎦
Periodic payment
= $50,000
= $490,907.37
×
Annuity factor
9.8181
Rather than being overjoyed at winning, Mr. Young sues the state for misrepresentation and fraud.
His legal brief states that he was promised $1 million but received only $490,907.37.
Lottery Valuation
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Our experience is that annuity formulas are not hard, but tricky, for the beginning
student. We present four tricks below.
TRICK 1: A DELAYED ANNUITY One of the tricks in working with annuities or perpetuities
is getting the timing exactly right. This is particularly true when an annuity or perpetuity
begins at a date many periods in the future. We have found that even the brightest begin-
ning student can make errors here. Consider the following example:
We can also provide a formula for the future value of an annuity:
FV = C [
(1 + r)T
______
r
− 1 __
r
] = C [
(1 + r)T − 1 __________
r
] [4.16]
As with present value factors for annuities, we have compiled future value factors
in Table A.4 in the back of this book. Of course, you can also use a spreadsheet as we
illustrate in the nearby Spreadsheet Techniques box.
SPREADSHEET TECHNIQUESAnnui ty Present Values
Using a spreadsheet to find annuity present values goes like this:
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
A B C D E F G
What is the present value of $500 per year for 3 years if the discount rate is 10 percent?
We need to solve for the unknown present value, so we use the formula PV(rate, nper, pmt, fv).
Payment amount per period: $500
Number of payments: 3
Discount rate: .1
Annuity present value: $1,243.43
The formula entered in cell B11 is =PV(B9,B8,-B7,0); notice that fv is zero and that
pmt has a negative sign on it. Also notice that rate is entered as a decimal, not a percentage.
Using a spreadsheet to find annuity present values
Suppose you put $3,000 per year into a Roth IRA. The account pays 6 percent per year. How much will
you have when you retire in 30 years?
This question asks for the future value of an annuity of $3,000 per year for 30 years at 6 percent,
which we can calculate as follows:
FV = C [
(1 + r)T − 1
___________
r
] = $3,000 × [
1.0630 − 1
__________
.06
]
= $3,000 × 79.0582
= $237,174.56
So, you’ll have close to a quarter million dollars in the account.
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TRICK 2: ANNUITY DUE The annuity formula of Formula 4.15 assumes that the first
annuity payment begins a full period hence. This type of annuity is sometimes called
an annuity in arrears or an ordinary annuity. What happens if the annuity begins today,
in other words, at Date 0?
Danielle Caravello will receive a four-year annuity of $500 per year, beginning at Date 6. If the interest
rate is 10 percent, what is the present value of her annuity? This situation can be graphed as:
0 1 2 3 4 5 6 7 8 9 10
$500 $500 $500 $500
The analysis involves two steps:
1. Calculate the present value of the annuity using Formula 4.15. This is:
Present Value of Annuity at Date 5:
$500 ×
⎡
⎢ ⎣
1 − 1 _______
(1.10)4
___________
.10
⎤
⎥ ⎦ = $500 × PVIFA10%,4
= $500 × 3.1699
= $1,584.93
Note that $1,584.93 represents the present value at Date 5.
Students frequently think that $1,584.93 is the present value at Date 6, because the annuity begins
at Date 6. However, our formula values the annuity as of one period prior to the first payment. This can
be seen in the most typical case where the first payment occurs at Date 1. The equation values the
annuity as of Date 0 in that case.
2. Discount the present value of the annuity back to Date 0. That is:
Present Value at Date 0:
$1,584.93
__________
(1.10)5
= $984.12
Again, it is worthwhile mentioning that, because the annuity formula brings Danielle’s annuity back
to Date 5, the second calculation must discount over the remaining 5 periods. The two-step proce-
dure is graphed in Figure 4.12.
FIGURE 4.12 Discounting Danielle Caravello’s Annuity
109Date
Cash flow
$984.13 $1,584.93
$500 $500 $500 $500
876543210
Step one: Discount the four payments back to Date 5 by using the annuity formula.
Step two: Discount the present value at Date 5 ($1,584.93) back to present value at Date 0.
Delayed Annuities
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In a previous example, Mark Young received $50,000 a year for 20 years from the state lottery. In that
example, he was to receive the first payment a year from the winning date. Let us now assume that the
first payment occurs immediately. The total number of payments remains 20.
Under this new assumption, we have a 19-date annuity with the first payment occurring at Date
1—plus an extra payment at Date 0. The present value is:
$50,000 + $50,000 × PVIFA8%,19
Payment at Date 0 19 − year annuity
= $50,000 + ($50,000 × 9.6036)
= $530,180
The present value in this example, $530,180, is greater than $490,907.37, the present value in the
earlier lottery example. This is to be expected because the annuity of the current example begins earlier.
An annuity with an immediate initial payment is called an annuity in advance or, more commonly, an
annuity due. Always remember that Formula 4.15 and Table A.2 in this book refer to an ordinary annuity.
Annuity Due
Ms. Ann Chen receives an annuity of $450, payable once every two years. The annuity stretches out
over 20 years. The first payment occurs at Date 2, that is, two years from today. The annual interest rate
is 6 percent.
The trick is to determine the interest rate over a two-year period. The interest rate over two years is:
(1.06 × 1.06) − 1 = 12.36%
That is, $100 invested over two years will yield $112.36.
What we want is the present value of a $450 annuity over 10 periods, with an interest rate of 12.36
percent per period. This is:
$450 ×
⎡
⎢ ⎣
1 − 1 ____________
(1 + .1236)10
_________________
.1236
⎤
⎥ ⎦ = $450 × PVIFA12.36%,10 = $2,505.57
Infrequent Annuities
TRICK 3: THE INFREQUENT ANNUITY The following example treats an annuity with pay-
ments occurring less frequently than once a year.
TRICK 4: EQUATING PRESENT VALUE OF TWO ANNUITIES The following example equates
the present value of inflows with the present value of outflows.
Harold and Helen Nash are saving for the college education of their newborn daughter, Susan.
The Nashes estimate that college expenses will run $30,000 per year when their daughter reaches
college in 18 years. The annual interest rate over the next few decades will be 14 percent. How much
money must they deposit in the bank each year so that their daughter will be completely supported
through four years of college?
To simplify the calculations, we assume that Susan is born today. Her parents will make the first of
her four annual tuition payments on her 18th birthday. They will make equal bank deposits on each of
her first 17 birthdays, but no deposit at Date 0. This is illustrated as:
Working with Annuities
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Date 0 1 2 . . . 17 18 19 20 21
Susan’s Parents’ Parents’ . . . Parents’ Tuition Tuition Tuition Tuition
birth 1st 2nd 17th and payment payment payment payment
deposit deposit last 1 2 3 4
deposit
Mr. and Ms. Nash will be making deposits to the bank over the next 17 years. They will be withdraw-
ing $30,000 per year over the following four years. We can be sure they will be able to withdraw fully
$30,000 per year if the present value of the deposits is equal to the present value of the four $30,000
withdrawals.
This calculation requires three steps. The first two determine the present value of the withdraw-
als. The final step determines yearly deposits that will have a present value equal to that of the
withdrawals.
1. We calculate the present value of the four years at college using the annuity formula:
$30,000 ×
⎡
⎢ ⎣
1 − 1 _______
(1.14)4
___________
.14
⎤
⎥ ⎦ = $30,000 × PVIFA14%,4
= $30,000 × 2.9137 = $87,411.37
We assume that Susan enters college on her 18th birthday. Given our discussion in Trick 1, $87,411.37
represents the present value at Date 17.
2. We calculate the present value of the college education at Date 0 as:
$87,411.37
___________
(1.14)17
= $9,422.92
3. Assuming that Helen and Harold Nash make deposits to the bank at the end of each of the 17 years,
we calculate the annual deposit that will yield a present value of all deposits of $9,422.92. This is
calculated as:
C × PVIFA14%,17 = $9,422.92
Because PVIFA14%,17 = 6.3729
C = $9,422.92 __________
6.3729
= $1,478.60
Thus, deposits of $1,478.60 made at the end of each of the first 17 years and invested at 14 percent will
provide enough money to make tuition payments of $30,000 over the following four years. Alternatively,
we could have set $84,411.37 as the future value of an annuity and solved for the payment that way.
Do this yourself and see if you don’t get the same annuity payment.
An alternative method would be to (1) calculate the present value of the tuition pay-
ments at Susan’s 18th birthday and (2) calculate annual deposits such that the future value
of the deposits at her 18th birthday equals the present value of the tuition payments at that
date. Although this technique can also provide the right answer, we have found that it is
more likely to lead to errors. Therefore, we only equate present values in our presentation.
Growing Annuity
Cash flows in business are very likely to grow over time, due either to real growth or to
inflation. The growing perpetuity, which assumes an infinite number of cash flows, pro-
vides one formula to handle this growth. We now consider a growing annuity, which is a
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110
finite number of growing cash flows. Because perpetuities of any kind are rare, a formula
for a growing annuity would be useful indeed. The formula is:
Formula for Present Value of Growing Annuity:
PV = C [
1 _____
r − g
− 1 _____
r − g
× (
1 + g
_____
1 + r
)
T
] = C
⎛
⎜ ⎝
1 − (
1 + g
_____
1 + r
)
T
____________
r − g
⎞
⎟ ⎠ [4.17]
where, as before, C is the payment to occur at the end of the first period, r is the interest
rate, g is the rate of growth per period, expressed as a percentage, and T is the number of
periods for the annuity.
Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He antici-
pates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate
of 20 percent, what is the present value of his lifetime salary?
We simplify by assuming he will be paid his $80,000 salary exactly one year from now, and that his
salary will continue to be paid in annual installments. From [4.17], the calculation is:
Present value
of Stuart’s
lifetime salary
= $80,000 ×
⎡
⎢ ⎣
1 − (
1.09
_____
1.20
)
40
______________
.20 − .09
⎤
⎥ ⎦ = $711,731
Though the growing annuity is quite useful, it is more tedious than the other simplifying formulas.
Whereas most sophisticated calculators have special programs for perpetuity, growing perpetuity, and
annuity, there is no special program for growing annuity. Hence, one must calculate all the terms in
Formula 4.17 directly.
Growing Annuities
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In a previous example, Harold and Helen Nash planned to make 17 identical payments in order to fund
the college education of their daughter, Susan. Alternatively, imagine that they planned to increase their
payments at 4 percent per year. What would their first payment be?
The first two steps of the previous Nash family example showed that the present value of the college
costs was $9,422.92. These two steps would be the same here. However, the third step must be altered.
Now we must ask, How much should their first payment be so that, if payments increase by 4 percent
per year, the present value of all payments will be $9,422.92?
We set the growing annuity formula equal to $9,422.92 and solve for C.
C
⎡
⎢ ⎣
1 − (
1 + g
______
1 + r
)
T
______________
r − g
⎤
⎥ ⎦ = C
⎡
⎢ ⎣
1 − (
1.04
_____
1.14
)
17
______________
.14 − .04
⎤
⎥ ⎦ = $9,422.92
Here, C = $1,192.75. Thus, the deposit on their daughter’s first birthday is $1,192.75, the deposit on the
second birthday is $1,240.46 (= 1.04 × $1,192.75), and so on.
More Growing Annuities
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4.5 LOAN TYPES AND LOAN AMORTIZATION
Whenever a lender extends a loan, some provision will be made for repayment of the prin-
cipal (the original loan amount). A loan might be repaid in equal installments, for example,
or it might be repaid in a single lump sum. Because the way that the principal and interest
are paid is up to the parties involved, there are actually an unlimited number of possibilities.
In this section, we describe a few forms of repayment that come up quite often, and
more complicated forms can usually be built up from these. The three basic types of loans
are pure discount loans, interest-only loans, and amortized loans. Working with these loans
is a very straightforward application of the present value principles that we have already
developed.
Pure Discount Loans
The pure discount loan is the simplest form of loan. With such a loan, the borrower
receives money today and repays a single lump sum at some time in the future. A one-year,
10 percent pure discount loan, for example, would require the borrower to repay $1.10 in
one year for every dollar borrowed today.
Because a pure discount loan is so simple, we already know how to value one. Suppose
a borrower was able to repay $25,000 in five years. If we, acting as the lender, wanted a
12 percent interest rate on the loan, how much would we be willing to lend? Put another
way, what value would we assign today to that $25,000 to be repaid in five years? Based on
our previous work we know the answer is just the present value of $25,000 at 12 percent
for five years:
Present value = $25,000/1.125
= $25,000/1.7623
= $14,186
Pure discount loans are common when the loan term is short, say a year or less. In recent
years, they have become increasingly common for much longer periods.
ExcelMaster
coverage online
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Interest-Only Loans
A second type of loan repayment plan calls for the borrower to pay interest each period and
to repay the entire principal (the original loan amount) at some point in the future. Loans
with such a repayment plan are called interest-only loans. Notice that if there is just one
period, a pure discount loan and an interest-only loan are the same thing.
For example, with a three-year, 10 percent, interest-only loan of $1,000, the borrower
would pay $1,000 × .10 = $100 in interest at the end of the first and second years. At the
When the U.S. government borrows money on a short-term basis (a year or less), it does so by selling
what are called Treasury bills, or T-bills for short. A T-bill is a promise by the government to repay a fixed
amount at some time in the future—for example, 3 months or 12 months.
Treasury bills are pure discount loans. If a T-bill promises to repay $10,000 in 12 months, and the
market interest rate is 7 percent, how much will the bill sell for in the market?
Because the going rate is 7 percent, the T-bill will sell for the present value of $10,000 to be repaid in
one year at 7 percent:
Present value = $10,000/1.07 = $9,345.79
Treasury Bills
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112
end of the third year, the borrower would return the $1,000 along with another $100 in
interest for that year. Similarly, a 50-year interest-only loan would call for the borrower to
pay interest every year for the next 50 years and then repay the principal. In the extreme,
the borrower pays the interest every period forever and never repays any principal. As we
discussed earlier in the chapter, the result is a perpetuity.
Most corporate bonds have the general form of an interest-only loan. Because we will
be considering bonds in some detail in the next chapter, we will defer further discussion of
them for now.
Amortized Loans
With a pure discount or interest-only loan, the principal is repaid all at once. An alterna-
tive is an amortized loan, with which the lender may require the borrower to repay parts
of the loan amount over time. The process of providing for a loan to be paid off by making
regular principal reductions is called amortizing the loan.
A simple way of amortizing a loan is to have the borrower pay the interest each period
plus some fixed amount. This approach is common with medium-term business loans.
For example, suppose a business takes out a $5,000, five-year loan at 9 percent. The loan
agreement calls for the borrower to pay the interest on the loan balance each year and to
reduce the loan balance each year by $1,000. Because the loan amount declines by $1,000
each year, it is fully paid in five years.
In the case we are considering, notice that the total payment will decline each year.
The reason is that the loan balance goes down, resulting in a lower interest charge each
year, whereas the $1,000 principal reduction is constant. For example, the interest in the
first year will be $5,000 × .09 = $450. The total payment will be $1,000 + 450 = $1,450.
In the second year, the loan balance is $4,000, so the interest is $4,000 × .09 = $360, and
the total payment is $1,360. We can calculate the total payment in each of the remaining
years by preparing a simple amortization schedule as follows:
YEAR
BEGINNING
BALANCE
TOTAL
PAYMENT
INTEREST
PAID
PRINCIPAL
PAID
ENDING
BALANCE
1 $5,000 $1,450 $ 450 $1,000 $4,000
2 4,000 1,360 360 1,000 3,000
3 3,000 1,270 270 1,000 2,000
4 2,000 1,180 180 1,000 1,000
5 1,000 1,090 90 1,000 0
Totals $6,350 $1,350 $5,000
Notice that in each year, the interest paid is given by the beginning balance multiplied by
the interest rate. Also notice that the beginning balance is given by the ending balance
from the previous year.
Probably the most common way of amortizing a loan is to have the borrower make a
single, fixed payment every period. Almost all consumer loans (such as car loans) and
mortgages work this way. For example, suppose our five-year, 9 percent, $5,000 loan was
amortized this way. How would the amortization schedule look?
We first need to determine the payment. From our discussion earlier in the chapter, we
know that this loan’s cash flows are in the form of an ordinary annuity. In this case, we can
solve for the payment as follows:
$5,000 = C × {[1 − (1/1.095)]/.09}
= C × [(1 − .6499)/.09]
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This gives us:
C = $5,000/3.8897
= $1,285.46
The borrower will therefore make five equal payments of $1,285.46. Will this pay off the
loan? We will check by filling in an amortization schedule.
In our previous example, we knew the principal reduction each year. We then calculated
the interest owed to get the total payment. In this example, we know the total payment.
We will thus calculate the interest and then subtract it from the total payment to calculate
the principal portion in each payment.
In the first year, the interest is $450, as we calculated before. Because the total payment
is $1,285.46, the principal paid in the first year must be:
Principal paid = $1,285.46 − 450 = $835.46
The ending loan balance is thus:
Ending balance = $5,000 − 835.46 = $4,164.54
The interest in the second year is $4,164.54 × .09 = $374.81, and the loan balance declines
by $1,285.46 – 374.81 = $910.65. We can summarize all of the relevant calculations in the
following schedule:
YEAR
BEGINNING
BALANCE
TOTAL
PAYMENT
INTEREST
PAID
PRINCIPAL
PAID
ENDING
BALANCE
1 $5,000.00 $1,285.46 $ 450.00 $ 835.46 $4,164.54
2 4,164.54 1,285.46 374.81 910.65 3,253.88
3 3,253.88 1,285.46 292.85 992.61 2,261.27
4 2,261.27 1,285.46 203.51 1,081.95 1,179.32
5 1,179.32 1,285.46 106.14 1,179.32 0.00
Totals $6,427.30 $1,427.31 $5,000.00
Because the loan balance declines to zero, the five equal payments do pay off the loan.
Notice that the interest paid declines each period. This isn’t surprising because the loan
balance is going down. Given that the total payment is fixed, the principal paid must
be rising each period. To see how to calculate this loan in Excel, see the upcoming
Spreadsheet Techniques box.
If you compare the two loan amortizations in this section, you will see that the total
interest is greater for the equal total payment case: $1,427.31 versus $1,350. The reason
for this is that the loan is repaid more slowly early on, so the interest is somewhat higher.
This doesn’t mean that one loan is better than the other; it means that one is effectively paid
off faster than the other. For example, the principal reduction in the first year is $835.46 in
the equal total payment case as compared to $1,000 in the first case.
A common arrangement in real estate lending might call for a 5-year loan with, say, a 15-year amortiza-
tion. What this means is that the borrower makes a payment every month of a fixed amount based on
a 15-year amortization. However, after 60 months, the borrower makes a single, much larger payment
called a “balloon” or “bullet” to pay off the loan. Because the monthly payments don’t fully pay off the
loan, the loan is said to be partially amortized.
Partial Amortization, or “Bite the Bullet”
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Suppose we have a $100,000 commercial mortgage with a 12 percent APR and a 20-year (240-
month) amortization. Further suppose the mortgage has a five-year balloon. What will the monthly
payment be? How big will the balloon payment be?
The monthly payment can be calculated based on an ordinary annuity with a present value of
$100,000. There are 240 payments, and the interest rate is 1 percent per month. The payment is:
$100,000 = C × [(1 − 1/1.01240 ) /.01]
= C × 90.8194
C = $1,101.09
Now, there is an easy way and a hard way to determine the balloon payment. The hard way is to actually
amortize the loan for 60 months to see what the balance is at that time. The easy way is to recognize
that after 60 months, we have a 240 – 60 = 180-month loan. The payment is still $1,101.09 per month,
and the interest rate is still 1 percent per month. The loan balance is thus the present value of the
remaining payments:
Loan balance = $1,101.09 × [(1 − 1/1.01180 )/.01]
= $1,101.09 × 83.3217
= $91,744.69
The balloon payment is a substantial $91,744. Why is it so large? To get an idea, consider the first
payment on the mortgage. The interest in the first month is $100,000 × .01 = $1,000. Your payment is
$1,101.09, so the loan balance declines by only $101.09. Because the loan balance declines so slowly,
the cumulative “pay down” over five years is not great.
We will close this section with an example that may be of particular relevance. Federal
Stafford loans are an important source of financing for many college students, helping
to cover the cost of tuition, books, new cars, condominiums, and many other things.
Sometimes students do not seem to fully realize that Stafford loans have a serious draw-
back: They must be repaid in monthly installments, usually beginning six months after the
student leaves school.
Some Stafford loans are subsidized, meaning that the interest does not begin to accrue
until repayment begins (this is a good thing). If you are a dependent undergraduate student
under this particular option, the total debt you can run up is, at most, $23,000. For loans
between July 2015 and July 2016, the interest rate is 4.29 percent, or 4.29/12 = .3575
percent per month. Under the “standard repayment plan,” the loans are amortized over 10
years (subject to a minimum payment of $50).
Suppose you max out borrowing under this program and also get stuck paying the
maximum interest rate. Beginning six months after you graduate (or otherwise depart the
ivory tower), what will your monthly payment be? How much will you owe after making
payments for four years?
Given our earlier discussions, see if you don’t agree that your monthly payment assum-
ing a $23,000 total loan is $236.05 per month. Also, as explained in Example 4.28, after
making payments for four years, you still owe the present value of the remaining payments.
There are 120 payments in all. After you make 48 of them (the first four years), you have
72 to go. By now, it should be easy for you to verify that the present value of $236.05 per
month for 72 months at .3575 percent per month is just under $15,000, so you still have a
long way to go.
Of course, it is possible to rack up much larger debts. According to the Association of
American Medical Colleges, students who borrowed to attend medical school and gradu-
ated in 2014 had an average student loan balance of $176,000. Ouch! How long will it take
the average student to pay off her medical school loans?
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Let’s say she makes a monthly payment of $1,200, and the loan has an interest rate
of 7 percent per year, or .5833 percent per month. See if you agree that it will take
333 months, or just about 28 years, to pay off the loan. Maybe MD really stands for
“mucho debt!”
4.6 WHAT IS A FIRM WORTH?
Suppose you are in the business of trying to determine the value of small companies.
(You are a business appraiser.) How can you determine what a firm is worth? One way to
think about the question of how much a firm is worth is to calculate the present value of
its future cash flows.
Let us consider the example of a firm that is expected to generate net cash flows (cash
inflows minus cash outflows) of $5,000 in the first year and $2,000 for each of the next
five years. The firm can be sold for $10,000 seven years from now. The owners of the firm
would like to be able to make 10 percent on their investment in the firm.
Loan amortization is a common spreadsheet application. To illustrate, we will set up the problem that
we examined earlier: a five-year, $5,000, 9 percent loan with constant payments. Our spreadsheet
looks like this:
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
3 0
3 1
A B C D E F G H
Loan amount: $5,000
Interest rate: .09
Loan term: 5
Loan payment: $1,285.46
Note: Payment is calculated using PMT(rate, nper, -pv, fv).
Amortization table:
Year Beginning Total Interest Principal Ending
Balance Payment Paid Paid Balance
1 $5,000.00 $1,285.46 $450.00 $835.46 $4,164.54
2 4,164.54 1,285.46 374.81 910.65 3,253.88
3 3,253.88 1,285.46 292.85 992.61 2,261.27
4 2,261.27 1,285.46 203.51 1,081.95 1,179.32
5 1,179.32 1,285.46 106.14 1,179.32 0.00
Totals 6,427.31 1,427.31 5,000.00
Formulas in the amortization table:
Year Beginning Total Interest Principal Ending
Balance Payment Paid Paid Balance
1 =+D4 =$D$7 =+$D$5*C13 =+D13-E13 =+C13-F13
2 =+G13 =$D$7 =+$D$5*C14 =+D14-E14 =+C14-F14
3 =+G14 =$D$7 =+$D$5*C15 =+D15-E15 =+C15-F15
4 =+G15 =$D$7 =+$D$5*C16 =+D16-E16 =+C16-F16
5 =+G16 =$D$7 =+$D$5*C17 =+D17-E17 =+C17-F17
Note: Totals in the amortization table are calculated using the SUM formula.
Using a spreadsheet to amortize a loan
Loan Amort izat ion Using a
Spreadsheet SPREADSHEET TECHNIQUES
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116
The value of the firm is found by multiplying the net cash flows by the appropriate
present value factor. The value of the firm is the sum of the present values of the individual
net cash flows.
The present value of the net cash flows is given next.
END OF YEAR
THE PRESENT VALUE OF THE F IRM
NET CASH FLOW OF
THE F IRM
PRESENT VALUE
FACTOR (10%)
PRESENT VALUE OF
NET CASH FLOWS
1 $ 5,000 .90909 $ 4,545.45
2 2,000 .82645 1,652.89
3 2,000 .75131 1,502.63
4 2,000 .68301 1,366.03
5 2,000 .62092 1,241.84
6 2,000 .56447 1,128.95
7 10,000 .51316 5,131.58
Present value of firm $16,569.38
We can also use the simplifying formula for an annuity to give us:
$5,000 _______
1.1
+
(2,000 × PVIFA10%,5 ) _________________
1.1
+ 10,000 _______
(1.1)7
= $16,569.38
Suppose you have the opportunity to acquire the firm for $12,000. Should you acquire the
firm? The answer is yes because the NPV is positive.
NPV = PV − Cost
$4,569.38 = $16,569.38 − 12,000
The incremental value (NPV) of acquiring the firm is $4,569.38.
The Trojan Pizza Company is contemplating investing $1 million in four new outlets in Los Angeles.
Andrew Lo, the firm’s chief financial officer (CFO), has estimated that the investments will pay out cash
flows of $200,000 per year for nine years and nothing thereafter. (The cash flows will occur at the end
of each year and there will be no cash flow after Year 9.) Mr. Lo has determined that the relevant
discount rate for this investment is 15 percent. This is the rate of return that the firm can earn at
comparable projects. Should the Trojan Pizza Company make the investments in the new outlets?
The decision can be evaluated as:
NPV = −$1,000,000 + $200,000 _________
1.15
+ $200,000 _________
(1.15)2
+ . . . + $200,000 _________
(1.15)9
= −$1,000,000 + $200,000 × PVIFA15%,9
= −$1,000,000 + $954,316.78
= −$45,683.22
The present value of the four new outlets is only $954,316.78. The outlets are worth less than they
cost. The Trojan Pizza Company should not make the investment because the NPV is −$45,683.22.
If the Trojan Pizza Company requires a 15 percent rate of return, the new outlets are not a good
investment.
Firm Valuation
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CHAPTER 4 Discounted Cash Flow Valuation 117
SUMMARY AND CONCLUSIONS
1. Two basic concepts, future value and present value, were introduced in the beginning of this chapter.
With a 10 percent interest rate, an investor with $1 today can generate a future value of $1.10 in a year,
$1.21 [=$1 × (1.10)2] in two years, and so on. Conversely, present value analysis places a current value
on a later cash flow. With the same 10 percent interest rate, a dollar to be received in one year has a
present value of $.909 [=$1/1.10] in Year 0. A dollar to be received in two years has a present value of
$.826 [=$1/(1.10)2].
2. One commonly expresses the interest rate as, say, 12 percent per year. However, one can speak of
the interest rate as 3 percent per quarter. Although the annual percentage rate remains 12 percent
[=3 percent × 4], the effective annual interest rate is 12.55 percent [=(1.03)4 − 1]. In other words, the
compounding process increases the future value of an investment. The limiting case is continuous
compounding, where funds are assumed to be reinvested every infinitesimal instant.
3. A basic quantitative technique for financial decision making is net present value analysis. The net
present value formula for an investment that generates cash flows (Ci) in future periods is:
NPV = −C0 +
C1 ______
(1 + r )
+ C2 _______
(1 + r)2
+ . . . + CT _______
(1 + r)T
= −C0 + ∑
i =1
T
Ci _______
(1 + r )i
The formula assumes that the cash flow at Date 0 is the initial investment (a cash outflow).
4. Frequently, the actual calculation of present value is long and tedious. The computation of the present
value of a long-term mortgage with monthly payments is a good example of this. We presented four
simplifying formulas:
Perpetuity: PV = C __
r
Growing perpetuity: PV = C _____
r − g
Annuity: PV = C
⎡
⎢ ⎣
1 − 1 _______
(1 + r)T
___________
r
⎤
⎥ ⎦
Growing annuity: PV = C
⎡
⎢ ⎣
1 − (
1 + g
______
1 + r
)
T
______________
r − g
⎤
⎥ ⎦
5. We stressed a few practical considerations in the application of these formulas:
a. The numerator in each of the formulas, C, is the cash flow to be received one full period hence.
b. Cash flows are generally irregular in practice. To avoid unwieldy problems, assumptions to create
more regular cash flows are made both in this textbook and in the real world.
c. A number of present value problems involve annuities (or perpetuities) beginning a few periods
hence. Students should practice combining the annuity (or perpetuity) formula with the discounting
formula to solve these problems.
d. Annuities and perpetuities may have periods of every two or every n years, rather than once a year.
The annuity and perpetuity formulas can easily handle such circumstances.
e. One frequently encounters problems where the present value of one annuity must be equated with
the present value of another annuity.
6. Many loans are annuities. The process of providing for a loan to be paid off gradually is called amortizing
the loan, and we discussed how amortization schedules are prepared and interpreted.
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118 PART 2 Valuation and Capital Budgeting
1. Compounding and Period As you increase the length of time involved, what happens to future
values? What happens to present values?
2. Interest Rates What happens to the future value of an annuity if you increase the rate r? What
happens to the present value?
3. Present Value Suppose two athletes sign 10-year contracts for $80 million. In one case, we’re told
that the $80 million will be paid in 10 equal installments. In the other case, we’re told that the $80
million will be paid in 10 installments, but the installments will increase by 5 percent per year. Who got
the better deal?
4. APR and EAR Should lending laws be changed to require lenders to report EARs instead of APRs?
Why or why not?
5. Time Value On subsidized Stafford loans, a common source of financial aid for college students,
interest does not begin to accrue until repayment begins. Who receives a bigger subsidy, a freshman
or a senior? Explain.
Use the following information for Questions 6-10:
Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor Corporation, offered some
securities for sale to the public on March 28, 2008. Under the terms of the deal, TMCC promised to
repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive
nothing until then. Investors paid TMCC $24,099 for each of these securities, so they gave up $24,099
on March 28, 2008, for the promise of a $100,000 payment 30 years later.
6. Time Value of Money Why would TMCC be willing to accept such a small amount today ($24,099) in
exchange for a promise to repay about four times that amount ($100,000) in the future?
7. Call Provisions TMCC has the right to buy back the securities on the anniversary date at a price
established when the securities were issued (this feature is a term of this particular deal). What impact
does this feature have on the desirability of this security as an investment?
8. Time Value of Money Would you be willing to pay $24,099 today in exchange for $100,000 in 30
years? What would be the key considerations in answering yes or no? Would your answer depend on
who is making the promise to repay?
9. Investment Comparison Suppose that when TMCC offered the security for $24,099 the U.S. Treasury
had offered an essentially identical security. Do you think it would have had a higher or lower price? Why?
10. Length of Investment The TMCC security is bought and sold on the New York Stock Exchange. If you
looked at the price today, do you think the price would exceed the $24,099 original price? Why? If you
looked in the year 2019, do you think the price would be higher or lower than today’s price? Why?
CONCEPT QUESTIONS
1. Simple Interest versus Compound Interest First City Bank pays 7 percent simple interest on its
savings account balances, whereas Second City Bank pays 7 percent interest compounded annually.
If you made a $4,800 deposit in each bank, how much more money would you earn from your Second
City Bank account at the end of 10 years?
2. Calculating Future Values Compute the future value of $3,550 compounded annually for:
a. 10 years at 6 percent.
b. 10 years at 8 percent.
c. 20 years at 6 percent.
d. Why is the interest earned in part (c) not twice the amount earned in part (a)?
Basic
(Questions 1–20)
QUESTIONS AND PROBLEMS
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CHAPTER 4 Discounted Cash Flow Valuation 119
3. Calculating Present Values For each of the following, compute the present value:
PRESENT VALUE YEARS INTEREST RATE FUTURE VALUE
9 7% $ 15,451
13 9 51,557
16 14 886,073
24 11 550,164
4. Calculating Interest Rates Solve for the unknown interest rate in each of the following:
PRESENT VALUE YEARS INTEREST RATE FUTURE VALUE
$ 217 3 $ 293
432 10 1,053
41,000 16 162,181
54,382 19 483,500
5. Calculating the Number of Periods Solve for the unknown number of years in each of the following:
PRESENT VALUE YEARS INTEREST RATE FUTURE VALUE
$ 625 6% $ 1,284
810 9 4,341
18,400 7 234,162
21,500 10 215,000
6. Calculating the Number of Periods At 5.75 percent interest, how long does it take to double your
money? To quadruple it?
7. Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $540 million that
must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this
liability back to the present. If the relevant discount rate is 5.6 percent, what is the present value of this
liability?
8. Calculating Rates of Return Although appealing to more refined tastes, art as a collectible has not
always performed so profitably. In 2010, Deutscher-Menzies sold Arkie Under the Shower, a painting
by renowned Australian painter Brett Whiteley, at auction for a price of $1,100,000. Unfortunately for
the previous owner, he had purchased it three years earlier at a price of $1,680,000. What was his
annual rate of return on this painting?
9. Perpetuities An investor purchasing a British consol is entitled to receive annual payments from the
British government forever. What is the price of a consol that pays $80 annually if the next payment
occurs one year from today? The market interest rate is 2.6 percent.
10. Continuous Compounding Compute the future value of $1,625 continuously compounded for
a. Five years at an annual percentage rate of 14 percent.
b. Three years at an annual percentage rate of 6 percent.
c. Ten years at an annual percentage rate of 8 percent.
d. Eight years at an annual percentage rate of 9 percent.
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11. Present Value and Multiple Cash Flows Machine Co. has identified an investment project with the
following cash flows. If the discount rate is 5 percent, what is the present value of these cash flows?
What is the present value at 13 percent? At 18 percent?
YEAR CASH FLOW
1 $ 585
2 815
3 1,630
4 2,140
12. Present Value and Multiple Cash Flows Investment X offers to pay you $4,850 per year for nine
years, whereas Investment Y offers to pay you $6,775 per year for five years. Which of these cash flow
streams has the higher present value if the discount rate is 5 percent? If the discount rate is
21 percent?
13. Calculating Annuity Present Value An investment offers $5,500 per year for 15 years, with
the first payment occurring one year from now. If the required return is 7.5 percent, what is
the value of the investment? What would the value be if the payments occurred for 40 years?
For 75 years? Forever?
14. Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you an investment
policy that will pay you and your heirs $18,000 per year forever. If the required return on this
investment is 4.3 percent, how much will you pay for the policy? Suppose the company told you the
policy costs $445,000. At what interest rate would this be a fair deal?
15. Calculating EAR Find the EAR in each of the following cases:
APR NUMBER OF T IMES COMPOUNDED EAR
9.8% Quarterly
12.4 Monthly
7.6 Daily
8.4 Infinite
16. Calculating APR Find the APR in each of the following cases:
APR NUMBER OF T IMES COMPOUNDED EAR
Semiannually 10.4%
Monthly 8.9
Weekly 11.6
Infinite 15.4
17. Calculating EAR First National Bank charges 15.7 percent compounded monthly on its business
loans. First United Bank charges 16.2 percent compounded semiannually. As a potential borrower,
which bank would you go to for a new loan?
18. Interest Rates Well-known financial writer Andrew Tobias argues that he can earn 177 percent per
year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle of fine
Bordeaux per week for the next 12 weeks. He can either pay $10 per week or buy a case of 12 bottles
today. If he buys the case, he receives a 10 percent discount, and, by doing so, earns the 177 percent.
Assume he buys the wine and consumes the first bottle today. Do you agree with his analysis? Do you
see a problem with his numbers?
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CHAPTER 4 Discounted Cash Flow Valuation 121
19. Calculating Number of Periods One of your customers is delinquent on his accounts payable
balance. You’ve mutually agreed to a repayment schedule of $450 per month. You will charge 1.3
percent per month interest on the overdue balance. If the current balance is $18,700, how long will it
take for the account to be paid off?
20. Calculating EAR Friendly’s Quick Loans, Inc., offers you “three for four or I knock on your door.”
This means you get $3 today and repay $4 when you get your paycheck in one week (or else). What’s
the effective annual return Friendly’s earns on this lending business? If you were brave enough to ask,
what APR would Friendly’s say you were paying?
21. Future Value What is the future value in six years of $1,500 invested in an account with an annual
percentage rate of 7.2 percent
a. Compounded annually?
b. Compounded semiannually?
c. Compounded monthly?
d. Compounded continuously?
e. Why does the future value increase as the compounding period shortens?
22. Simple Interest versus Compound Interest First Simple Bank pays 7.4 percent simple interest on its
investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what
rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years?
23. Calculating Annuities You are planning to save for retirement over the next 30 years. To do this, you
will invest $750 per month in a stock account and $325 per month in a bond account. The return of the
stock account is expected to be an APR of 10.5 percent, and the bond account will earn an APR of 6.1
percent. When you retire, you will combine your money into an account with an APR of 6.9 percent.
All interest rates are compounded monthly. How much can you withdraw each month from your
account assuming a withdrawal period of 25 years?
24. Calculating Rates of Return Suppose an investment offers to triple your money in 12 months
(don’t believe it). What rate of return per quarter are you being offered?
25. Calculating Rates of Return You’re trying to choose between two different investments, both of
which have up-front costs of $55,000. Investment G returns $105,000 in five years. Investment H
returns $235,000 in 11 years. Which of these investments has the higher return?
26. Growing Perpetuities Mark Weinstein has been working on an advanced technology in laser eye
surgery. His technology will be available in the near term. He anticipates his first annual cash flow from
the technology to be $210,000, received three years from today. Subsequent annual cash flows will grow
at 2.5 percent in perpetuity. What is the value today of the technology if the discount rate is 11 percent?
27. Perpetuities A prestigious investment bank designed a new security that pays a quarterly dividend of
$1.75 in perpetuity. The first dividend occurs one quarter from today. What is the price of the security if
the annual percentage rate is 5.5 percent compounded quarterly?
28. Annuity Present Values What is the value today of an annuity of $5,700 per year, with the first cash
flow received 3 years from today and the last one received 25 years from today? Use a discount rate of
6.8 percent.
29. Annuity Present Values What is the value today of a 15-year annuity that pays $825 a year? The
annuity’s first payment occurs six years from today. The annual interest rate is 9 percent for Years 1
through 5, and 12 percent thereafter.
30. Balloon Payments Mike Bayles has just arranged to purchase a $825,000 vacation home in the
Bahamas with a 20 percent down payment. The mortgage has an APR of 5.4 percent, compounded
monthly, and calls for equal monthly payments over the next 30 years. His first payment will be due
one month from now. However, the mortgage has an eight-year balloon payment, meaning that the
balance of the loan must be paid off at the end of Year 8. There were no other transaction costs or
finance charges. How much will Mike’s balloon payment be in eight years?
Intermediate
(Questions 21–52)
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31. Calculating Interest Expense You receive a credit card application from Shady Banks Savings and
Loan offering an introductory rate of 1.9 percent per year, compounded monthly for the first six
months, increasing thereafter to 16 percent compounded monthly. Assuming you transfer the $7,500
balance from your existing credit card and make no subsequent payments, how much interest will you
owe at the end of the first year?
32. Perpetuities Reigle Pharmaceuticals is considering a drug project that costs $1,650,000 today and is
expected to generate end-of-year annual cash flows of $185,000, forever. At what discount rate would
the company be indifferent between accepting or rejecting the project?
33. Growing Annuity Southern California Publishing Company is trying to decide whether or not
to revise its popular textbook, Financial Psychoanalysis Made Simple. It has estimated that the
revision will cost $135,000. Cash flows from increased sales will be $38,000 the first year.
These cash flows will increase by 5.5 percent per year. The book will go out of print five years
from now. Assume that the initial cost is paid now and revenues are received at the end of each
year. If the company requires a return of 11 percent for such an investment, should it undertake
the revision?
34. Growing Annuity Your job pays you only once a year, for all the work you did over the previous
12 months. Today, December 31, you just received your salary of $75,000 and you plan to spend all
of it. However, you want to start saving for retirement beginning next year. You have decided that one
year from today you will begin depositing 10 percent of your annual salary in an account that will
earn 9.5 percent per year. Your salary will increase at 3.4 percent per year throughout your career.
How much money will you have on the date of your retirement 35 years from today?
35. Present Value and Interest Rates What is the relationship between the value of an annuity and the
level of interest rates? Suppose you just bought a 15-year annuity of $5,250 per year at the current
interest rate of 10 percent per year. What happens to the value of your investment if interest rates
suddenly drop to 5 percent? What if interest rates suddenly rise to 15 percent?
36. Calculating the Number of Payments You’re prepared to make monthly payments of $190,
beginning at the end of this month, into an account that pays 8.75 percent interest compounded
monthly. How many payments will you have made when your account balance reaches $25,000?
37. Calculating Annuity Present Values You want to borrow $105,000 from your local bank to buy a
new sailboat. You can afford to make monthly payments of $2,025, but no more. Assuming monthly
compounding, what is the highest APR you can afford on a 60-month loan?
38. Calculating Loan Payments You need a 30-year, fixed-rate mortgage to buy a new home for
$225,000. Your mortgage bank will lend you the money at an APR of 5.1 percent. However, you can
only afford monthly payments of $875, so you offer to pay off any remaining loan balance at the end
of the loan in the form of a single balloon payment. How large will this balloon payment have to be for
you to keep your monthly payments at $875?
39. Present and Future Values The present value of the following cash flow stream is $5,800 when
discounted at 8 percent annually. What is the value of the missing cash flow?
YEAR CASH FLOW
1 $1,300
2 ?
3 1,900
4 2,450
40. Calculating Present Values You have just won the TVM Lottery. You will receive $1 million today
plus another 10 annual payments that increase by $165,000 per year. Thus, in one year you receive
$1.165 million. In two years, you get $1.33 million, and so on. If the appropriate interest rate is
7.5 percent, what is the value of your winnings today?
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CHAPTER 4 Discounted Cash Flow Valuation 123
41. EAR versus APR You have just purchased a new warehouse. To finance the purchase, you’ve
arranged for a 30-year mortgage loan for 80 percent of the $3.9 million purchase price. The monthly
payment on this loan will be $18,250. What is the APR on this loan? The EAR?
42. Present Value and Break-Even Interest Consider a firm with a contract to sell an asset for $150,000
three years from now. The asset costs $102,000 to produce today. Given a relevant discount rate of
11 percent per year, will the firm make a profit on this asset? At what rate does the firm just break even?
43. Present Value and Multiple Cash Flows What is the value today of $3,500 per year, at a discount
rate of 7.6 percent, if the first payment is received 7 years from now and the last payment is received
30 years from now?
44. Variable Interest Rates A 15-year annuity pays $1,750 per month, and payments are made at the
end of each month. If the interest rate is 11.4 percent compounded monthly for the first seven years,
and 8.6 percent compounded monthly thereafter, what is the value of the annuity today?
45. Comparing Cash Flow Streams You have your choice of two investment accounts. Investment
A is a 15-year annuity that features end-of-month $1,250 payments and has an interest rate of 6.15
percent compounded monthly. Investment B is a continuously compounded lump-sum investment with
an interest rate of 7 percent also good for 15 years. How much money would you need to invest in
B today for it to be worth as much as Investment A 15 years from now?
46. Calculating Present Value of a Perpetuity Given an interest rate of 6.4 percent per year, what is the
value at t = 7 of a perpetual stream of $3,250 payments that begin at t = 15?
47. Calculating EAR A local finance company quotes an interest rate of 16.6 percent on one-year loans.
So, if you borrow $23,000, the interest for the year will be $3,818. Because you must repay a total of
$26,818 in one year, the finance company requires you to pay $26,818/12, or $2,234.83, per month
over the next 12 months. Is the interest rate on the loan 16.6 percent? What rate would legally have to
be quoted? What is the effective annual rate?
48. Calculating Present Values A 5-year annuity of 10 $6,500 semiannual payments will begin 9
years from now, with the first payment coming 9.5 years from now. If the discount rate is 9 percent
compounded monthly, what is the value of this annuity five years from now? What is the value three
years from now? What is the current value of the annuity?
49. Calculating Annuities Due Suppose you are going to receive $17,500 per year for five years.
The appropriate interest rate is 7.4 percent.
a. What is the present value of the payments if they are in the form of an ordinary annuity? What is the
present value if the payments are an annuity due?
b. Suppose you plan to invest the payments for five years. What is the future value if the payments are
an ordinary annuity? What if the payments are an annuity due?
c. Which has the highest present value, the ordinary annuity or the annuity due? Which has the
highest future value? Will this always be true?
50. Calculating Annuities Due You want to buy a new sports car from Muscle Motors for $83,000.
The contract is in the form of a 60-month annuity due at an APR of 4.89 percent, compounded
monthly. What will your monthly payment be?
51. Amortization with Equal Payments Prepare an amortization schedule for a three-year loan of
$51,000. The interest rate is 9 percent per year, and the loan calls for equal annual payments. How
much interest is paid in the third year? How much total interest is paid over the life of the loan?
52. Amortization with Equal Principal Payments Rework Problem 51 assuming that the loan agreement
calls for a principal reduction of $17,000 every year instead of equal annual payments.
53. Calculating Annuities Due You want to lease a set of golf clubs from Pings Ltd. The lease contract is
in the form of 24 equal monthly payments at an APR of 9.7 percent, compounded monthly. Since the
clubs cost $3,100 retail, Pings wants the present value of the lease payments to equal $3,100 and
your first payment is due immediately. What will your monthly lease payments be?
Challenge
(Questions 53–80)
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124 PART 2 Valuation and Capital Budgeting
54. Annuities You are saving for the college education of your two children. They are two years apart
in age; one will begin college 15 years from today and the other will begin 17 years from today.
You estimate your children’s college expenses to be $55,000 per year per child, payable at the
beginning of each school year. The annual interest rate is 9.2 percent. How much money must you
deposit in an account each year to fund your children’s education? Your deposits begin one year from
today. You will make your last deposit when your oldest child enters college. Assume your children will
be on the four-year plan.
55. Growing Annuities Tom Adams has received a job offer from a large investment bank as a clerk to an
associate banker. His base salary will be $65,000. He will receive his first annual salary payment one
year from the day he begins to work. In addition, he will get an immediate $12,000 bonus for joining
the company. His salary will grow at 3.2 percent each year. Each year he will receive a bonus equal to
10 percent of his salary. Mr. Adams is expected to work for 35 years. What is the present value of the
offer if the discount rate is 9 percent?
56. Calculating Annuities You have recently won the super jackpot in the Set for Life Lottery. On reading
the fine print, you discover that you have the following two options:
a. You will receive 31 annual payments of $400,000, with the first payment being delivered today.
The income will be taxed at a rate of 36 percent. Taxes will be withheld when the checks are
issued.
b. You will receive $1,000,000 now, and you will not have to pay taxes on this amount. In addition,
beginning one year from today, you will receive $325,000 each year for 30 years. The cash flows
from this annuity will be taxed at 36 percent.
Using a discount rate of 4.5 percent, which option should you select?
57. Calculating Growing Annuities You have 30 years left until retirement and want to retire with
$2.2 million. Your salary is paid annually and you will receive $70,000 at the end of the current year.
Your salary will increase at 3 percent per year, and you can earn a return of 9.7 percent on the money
you invest. If you save a constant percentage of your salary, what percentage of your salary must you
save each year?
58. Balloon Payments On September 1, 2014, Susan Chao bought a motorcycle for $35,000. She paid
$1,000 down and financed the balance with a five-year loan at an APR of 5.8 percent compounded
monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1,
2014). Two years later, at the end of October 2016, Susan got a new job and decided to pay off the
loan. If the bank charges her a 1 percent prepayment penalty based on the loan balance, how much
must she pay the bank on November 1, 2016?
59. Calculating Annuity Values Bilbo Baggins wants to save money to meet three objectives. First, he
would like to be able to retire 30 years from now with a retirement income of $25,000 per month for
20 years, with the first payment received 30 years and 1 month from now. Second, he would like to
purchase a cabin in Rivendell in 10 years at an estimated cost of $340,000. Third, after he passes on
at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to his
nephew Frodo. He can afford to save $2,200 per month for the next 10 years. If he can earn an EAR
of 11 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save
each month in Years 11 through 30?
60. Calculating Annuity Values After deciding to get a new car, you can either lease the car or purchase
it with a three-year loan. The car you wish to buy costs $38,000. The dealer has a special leasing
arrangement where you pay $2,500 today and $425 per month for the next three years. If you
purchase the car, you will pay it off in monthly payments over the next three years at an APR of 3.8
percent, compounded monthly. You believe that you will be able to sell the car for $24,500 in three
years. Should you buy or lease the car? What break-even resale price in three years would make you
indifferent between buying and leasing?
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CHAPTER 4 Discounted Cash Flow Valuation 125
61. Calculating Annuity Values An All-Pro defensive lineman is in contract negotiations. The team has
offered the following salary structure:
TIME SALARY
0 $7,000,000
1 6,100,000
2 6,900,000
3 7,600,000
4 8,200,000
5 9,500,000
6 8,400,000
All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate
the terms. He wants a signing bonus of $9 million payable today and a contract value increase of
$2.5 million. He also wants an equal salary paid every three months, with the first paycheck three
months from now. If the interest rate is an APR of 5 percent compounded daily, what is the amount of
his quarterly check? Assume 365 days in a year.
62. Discount Interest Loans This question illustrates what is known as discount interest. Imagine you
are discussing a loan with a somewhat unscrupulous lender. You want to borrow $20,000 for one year.
The interest rate is 14.5 percent. You and the lender agree that the interest on the loan will be
.145 × $20,000 = $2,900. So the lender deducts this interest amount from the loan up front and
gives you $17,100. In this case, we say that the discount is $2,900. What’s wrong here?
63. Calculating Annuity Values You are serving on a jury. A plaintiff is suing the city for injuries sustained
after a freak street sweeper accident. In the trial, doctors testified that it will be five years before the
plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the
foreperson of the jury and propose that the jury give the plaintiff an award to cover the following:
(1) The present value of two years’ back pay. The plaintiff’s annual salary for the last two years
would have been $42,000 and $45,000, respectively. (2) The present value of five years’ future salary.
You assume the salary will be $49,000 per year. (3) $150,000 for pain and suffering. (4) $25,000 for
court costs. Assume that the salary payments are equal amounts paid at the end of each month. If the
interest rate you choose is an EAR of 9 percent, what is the size of the settlement? If you were the
plaintiff, would you like to see a higher or lower interest rate?
64. Calculating EAR with Points You are looking at a one-year loan of $10,000. The interest rate is
quoted as 12.5 percent plus two points. A point on a loan is 1 percent (one percentage point) of the
loan amount. Quotes similar to this one are very common with home mortgages. The interest rate
quotation in this example requires the borrower to pay two points to the lender up front and repay the
loan later with 12.5 percent interest. What rate would you actually be paying here?
65. Calculating EAR with Points The interest rate on a one-year loan is quoted as 9 percent plus three
points (see the previous problem). What is the EAR? Is your answer affected by the loan amount?
66. EAR versus APR There are two banks in the area that offer 30-year, $225,000 mortgages at 5.4
percent compounded monthly and charge a $2,400 loan application fee. However, the application
fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that
charged by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any
fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not
required with nonrefundable fees (presumably because refundable fees are part of the loan rather than
a fee). What are the EARs on these two loans? What are the APRs?
67. Calculating EAR with Add-On Interest This problem illustrates a deceptive way of quoting interest
rates called add-on interest. Imagine that you see an advertisement for Crazy Judy’s Stereo City that
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126 PART 2 Valuation and Capital Budgeting
reads something like this: “$2,500 Instant Credit! 17.5% Simple Interest! Three Years to Pay! Low,
Low Monthly Payments!” You’re not exactly sure what all this means and somebody has spilled ink
over the APR on the loan contract, so you ask the manager for clarification.
Judy explains that if you borrow $2,500 for three years at 17.5 percent interest, in three years you
will owe
$2,500 × 1.1753 = $2,500 × 1.622234 = $4,055.59
Now, Judy recognizes that coming up with $4,055.59 all at once might be a strain, so she lets you
make “low, low monthly payments” of $4,055.59/36 = $112.66 per month, even though this is extra
bookkeeping work for her.
Is the interest rate on this loan 17.5 percent? Why or why not? What is the APR on this loan?
What is the EAR? Why do you think this is called add-on interest?
68. Growing Annuities You have successfully started and operated a company for the past 10 years.
You have decided that it is time to sell your company and spend time on the beaches of Hawaii.
A potential buyer is interested in your company, but he does not have the necessary capital to pay you
a lump sum. Instead, he has offered $500,000 today and annuity payments for the balance. The first
payment will be for $220,000 in three months. The payments will increase at 2.5 percent per quarter
and a total of 25 quarterly payments will be made. If you require an EAR of 11 percent, how much are
you being offered for your company?
69. Calculating the Number of Periods Your Christmas ski vacation was great, but it unfortunately ran a
bit over budget. All is not lost, because you just received an offer in the mail to transfer your $10,000
balance from your current credit card, which charges an annual rate of 18.2 percent, to a new credit
card charging a rate of 7.9 percent. How much faster could you pay the loan off by making your
planned monthly payments of $175 with the new card? What if there was a fee of 3 percent charged
on any balances transferred?
70. Future Value and Multiple Cash Flows An insurance company is offering a new policy to its
customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth.
The details of the policy are as follows: The purchaser (say, the parent) makes the following six
payments to the insurance company:
First birthday: $750
Second birthday: 750
Third birthday: 850
Fourth birthday: 850
Fifth birthday: 950
Sixth birthday: 950
After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she
receives $500,000. If the relevant interest rate is 10 percent for the first six years and 8 percent for all
subsequent years, is the policy worth buying?
71. Annuity Present Values and Effective Rates You have just won the lottery. You will receive
$4,000,000 today, and then receive 40 payments of $1,750,000. These payments will start one year
from now and will be paid every six months. A representative from Greenleaf Investments has offered
to purchase all the payments from you for $35 million. If the appropriate interest rate is an APR of 8
percent compounded daily, should you take the offer? Assume there are 365 days per year.
72. Calculating Interest Rates A financial planning service offers a college savings program. The plan
calls for you to make six annual payments of $15,000 each, with the first payment occurring today,
your child’s 12th birthday. Beginning on your child’s 18th birthday, the plan will provide $32,000 per
year for four years. What return is this investment offering?
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CHAPTER 4 Discounted Cash Flow Valuation 127
73. Break-Even Investment Returns Your financial planner offers you two different investment plans.
Plan X is a $15,000 annual perpetuity. Plan Y is a 10-year, $31,000 annual annuity. Both plans will
make their first payment one year from today. At what discount rate would you be indifferent between
these two plans?
74. Perpetual Cash Flows What is the value of an investment that pays $30,000 every other year
forever, if the first payment occurs one year from today and the discount rate is an APR of 11 percent
compounded daily? What is the value today if the first payment occurs four years from today?
75. Ordinary Annuities and Annuities Due As discussed in the text, an annuity due is identical to an
ordinary annuity except that the periodic payments occur at the beginning of each period and not at
the end of the period. Show that the relationship between the value of an ordinary annuity and the
value of an otherwise equivalent annuity due is
Annuity due value = Ordinary annuity value × (1 + r )
Show this for both present and future values.
76. Calculating Annuities You have just won the Life’s Downhill After 30 lottery. The lottery payments will
be made for the next 30 years. The payments are slightly unusual in that you will be paid $600,000
every six months starting six months from today, for a total of 60 payments. You will also receive
$900,000 every nine months starting nine months from today, for a total of 40 payments. When the
payments coincide, for example 18 months from today, you will receive both payments. If the interest
rate is an APR of 8.1 percent compounded monthly, what is the present value of your winnings?
77. Calculating EAR A check-cashing store is in the business of making personal loans to walk-up
customers. The store makes only one-week loans at 5.5 percent interest per week.
a. What APR must the store report to its customers? What is the EAR that the customers are actually
paying?
b. Now suppose the store makes one-week loans at 5.5 percent discount interest per week (see
Question 62). What’s the APR now? The EAR?
c. The check-cashing store also makes one-month add-on interest loans at 5.5 percent discount interest
per week. Thus, if you borrow $100 for one month (four weeks), the interest will be ($100 × 1.0554 )
− 100 = $23.88. Because this is discount interest, your net loan proceeds today will be $76.12. You
must then repay the store $100 at the end of the month. To help you out, though, the store lets you
pay off this $100 in installments of $25 per week. What is the APR of this loan? What is the EAR?
78. Present Value of a Growing Perpetuity What is the equation for the present value of a growing
perpetuity with a payment of C one period from today if the payments grow by C each period?
79. Rule of 72 A useful rule of thumb for the time it takes an investment to double with discrete
compounding is the “Rule of 72.” To use the Rule of 72, you divide 72 by the interest rate to determine
the number of periods it takes for a value today to double. For example, if the interest rate is 6 percent,
the Rule of 72 says it will take 72/6 = 12 years to double. This is approximately equal to the actual
answer of 11.90 years. The Rule of 72 can also be applied to determine what interest rate is needed to
double money in a specified period. This is a useful approximation for many interest rates and periods.
At what rate is the Rule of 72 exact?
80. Rule of 69.3 A corollary to the Rule of 72 is the Rule of 69.3. The Rule of 69.3 is exactly correct
except for rounding when interest rates are compounded continuously. Prove the Rule of 69.3 for
continuously compounded interest.
WHAT’S ON THE WEB?
1. Calculating Future Values Go to www.dinkytown.net and follow the “Investment Calculators” link. If you
currently have $10,000 and invest this money at 9 percent, how much will you have in 30 years? Assume
you will not make any additional contributions. How much will you have if you can earn 11 percent?
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128 PART 2 Valuation and Capital Budgeting
CLOSING CASE
THE MBA DECISION
Ben Bates graduated from college six years ago with a finance undergraduate degree. Since graduation,
he has been employed in the finance department at East Coast Yachts. Although he is satisfied with his
current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to
achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount
Perry College. Although internships are encouraged by both schools, to get class credit for the internship,
no salary can be paid. Other than internships, neither school will allow its students to work while enrolled
in its MBA program.
Ben’s annual salary at East Coast Yachts is $57,000 per year, and his salary is expected to increase at
3 percent per year until retirement. He is currently 28 years old and expects to work for 40 more years.
His current job includes a fully paid health insurance plan, and his current average tax rate is 26 percent.
Ben has a savings account with enough money to cover the entire cost of his MBA program.
2. Future Values and Taxes Taxes can greatly affect the future value of your investment. The website at
www.fincalc.com has a financial calculator that adjusts your return for taxes. Suppose you have $50,000
to invest today. If you can earn a 12 percent return and no additional annual savings, how much will
you have in 20 years? (Enter 0 percent as the tax rate.) Now, assume that your marginal tax rate is
27.5 percent. How much will you have at this tax rate?
Excel is a great tool for solving problems, but with many time value of money problems, you may still need to
draw a time line. For example, consider a classic retirement problem. A friend is celebrating her birthday and
wants to start saving for her anticipated retirement. She has the following years to retirement and retirement
spending goals:
Years until retirement: 30
Amount to withdraw each year: $90,000
Years to withdraw in retirement: 20
Interest rate: 8%
Because your friend is planning ahead, the first withdrawal will not take place until one year after she
retires. She wants to make equal annual deposits into her account for her retirement fund.
a. If she starts making these deposits in one year and makes her last deposit on the day she retires, what
amount must she deposit annually to be able to make the desired withdrawals at retirement?
b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual
payments, she has decided to make one lump-sum deposit today to cover her retirement needs. What
amount does she have to deposit today?
c. Suppose your friend’s employer will contribute to the account each year as part of the company’s profit-
sharing plan. In addition, your friend expects a distribution from a family trust several years from now.
What amount must she deposit annually now to be able to make the desired withdrawals at retirement?
The details are
Employer’s annual contribution: $1,500
Years until trust fund distribution: 20
Amount of trust fund distribution: $25,000
EXCEL MASTER IT ! PROBLEM
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CHAPTER 4 Discounted Cash Flow Valuation 129
The Ritter College of Business at Wilton University is one of the top MBA programs in the country.
The MBA degree requires two years of full-time enrollment at the university. The annual tuition is $63,000,
payable at the beginning of each school year. Books and other supplies are estimated to cost $2,500 per year.
Ben expects that after graduation from Wilton, he will receive a job offer for about $105,000 per year, with an
$18,000 signing bonus. The salary at this job will increase at 4 percent per year. Because of the higher salary,
his average income tax rate will increase to 31 percent.
The Bradley School of Business at Mount Perry College began its MBA program 16 years ago. The Bradley
School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one-year pro-
gram, with a tuition cost of $75,000 to be paid upon matriculation. Books and other supplies for the program
are expected to cost $3,500. Ben thinks that after graduation from Mount Perry, he will receive an offer of
$88,000 per year, with a $15,000 signing bonus. The salary at this job will increase at 3.5 percent per year.
His average income tax rate at this level of income will be 29 percent.
Both schools offer a health insurance plan that will cost $3,000 per year, payable at the beginning of the
year. Ben also estimates that room and board expenses will cost $2,000 more per year at both schools than his
current expenses, payable at the beginning of each year. The appropriate discount rate is 6.1 percent. Assume
all salaries are paid at the end of each year.
1. How does Ben’s age affect his decision to get an MBA?
2. What other, perhaps nonquantifiable factors, affect Ben’s decision to get an MBA?
3. Assuming all salaries are paid at the end of each year, what is the best option for Ben—from a strictly
financial standpoint?
4. In choosing between the two schools, Ben believes that the appropriate analysis is to calculate the
future value of each option. How would you evaluate this statement?
5. What initial salary would Ben need to receive to make him indifferent between attending Wilton
University and staying in his current position? Assume his tax rate after graduating from Wilton University
will be 31 percent regardless of his income level.
6. Suppose that instead of being able to pay cash for his MBA, Ben must borrow the money. The current
borrowing rate is 5.4 percent. How would this affect his decision to get an MBA?
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PART 2 Valuation and Capital Budgeting130
5
OPENING
CASE
Interest Rates
and Bond Valuation
2015 and early 2016 proved to be a very unusual period for bonds. For example, in February
2016, Sweden’s central bank lowered its interest rate from negative .35 percent to negative
.5 percent! Sweden was not alone as the Eurozone, Switzerland, and Japan, among others,
all had negative interest rates set by the respective central banks. Why was this happening?
Central banks were in a race to the bot tom, lowering interest rates in an attempt to improve
their domestic economies.
While central bank interest rates are a monetary policy tool, you would expect that the
interest rates determined by the market would never be negative. After all, why would you
accept less in the future than you would now? However, this proved to be incorrect as the yield
on the two-year Swiss government bond was negative 1.12 percent. And, in an event that had
never previously occurred, bonds issued by chocolate giant Nestlé and Deutsche Bank AG
both traded with negative yields.
This chapter takes what we have learned about the time value of money and shows how it
can be used to value one of the most common of all financial assets, a bond. It then discusses
bond features, bond types, and the operation of the bond market. What we will see is that bond
prices depend critically on interest rates, so we will go on to discuss some very fundamental
issues regarding interest rates. Clearly, interest rates are important to everybody because
they underlie what businesses of all types—small and large—must pay to borrow money.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
Our goal in this chapter is to introduce you to bonds. We begin by showing how the tech-
niques we developed in Chapter 4 can be applied to bond valuation. From there, we go on
to discuss bond features and how bonds are bought and sold. One important thing we learn
is that bond values depend, in large part, on interest rates. We therefore close out the chap-
ter with an examination of interest rates and their behavior.
5.1 BONDS AND BOND VALUATION
When a corporation (or government) wishes to borrow money from the public on a
long-term basis, it usually does so by issuing or selling debt securities that are generi-
cally called bonds. In this section, we describe the various features of corporate bonds
ExcelMaster
coverage online
www.mhhe.com/RossCore5e
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CHAPTER 5 Interest Rates and Bond Valuation 131
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and some of the terminology associated with bonds. We then discuss the cash flows
associated with a bond and how bonds can be valued using our discounted cash
flow procedure.
Bond Features and Prices
A bond is normally an interest-only loan, meaning that the borrower will pay the interest
every period, but none of the principal will be repaid until the end of the loan. For exam-
ple, suppose the Beck Corporation wants to borrow $1,000 for 30 years. The interest rate
on similar debt issued by similar corporations is 12 percent. Beck will thus pay .12 ×
$1,000 = $120 in interest every year for 30 years. At the end of 30 years, Beck will repay
the $1,000. As this example suggests, a bond is a fairly simple financing arrangement.
There is, however, a rich jargon associated with bonds, so we will use this example to
define some of the more important terms.
In our example, the $120 regular interest payments that Beck promises to make are called
the bond’s coupons. Because the coupon is constant and paid every year, the type of bond
we are describing is sometimes called a level coupon bond. The amount that will be repaid
at the end of the loan is called the bond’s face value, or par value. As in our example, this
par value is usually $1,000 for corporate bonds, and a bond that sells for its par value is
called a par value bond. Government bonds frequently have much larger face, or par, val-
ues. Finally, the annual coupon divided by the face value is called the coupon rate on the
bond; in this case, because $120/1,000 = 12 percent, the bond has a 12 percent coupon rate.
The number of years until the face value is paid is called the bond’s time to maturity.
A corporate bond will frequently have a maturity of 30 years when it is originally issued,
but this varies. Once the bond has been issued, the number of years to maturity declines as
time goes by.
Bond Values and Yields
As time passes, interest rates change in the marketplace. The cash flows from a bond, how-
ever, stay the same. As a result, the value of the bond will fluctuate. When interest rates
rise, the present value of the bond’s remaining cash flows declines, and the bond is worth
less. When interest rates fall, the bond is worth more.
To determine the value of a bond at a particular point in time, we need to know the num-
ber of periods remaining until maturity, the face value, the coupon, and the market interest
rate for bonds with similar features. This interest rate required in the market on a bond is
called the bond’s yield to maturity (YTM). This rate is sometimes called the bond’s yield
for short. Given all this information, we can calculate the present value of the cash flows as
an estimate of the bond’s current market value.
For example, suppose the Xanth (pronounced “zanth”) Co. were to issue a bond with
10 years to maturity. The Xanth bond has an annual coupon of $80. (Most, but not all,
straight coupon bonds in the U.S. pay interest semiannually. Practice differs around the
world.) Similar bonds have a yield to maturity of 8 percent. Based on our preceding dis-
cussion, the Xanth bond will pay $80 per year for the next 10 years in coupon interest. In
10 years, Xanth will pay $1,000 to the owner of the bond. The cash flows from the bond
are shown in Figure 5.1 What would this bond sell for?
As illustrated in Figure 5.1, the Xanth bond’s cash flows have an annuity component
(the coupons) and a lump sum (the face value paid at maturity). We thus estimate the mar-
ket value of the bond by calculating the present value of these two components separately
and adding the results together. First, at the going rate of 8 percent, the present value of the
$1,000 paid in 10 years is:
Present value = $1,000/1.08 10 = $1,000 / 2.1589 = $463.19
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ros89907_ch05_130-164.indd 132 12/05/16 02:55 PM
132
Second, the bond offers $80 per year for 10 years; the present value of this annuity
stream is:
Annuity present value
= $80 × (1 − 1/1.0 8 10 )/.08
= $80 × (1 − 1/2.1589)/.08
= $80 × 6.7101
= $536.81
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $463.19 + 536.81 = $1,000
This bond sells for exactly its face value. This is not a coincidence. The going interest rate
in the market is 8 percent. Considered as an interest-only loan, what interest rate does this
bond have? With an $80 coupon, this bond pays exactly 8 percent interest only when it
sells for $1,000.
To illustrate what happens as interest rates change, suppose that a year has gone by. The
Xanth bond now has nine years to maturity. If the interest rate in the market has risen to
10 percent, what will the bond be worth? To find out, we repeat the present value calcula-
tions with 9 years instead of 10, and a 10 percent yield instead of an 8 percent yield. First,
the present value of the $1,000 paid in nine years at 10 percent is:
Present value = $1,000/1.10 9 = $1,000 / 2.3579 = $424.10
Second, the bond now offers $80 per year for nine years; the present value of this annuity
stream at 10 percent is:
Annuity present value
= $80 × (1 − 1/1.1 0 9 )/.10
= $80 × (1 − 1/2.3579)/.10
= $80 × 5.7590
= $460.72
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $424.10 + 460.72 = $884.82
Therefore, the bond should sell for about $885. In the vernacular, we say that this bond,
with its 8 percent coupon, is priced to yield 10 percent at $885.
The Xanth Co. bond now sells for less than its $1,000 face value. Why? The market
interest rate is 10 percent. Considered as an interest-only loan of $1,000, this bond only
pays 8 percent, its coupon rate. Because this bond pays less than the going rate, investors
A good bond site to visit
is finance.yahoo.com/
bonds, which has loads of
useful information.
FIGURE 5.1 Cash Flows for Xanth Co. Bond
Year
Cash flows
Coupon
Face value
As shown, the Xanth bond has an annual coupon of $80 and a face, or par, value of $1,000 paid at maturity in 10 years.
$ 80
1,000
$1,080
0 1 2 3 4 5 6 7 8 9 10
$80 $80 $80 $80 $80 $80 $80 $80 $80
$80$80$80$80$80$80$80$80$80
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CHAPTER 5 Interest Rates and Bond Valuation 133
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are willing to lend only something less than the $1,000 promised repayment. Because the
bond sells for less than face value, it is said to be a discount bond.
The only way to get the interest rate up to 10 percent is to lower the price to less than
$1,000 so that the purchaser, in effect, has a built-in gain. For the Xanth bond, the price
of $885 is $115 less than the face value, so an investor who purchased and kept the bond
would get $80 per year and would have a $115 gain at maturity as well. This gain compen-
sates the lender for the below-market coupon rate.
Another way to see why the bond is discounted by $115 is to note that the $80 cou-
pon is $20 below the coupon on a newly issued par value bond, based on current market
conditions. The bond would be worth $1,000 only if it had a coupon of $100 per year. In
a sense, an investor who buys and keeps the bond gives up $20 per year for nine years. At
10 percent, this annuity stream is worth:
Annuity present value
= $20 × (1 − 1/1. 10 9 )/.10
= $20 × 5.7590
= $115.18
This is the amount of the discount.
What would the Xanth bond sell for if interest rates had dropped by 2 percent instead of
rising by 2 percent? As you might guess, the bond would sell for more than $1,000. Such a
bond is said to sell at a premium and is called a premium bond.
This case is just the opposite of that of a discount bond. The Xanth bond now has a
coupon rate of 8 percent when the market rate is only 6 percent. Investors are willing to
pay a premium to get this extra coupon amount. In this case, the relevant discount rate
is 6 percent, and there are nine years remaining. The present value of the $1,000 face
amount is:
Present value of face amount = $1,000/1.06 9 = $1,000/1.6895 = $591.89
The present value of the coupon stream is:
Annuity present value
= $80 × (1 − 1/1.0 6 9 )/.06
= $80 × (1 − 1/1.6895)/.06
= $80 × 6.8017
= $544.14
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $591.89 + 544.14 = $1,136.03
Total bond value is therefore about $136 in excess of par value. Once again, we can verify
this amount by noting that the coupon is now $20 too high, based on current market condi-
tions. The present value of $20 per year for nine years at 6 percent is:
Annuity present value
= $20 × (1 − 1/1. 6 9 )/.06
= $20 × 6.8017
= $136.03
This is just as we calculated.
Based on our examples, we can now write the general expression for the value of a
bond. If a bond has (1) a face value of F paid at maturity, (2) a coupon of C paid per period,
(3) T periods to maturity, and (4) a yield of r per period, its value is:
Bond value = C × [1 – 1/(1 + r ) T ]/r + F/(1 + r ) T [5.1]
Online bond calculators
are available at personal
.fidelity.com; interest
rate information is avail-
able at money.cnn.com/
data/bonds and www.
bankrate.com.
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134
As we have illustrated in this section, bond prices and interest rates always move in
opposite directions. When interest rates rise, a bond’s value, like any other present value,
will decline. Similarly, when interest rates fall, bond values rise. Even if we are considering
a bond that is riskless in the sense that the borrower is certain to make all the payments,
there is still risk in owning a bond. We discuss this next.
Interest Rate Risk
The risk that arises for bond owners from fluctuating interest rates is called interest rate
risk. How much interest rate risk a bond has depends on how sensitive its price is to inter-
est rate changes. This sensitivity directly depends on two things: the time to maturity and
the coupon rate. As we will see momentarily, you should keep the following in mind when
looking at a bond:
1. All other things being equal, the longer the time to maturity, the greater the
interest rate risk.
2. All other things being equal, the lower the coupon rate, the greater the interest
rate risk.
Learn more about bonds
at investorguide.com.
E
X
A
M
P
L
E
5
.1
In practice, bonds issued in the United States usually make coupon payments twice a year. So, if an ordi-
nary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, but this $140
will come in two payments of $70 each. Suppose we are examining such a bond. The yield to maturity is
quoted at 16 percent.
Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multiplied by
the number of periods. In this case, with a 16 percent quoted yield and semiannual payments, the true
yield is 8 percent per six months. The bond matures in seven years. What is the bond’s price? What is the
effective annual yield on this bond?
Based on our discussion, we know the bond will sell at a discount because it has a coupon rate of
7 percent every six months when the market requires 8 percent every six months. So, if our answer
exceeds $1,000, we know that we have made a mistake.
To get the exact price, we first calculate the present value of the bond’s face value of $1,000 paid
in seven years. This seven-year period has 14 periods of six months each. At 8 percent per period, the
value is:
Present value = $1,000/1.0814 = $1,000/2.9372 = $340.46
The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate, the
present value of such an annuity is:
Annuity present value
= $70 × (1 − 1/1.0 8 14 )/.08
= $70 × (1 − .3405)/.08
= $70 × 8.2442
= $577.10
The total present value gives us what the bond should sell for:
Total present value = $340.46 + 577.10 = $917.56
To calculate the effective yield on this bond, note that 8 percent every six months is equivalent to:
Effective annual rate = (1 + .08)2 − 1 = 16.64%
The effective yield, therefore, is 16.64 percent.
Semiannual Coupons
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We illustrate the first of these two points in Figure 5.2. As shown, we compute and plot
prices under different interest rate scenarios for 10 percent coupon bonds with maturities
of 1 year and 30 years. We assume coupons are paid semi-annually. Notice how the slope
of the line connecting the prices is much steeper for the 30-year maturity than it is for the
1-year maturity. This steepness tells us that a relatively small change in interest rates will
lead to a substantial change in the bond’s value. In comparison, the one-year bond’s price
is relatively insensitive to interest rate changes.
Intuitively, we can see that the reason that shorter-term bonds have less interest rate sensi-
tivity is that a large portion of a bond’s value comes from the $1,000 face amount. The pres-
ent value of this amount isn’t greatly affected by a small change in interest rates if the amount
is to be received in one year. Even a small change in the interest rate, however, once it is
compounded for 30 years, can have a significant effect on the present value. As a result, the
present value of the face amount will be much more volatile with a longer-term bond.
The other thing to know about interest rate risk is that, like most things in finance and
economics, it increases at a decreasing rate. In other words, if we compared a 10-year
bond to a 1-year bond, we would see that the 10-year bond has much greater interest rate
risk. However, if you were to compare a 20-year bond to a 30-year bond, you would find
that while the 30-year bond has somewhat greater interest rate risk because it has a longer
maturity, the difference in the risk would be fairly small.
The reason that bonds with lower coupons have greater interest rate risk is essentially
the same. As we discussed earlier, the value of a bond depends on the present value of its
coupons and the present value of the face amount. If two bonds with different coupon rates
have the same maturity, then the value of the one with the lower coupon is proportionately
more dependent on the face amount to be received at maturity. As a result, all other things
FIGURE 5.2
Interest Rate Risk and Time
to Maturity
1,000
2,000
1,500
500
5
Interest rate (%)
Bo
nd
v
al
ue
($
)
10 15 20
30-year bond
1-year bond
$501.64
$1,048.19
$1,772.72
$913.22
Value of a Bond with a 10 Percent Coupon Rate for Di�erent Interest Rates and Maturities
Time to Maturity
Interest Rate 1 Year 30 Years
5%
10
15
20
$1,048.19
1,000.00
955.11
913.22
$1,772.72
1,000.00
671.02
501.64
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136
being equal, its value will fluctuate more as interest rates change. Put another way, the
bond with the higher coupon has a larger cash flow early in its life, so its value is less sensi-
tive to changes in the discount rate.
Bonds are rarely issued with maturities longer than 30 years. However, low interest rates
in recent years have led to the issuance of bonds with much longer terms. In the 1990s, Walt
Disney issued “Sleeping Beauty” bonds with a 100-year maturity. Similarly, BellSouth,
Coca-Cola, and Dutch banking giant ABN AMRO all issued bonds with 100-year maturities.
These companies evidently wanted to lock in the historical low interest rates for a long
time. Before these fairly recent issues, it appears the last time 100-year bonds were issued
was in May 1954, by the Chicago and Eastern Railroad. And low interest rates in recent years
have led to more 100-year bonds. For example, in July 2015, Brazilian oil company Petrobras
issued 100-year bonds, and those weren’t the longest maturity bonds issued in 2015 as issu-
ance of perpetual bonds hit a record. For example, French energy company Total issued
$5.7 billion in perpetual bonds and Volkswagen issued $2.6 billion in perpetual debt.
We can illustrate the effect of interest rate risk using the 100-year BellSouth issue. The
following table provides some basic information on this issue, along with its prices on
December 31, 1995, July 31, 1996, and December 9, 2014.
MATURITY
COUPON
RATE
PRICE ON
12/31/95
PRICE ON
7/31/96
PERCENTAGE
CHANGE
IN PRICE
1995–96
PRICE ON
12/9/14
PERCENTAGE
CHANGE
IN PRICE
1996–2014
2095 7.00% $1,000.00 $800.00 −20.0% $1,235.59 +54.4%
Several things emerge from this table. First, interest rates apparently rose between
December 31, 1995, and July 31, 1996 (why?). After that, however, they fell (why?). The
bond’s price first lost 20 percent and then gained 54.4 percent. These swings illustrate that
longer-term bonds have significant interest rate risk.
Finding the Yield to Maturity:
More Trial and Error
Frequently, we will know a bond’s price, coupon rate, and maturity date, but not its yield
to maturity. For example, suppose we are interested in a six-year, 8 percent coupon bond
with annual coupons. A broker quotes a price of $955.14. What is the yield on this bond?
We’ve seen that the price of a bond can be written as the sum of its annuity and lump-
sum components. Knowing that there is an $80 coupon for six years and a $1,000 face
value, we can say that the price is:
$955.14 = $80 × [1 − 1/(1 + r ) 6 ]/ r + 1,000/(1 + r ) 6
where r is the unknown discount rate, or yield to maturity. We have one equation here and
one unknown, but we cannot solve for r explicitly. The only way to find the answer is to
use trial and error.
This problem is essentially identical to the one we examined in the last chapter when we
tried to find the unknown interest rate on an annuity. However, finding the rate (or yield)
on a bond is even more complicated because of the $1,000 face amount.
We can speed up the trial-and-error process by using what we know about bond prices
and yields. In this case, the bond has an $80 coupon and is selling at a discount. We thus
know that the yield is greater than 8 percent. If we compute the price at 10 percent:
Bond value
=
$80 × (1 − 1/1. 10 6 ) /.10 + 1,000/1. 10 6
= $80 × 4.3553 + 1,000/1.7716
=
$912.89
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CHAPTER 5 Interest Rates and Bond Valuation 137
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TABLE 5.1
Summary of Bond Valuation
At 10 percent, the value we calculate is lower than the actual price, so 10 percent is too
high. The true yield must be somewhere between 8 and 10 percent. At this point, it’s “plug
and chug” to find the answer. You would probably want to try 9 percent next. If you did,
you would see that this is in fact the bond’s yield to maturity.
A bond’s yield to maturity should not be confused with its current yield, which is
a bond’s annual coupon divided by its price. In the example we just worked, the bond’s
annual coupon was $80, and its price was $955.14. Given these numbers, we see that
the current yield is $80/955.14 = 8.38 percent, which is less than the yield to maturity
of 9 percent. The reason the current yield is too low is that it only considers the coupon
portion of your return; it doesn’t consider the built-in gain from the price discount. For a
premium bond, the reverse is true, meaning that current yield would be higher because it
ignores the built-in loss.
Our discussion of bond valuation is summarized in Table 5.1. A nearby Spreadsheet
Techniques box shows how to find prices and yields the easy way.
Current market rates
are available at
www.bankrate.com.
I. Finding the Value of a Bond
Bond value = C × [1 – 1/(1 + r ) T ] /r + F/(1 + r ) T
where
C = Coupon paid each period
r = Discount rate per period
T = Number of periods
F = Bond’s face value
II. Finding the Yield on a Bond
Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to
maturity, by trial and error only. To do this, try different discount rates until the calculated bond value equals the given
value (or let a spreadsheet or a financial calculator do it for you). Remember that increasing the rate decreases the
bond value.
E
X
A
M
P
L
E
5
.2
A bond has a quoted price of $1,080.42. It has a face value of $1,000, a semiannual coupon of $30, and
a maturity of five years. What is its current yield? What is its yield to maturity? Which is bigger? Why?
Notice that this bond makes semiannual payments of $30, so the annual payment is $60. The current
yield is thus $60/1,080.42 = 5.55 percent. To calculate the yield to maturity, refer back to Example 5.1.
Now, in this case, the bond pays $30 every six months and it has 10 six-month periods until maturity.
So, we need to find r as follows:
$1,080.42 = $30 × [ 1 − 1/(1 + r )
10 ] /r + 1,000/(1 + r )
10
After some trial and error, we find that r is equal to 2.1 percent. But, the tricky part is that this 2.1 percent
is the yield per six months. We have to double it to get the yield to maturity, so the yield to maturity is
4.2 percent, which is less than the current yield. The reason is that the current yield ignores the built-in
loss of the premium between now and maturity.
Current Events
5.2 MORE ON BOND FEATURES
In this section, we continue our discussion of corporate debt by describing in some detail
the basic terms and features that make up a typical long-term corporate bond. We discuss
additional issues associated with long-term debt in subsequent sections.
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138
How to Calculate Bond Pr ices and
Yie lds Us ing a Spreadsheet SPREADSHEET TECHNIQUES
Most spreadsheets have fairly elaborate routines available for calculating bond values and yields; many of
these routines involve details that we have not discussed. However, setting up a simple spreadsheet to cal-
culate prices or yields is straightforward, as our next two spreadsheets show:
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
A B C D E F G H
Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a yield to
maturity of 9 percent. If the bond makes semiannual payments, what is its price today?
Settlement date: 1/1/00
Maturity date: 1/1/22
Annual coupon rate: .08
Yield to maturity: .09
Face value (% of par): 100
Coupons per year: 2
Bond price (% of par): 90.49
The formula entered in cell B13 is =PRICE(B7,B8,B9,B10,B11,B12); notice that face value and bond
price are given as a percentage of face value.
Using a spreadsheet to calculate bond values
1
2
3
4
5
6
7
8
9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
A B C D E F G H
Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a price of
$960.17. If the bond makes semiannual payments, what is its yield to maturity?
Settlement date: 1/1/00
Maturity date: 1/1/22
Annual coupon rate: .08
Bond price (% of par): 96.017
Face value (% of par): 100
Coupons per year: 2
Yield to maturity: .084
The formula entered in cell B13 is =YIELD(B7,B8,B9,B10,B11,B12); notice that face value and bond
price are entered as a percentage of face value.
Using a spreadsheet to calculate bond yields
1 7
In our spreadsheets, notice that we had to enter two dates, a settlement date and a maturity date. The
settlement date is just the date you actually pay for the bond, and the maturity date is the day the bond
actually matures. In most of our problems, we don’t explicitly have these dates, so we have to make them
up. For example, since our bond has 22 years to maturity, we just picked 1/1/2000 (January 1, 2000) as
the settlement date and 1/1/2022 (January 1, 2022) as the maturity date. Any two dates would do as long
as they are exactly 22 years apart, but these are particularly easy to work with. Finally, notice that we had
to enter the coupon rate and yield to maturity in annual terms and then explicitly provide the number of
coupon payments per year.
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Securities issued by corporations may be classified roughly as equity securities
and debt securities. At the crudest level, a debt represents something that must
be repaid; it is the result of borrowing money. When corporations borrow, they gener-
ally promise to make regularly scheduled interest payments and to repay the original
amount borrowed (that is, the principal). The person or firm making the loan is called
the creditor, or lender. The corporation borrowing the money is called the debtor,
or borrower.
From a financial point of view, the main differences between debt and equity are the
following:
1. Debt is not an ownership interest in the firm. Creditors generally do not have
voting power.
2. The corporation’s payment of interest on debt is considered a cost of doing
business and is fully tax deductible. Dividends paid to stockholders are not tax
deductible.
3. Unpaid debt is a liability of the firm. If it is not paid, the creditors can legally
claim the assets of the firm. This action can result in liquidation or reorganiza-
tion, two of the possible consequences of bankruptcy. Thus, one of the costs of
issuing debt is the possibility of financial failure. This possibility does not arise
when equity is issued.
Long-Term Debt: The Basics
Ultimately, all long-term debt securities are promises made by the issuing firm to pay
principal when due and to make timely interest payments on the unpaid balance. Beyond
this, there are a number of features that distinguish these securities from one another. We
discuss some of these features next.
The maturity of a long-term debt instrument is the length of time the debt remains
outstanding with some unpaid balance. Debt securities can be short term (with maturities
of one year or less) or long term (with maturities of more than one year).1 Short-term
debt is sometimes referred to as unfunded debt.2
Debt securities are typically called notes, debentures, or bonds. Strictly speaking, a
bond is a secured debt. However, in common usage, the word bond refers to all kinds of
secured and unsecured debt. We will therefore continue to use the term generically to
refer to long-term debt. Also, usually, the only difference between a note and a bond is the
original maturity. Issues with an original maturity of 10 years or less are often called notes.
Longer-term issues are called bonds.
The two major forms of long-term debt are public issue and privately placed. We
concentrate on public-issue bonds. Most of what we say about them holds true for
private-issue, long-term debt as well. The main difference between public-issue and
privately placed debt is that the latter is directly placed with a lender and not offered
to the public. Because this is a private transaction, the specific terms are up to the par-
ties involved.
There are many other dimensions to long-term debt, including such things as security,
call features, sinking funds, ratings, and protective covenants. The following table illus-
trates these features for a bond issued by the Walt Disney Company. If some of these terms
are unfamiliar, have no fear. We will discuss them all presently.
Information for bond
investors can be found at
www.investinginbonds
.com.
Information on individual
bonds can be found at
finra-markets.morning-
star.com/MarketData/
Default.jsp.
1 There is no universally agreed-upon distinction between short-term and long-term debt. In addition, people often refer to intermediate-term
debt, which has a maturity of more than 1 year and less than 3 to 5, or even 10, years.
2 The word funding is part of the jargon of finance. It generally refers to the long term. Thus, a firm planning to “fund” its debt requirements
may be replacing short-term debt with long-term debt.
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140
Many of these features will be detailed in the bond indenture, so we discuss this first.
The Indenture
The indenture is the written agreement between the corporation (the borrower) and its
creditors. It is sometimes referred to as the deed of trust.3 Usually, a trustee (a bank per-
haps) is appointed by the corporation to represent the bondholders. The trust company
must (1) make sure the terms of the indenture are obeyed, (2) manage the sinking fund
(described in the following pages), and (3) represent the bondholders in default, that is, if
the company defaults on its payments to them.
The bond indenture is a legal document. It can run several hundred pages and gen-
erally makes for very tedious reading. It is an important document, however, because it
generally includes the following provisions:
1. The basic terms of the bonds.
2. The total amount of bonds issued.
3. A description of property used as security.
4. The repayment arrangements.
5. The call provisions.
6. Details of the protective covenants.
We discuss these features next.
TERMS OF A BOND Corporate bonds usually have a face value (that is, a denomination) of
$1,000. This is called the principal value and it is stated on the bond certificate. So, if a corpo-
ration wanted to borrow $1 million, 1,000 bonds would have to be sold. The par value (that is,
initial accounting value) of a bond is almost always the same as the face value, and the terms are
used interchangeably in practice. Although a par value of $1,000 is most common, essentially
any par value is possible. For example, looking at our Walt Disney bond, the par value is $2,000.
Corporate bonds are usually in registered form. For example, the indenture might read
as follows:
FEATURES OF A WALT DISNEY COMPANY BOND
TERM EXPLANATION
Amount of issue $1 billion The company issued $1 billion worth of bonds.
Date of issue 01/08/2016 The bonds were sold on 01/08/2016.
Maturity 02/13/2026 The bonds mature on 02/13/2026.
Face value $2,000 The denomination of the bonds is $2,000.
Annual coupon 3.00% Each bondholder will receive $60 per bond per year
(3.00% of face value).
Offer price 99.600 The offer price will be 99.600% of the $2,000 face
value, or $1,992, per bond.
Coupon payment dates 2/13, 8/13 Coupons of $60/2 = $30 will be paid on these dates.
Security None The bonds are not secured by specific assets.
Sinking fund None The bonds have no sinking fund.
Call provision At any time The bonds do not have a deferred call.
Call price Treasury rate plus .15% The bonds have a “make whole” call price.
Rating Moody’s A2, Fitch A The bonds have a medium-quality credit rating.
Interest is payable semiannually on July 1 and January 1 of each year to the person in whose
name the bond is registered at the close of business on June 15 or December 15, respectively.
3The words loan agreement or loan contract are usually used for privately placed debt and term loans.
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This means that the company has a registrar who will record the ownership of each
bond and record any changes in ownership. The company will pay the interest and princi-
pal by check mailed directly to the address of the owner of record. A corporate bond may
be registered and have attached “coupons.” To obtain an interest payment, the owner must
separate a coupon from the bond certificate and send it to the company registrar (the pay-
ing agent).
Alternatively, the bond could be in bearer form. This means that the certificate is the
basic evidence of ownership, and the corporation will “pay the bearer.” Ownership is not
otherwise recorded, and, as with a registered bond with attached coupons, the holder of the
bond certificate detaches the coupons and sends them to the company to receive payment.
There are two drawbacks to bearer bonds. First, they are difficult to recover if they are
lost or stolen. Second, because the company does not know who owns its bonds, it cannot
notify bondholders of important events. Bearer bonds were once the dominant type, but
they are now much less common (in the United States) than registered bonds.
SECURITY Debt securities are classified according to the collateral and mortgages used
to protect the bondholder.
Collateral is a general term that frequently means securities (for example, bonds and
stocks) that are pledged as security for payment of debt. For example, collateral trust bonds
often involve a pledge of common stock held by the corporation. However, the term col-
lateral is commonly used to refer to any asset pledged on a debt.
Mortgage securities are secured by a mortgage on the real property of the borrower. The
property involved is usually real estate, for example, land or buildings. The legal document
that describes the mortgage is called a mortgage trust indenture or trust deed.
Sometimes mortgages are on specific property, for example, a railroad car. More often,
blanket mortgages are used. A blanket mortgage pledges all the real property owned by the
company.4
Bonds frequently represent unsecured obligations of the company. A debenture is an
unsecured bond, for which no specific pledge of property is made. The term note is gener-
ally used for such instruments if the maturity of the unsecured bond is less than 10 or so
years when the bond is originally issued. Debenture holders have a claim only on property
not otherwise pledged, in other words, the property that remains after mortgages and col-
lateral trusts are taken into account.
The terminology that we use here and elsewhere in this chapter is standard in the United
States. Outside the United States, these same terms can have different meanings. For exam-
ple, bonds issued by the British government (“gilts”) are called treasury “stock.” Also, in
the United Kingdom, a debenture is a secured obligation.
At the current time, public bonds issued in the United States by industrial and financial
companies are typically debentures. However, most utility and railroad bonds are secured
by a pledge of assets.
SENIORITY In general terms, seniority indicates preference in position over other lend-
ers, and debts are sometimes labeled as senior or junior to indicate seniority. Some debt is
subordinated, as in, for example, a subordinated debenture.
In the event of default, holders of subordinated debt must give preference to other speci-
fied creditors. Usually, this means that the subordinated lenders will be paid off only after the
specified creditors have been compensated. However, debt cannot be subordinated to equity.
REPAYMENT Bonds can be repaid at maturity, at which time the bondholder will receive
the stated, or face, value of the bond, or they may be repaid in part or in entirety before
maturity. Early repayment in some form is more typical and is often handled through a
sinking fund.
The Securities Industry
and Financial Markets
Association (SIFMA) site is
www.sifma.org.
4 Real property includes land and things “affixed thereto.” It does not include cash or inventories.
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142
A sinking fund is an account managed by the bond trustee for the purpose of repaying
the bonds. The company makes annual payments to the trustee, who then uses the funds
to retire a portion of the debt. The trustee does this by either buying up some of the bonds
in the market or calling in a fraction of the outstanding bonds. This second option is dis-
cussed in the next section.
There are many different kinds of sinking fund arrangements, and the details would be
spelled out in the indenture. For example:
1. Some sinking funds start about 10 years after the initial issuance.
2. Some sinking funds establish equal payments over the life of the bond.
3. Some high-quality bond issues establish payments to the sinking fund that
are not sufficient to redeem the entire issue. As a consequence, there is the
possibility of a large “balloon payment” at maturity.
THE CALL PROVISION A call provision allows the company to repurchase, or “call,” part
or all of the bond issue at stated prices over a specific period. Corporate bonds are usually
callable.
Generally, the call price is above the bond’s stated value (that is, the par value). The
difference between the call price and the stated value is the call premium. The amount of
the call premium may become smaller over time. One arrangement is to initially set the call
premium equal to the annual coupon payment and then make it decline to zero as the call
date moves closer to the time of maturity.
Call provisions are often not operative during the first part of a bond’s life. This makes
the call provision less of a worry for bondholders in the bond’s early years. For example, a
company might be prohibited from calling its bonds for the first 10 years. This is a deferred
call provision. During this period of prohibition, the bond is said to be call protected.
In recent years, a new type of call provision, a “make-whole” call, has become very
widespread in the corporate bond market. With such a feature, bondholders receive
approximately what the bonds are worth if they are called. Because bondholders don’t suf-
fer a loss in the event of a call, they are “made whole.”
To determine the make-whole call price, we calculate the present value of the remain-
ing interest and principal payments at a rate specified in the indenture. For example, look-
ing at our Walt Disney issue, we see that the discount rate is “Treasury rate plus .15%.”
What this means is that we determine the discount rate by first finding a U.S. Treasury
issue with the same maturity. We calculate the yield to maturity on the Treasury issue and
then add on an additional .15 percent to get the discount rate we use.
Notice that, with a make-whole call provision, the call price is higher when interest
rates are lower and vice versa (why?). Also notice that, as is common with a make-whole
call, the Walt Disney issue does not have a deferred call feature. Why might investors not
be too concerned about the absence of this feature?
PROTECTIVE COVENANTS A protective covenant is that part of the indenture or loan
agreement that limits certain actions a company might otherwise wish to take during the
term of the loan. Protective covenants can be classified into two types: negative covenants
and positive (or affirmative) covenants.
A negative covenant is a “thou shalt not” type of covenant. It limits or prohibits actions
that the company might take. Here are some typical examples:
1. The firm must limit the amount of dividends it pays according to some formula.
2. The firm cannot pledge any assets to other lenders.
3. The firm cannot merge with another firm.
4. The firm cannot sell or lease any major assets without approval by the lender.
5. The firm cannot issue additional long-term debt.
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A positive covenant is a “thou shalt” type of covenant. It specifies an action that the
company agrees to take or a condition the company must abide by. Here are some examples:
1. The company must maintain its working capital at or above some specified mini-
mum level.
2. The company must periodically furnish audited financial statements to the
lender.
3. The firm must maintain any collateral or security in good condition.
This is only a partial list of covenants; a particular indenture may feature many different ones.
5.3 BOND RATINGS
Firms frequently pay to have their debt rated. The two leading bond-rating firms are
Moody’s and Standard & Poor’s (S&P). The debt ratings are an assessment of the credit-
worthiness of the corporate issuer. The definitions of creditworthiness used by Moody’s
and S&P are based on how likely the firm is to default and the protection creditors have in
the event of a default.
It is important to recognize that bond ratings are concerned only with the possibility of
default. Earlier, we discussed interest rate risk, which we defined as the risk of a change in
the value of a bond resulting from a change in interest rates. Bond ratings do not address
this issue. As a result, the price of a highly rated bond can still be quite volatile.
Bond ratings are constructed from information supplied by the corporation and other
sources. The rating classes and some information concerning them are shown in the
following table.
Want detailed information
on the amount and terms
of the debt issued by a
particular firm? Check out
its latest financial state-
ments by searching SEC
filings at www.sec.gov.
Want to know what cri-
teria are commonly used
to rate corporate and
municipal bonds? Go to
www.standardandpoors
.com, www.moodys.com,
and www.fitchratings
.com.
INVESTMENT-QUALITY BOND RATINGS
LOW-QUALITY, SPECULATIVE,
AND/OR “JUNK” BOND RATINGS
HIGH
GRADE
MEDIUM
GRADE
LOW
GRADE
LOW
GRADE
STANDARD & POOR’S
MOODY’S
AAA AA A BBB BB B CCC CC C D
AAA AA A BAA BA B CAA CA C
MOODY’S S&P
Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong.
Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the highest rat-
ing, this group comprises the high-grade bond class.
A A Debt rated A has a strong capacity to pay interest and repay principal, although it is somewhat more susceptible
to the adverse effects of changes in circumstances and economic conditions than debt in higher-rated categories.
Baa BBB Debt rated Baa and BBB is regarded as having an adequate capacity to pay interest and repay principal. Whereas
it normally exhibits adequate protection parameters, adverse economic conditions or changing circumstances
are more likely to lead to a weakened capacity to pay interest and repay principal for debt in this category than in
higher-rated categories. These bonds are medium-grade obligations.
Ba;B
Caa
Ca
C
BB;B
CCC
CC
C
Debt rated in these categories is regarded, on balance, as predominantly speculative with respect to capacity
to pay interest and repay principal in accordance with the terms of the obligation. BB and Ba indicate the lowest
degree of speculation, and Ca, CC, and C the highest degree of speculation. Although such debt is likely to have
some quality and protective characteristics, these are outweighed by large uncertainties or major risk exposures
to adverse conditions. Issues rated C by Moody’s are typically in default.
D Debt rated D is in default, and payment of interest and/or repayment of principal is in arrears.
Note: At times, both Moody’s and S&P use adjustments (called notches) to these ratings. S&P uses plus and minus signs: A1 is the strongest A rating and A− the weakest.
Moody’s uses a 1, 2, or 3 designation, with 1 being the highest. Moody’s has no D rating.
The highest rating a firm’s debt can have is AAA or Aaa, and such debt is judged to
be the best quality and to have the lowest degree of risk. For example, as of April 2016,
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144
Microsoft and Johnson & Johnson were the only U.S.-based nonfinancial companies with
a AAA credit rating. AA or Aa ratings indicate very good quality debt and are much more
common.
A large part of corporate borrowing takes the form of low-grade, or “junk,” bonds. If
these low-grade corporate bonds are rated at all, they are rated below investment grade by
the major rating agencies. Investment-grade bonds are bonds rated at least BBB by S&P or
Baa by Moody’s.
Rating agencies don’t always agree. For example, some bonds are known as “crossover”
or “5B” bonds. The reason is that they are rated triple-B (or Baa) by one rating agency and
double-B (or Ba) by another, a “split rating.” For example, in July 2015, Spanish cell tower
company Cellnex issued €600 million worth of seven-year notes that were rated BBB− by
Fitch and BB+ by S&P.
A bond’s credit rating can change as the issuer’s financial strength improves or dete-
riorates. For example, in February 2016, S&P cut the bond rating on British mining
company Anglo American from BBB- to BB, lowering the company’s bond rating from
investment-grade to junk bond status. S&P’s ratings cut followed a similar ratings cut by
both Moody’s and Fitch earlier that same week. Bonds that drop into junk territory like this
are called fallen angels. Anglo American was downgraded because metal prices had fallen
to a six-year low.
Credit ratings are important because defaults really do occur, and when they do, inves-
tors can lose heavily. For example, in 2000, AmeriServe Food Distribution, Inc., which
supplied restaurants such as Burger King with everything from burgers to giveaway toys,
defaulted on $200 million in junk bonds. After the default, the bonds traded at just 18 cents
on the dollar, leaving investors with a loss of more than $160 million.
Even worse in AmeriServe’s case, the bonds had been issued only four months earlier,
thereby making AmeriServe an NCAA champion. While that might be a good thing for a
college basketball team such as the University of Kentucky Wildcats, in the bond market
NCAA means “No Coupon At All,” and it’s not a good thing for investors.
5.4 SOME DIFFERENT TYPES OF BONDS
Thus far, we have considered only “plain vanilla” corporate bonds. In this section, we
briefly look at bonds issued by governments and also at bonds with unusual features.
Government Bonds
The biggest borrower in the world—by a wide margin—is everybody’s favorite fam-
ily member, Uncle Sam. In early 2016, the total debt of the U.S. government was about
$19 trillion, or approximately $59,000 per citizen (and growing!). When the government
wishes to borrow money for more than one year, it sells what are known as Treasury notes
and bonds to the public (in fact, it does so every month). Currently, outstanding Treasury
notes and bonds have original maturities ranging from 2 to 30 years.
Most U.S. Treasury issues are just ordinary coupon bonds. There are two important
things to keep in mind, however. First, U.S. Treasury issues, unlike essentially all other
bonds, have no default risk because (we hope) the Treasury can always come up with the
money to make the payments. Second, Treasury issues are exempt from state income taxes
(though not federal income taxes). In other words, the coupons you receive on a Treasury
note or bond are only taxed at the federal level.
State and local governments also borrow money by selling notes and bonds. Such issues
are called municipal notes and bonds, or just “munis.” Unlike Treasury issues, munis have
varying degrees of default risk, and, in fact, they are rated much like corporate issues.
Also, they are almost always callable. The most intriguing thing about munis is that their
coupons are exempt from federal income taxes (though not necessarily state income taxes),
which makes them very attractive to high-income, high-tax bracket investors.
Another good bond
market site is money.
cnn.com.
If you’re nervous about
the level of debt piled up
by the U.S. government,
don’t go to www.treasury
.gov/resource-center or
to www.brillig.com/
debt_clock! Learn all
about government bonds
at www.newyorkfed.org.
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Because of the enormous tax break they receive, the yields on municipal bonds are
much lower than the yields on taxable bonds. For example, in February 2016, long-term
AAA-rated corporate bonds were yielding about 3.65 percent. At the same time, long-
term AAA munis were yielding about 3.21 percent. Suppose an investor was in a 30 percent
tax bracket. All else being the same, would this investor prefer a AAA corporate bond or a
AAA municipal bond?
To answer, we need to compare the aftertax yields on the two bonds. Ignoring state
and local taxes, the muni pays 3.21 percent on both a pretax and an aftertax basis. The
corporate issue pays 3.65 percent before taxes, but it pays .0365 × (1 – .30) = .0256, or
2.56 percent, once we account for the 30 percent tax bite. Given this, the muni bond has a
better yield.
For information on munic-
ipal bonds, including
prices, checkout emma
.msrb.org.
E
X
A
M
P
L
E
5
.3
Suppose taxable bonds are currently yielding 8 percent, while at the same time, munis of comparable
risk and maturity are yielding 6 percent. Which is more attractive to an investor in a 40 percent tax
bracket? What is the break-even tax rate? How do you interpret this rate?
For an investor in a 40 percent tax bracket, a taxable bond yields 8 × (1 – .40) = 4.8 percent after
taxes, so the muni is much more attractive. The break-even tax rate is the tax rate at which an investor
would be indifferent between a taxable and a nontaxable issue. If we let t* stand for the break-even tax
rate, then we can solve for it as follows:
.08 × (1 − t *) = .06
1 − t * = .06/.08 = .75
t * = .25
Thus, an investor in a 25 percent tax bracket would make 6 percent after taxes from either bond.
Taxable versus Municipal Bonds
Zero Coupon Bonds
A bond that pays no coupons at all must be offered at a price that is much lower than its
stated value. Such bonds are called zero coupon bonds, or just zeroes.5
Suppose the Eight-Inch Nails (EIN) Company issues a $1,000 face value, five-year zero
coupon bond. The initial price is set at $508.35. Even though no interest payments are
made on the bond, zero coupon bond calculations use semiannual periods to be consistent
with coupon bond calculations. Using semiannual periods, it is straightforward to verify
that, at this price, the bond yields 14 percent to maturity. The total interest paid over the life
of the bond is $1,000 – 508.35 = $491.65.
For tax purposes, the issuer of a zero coupon bond deducts interest every year even
though no interest is actually paid. Similarly, the owner must pay taxes on interest accrued
every year, even though no interest is actually received.
The way in which the yearly interest on a zero coupon bond is calculated is governed by
tax law. Before 1982, corporations could calculate the interest deduction on a straight-line
basis, For EIN, the annual interest deduction would have been $491.65/5 = $98.33 per year.
Under current tax law, the implicit interest is determined by amortizing the loan. We do
this by first calculating the bond’s value at the beginning of each year. For example, after
one year, the bond will have four years until maturity, so it will be worth $1,000/1.078 =
$582.01; the value in two years will be $1,000/1.076 = $666.34; and so on. The implicit
interest each year is the change in the bond’s value for the year.
Notice that under the old rules, zero coupon bonds were more attractive for corporations
because the deductions for interest expense were larger in the early years (compare the
implicit interest expense with the straight-line expense).
5 A bond issued with a very low coupon rate (as opposed to a zero coupon rate) is an original-issue discount (OID) bond.
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Under current tax law, EIN could deduct $73.66 (= $582.01 – 508.35) in interest paid
the first year, and the owner of the bond would pay taxes on $73.66 of taxable income (even
though no interest was actually received). This second tax feature makes taxable zero cou-
pon bonds less attractive to individuals. However, they are still a very attractive investment
for tax-exempt investors with long-term dollar-denominated liabilities, such as pension
funds, because the future dollar value is known with relative certainty.
Some bonds are zero coupon bonds for only part of their lives. For example, at one time,
General Motors had a debenture outstanding that for the first 20 years of its life, no coupon
payments would be made, but after 20 years, it would begin paying coupons at a rate of
7.75 percent per year, payable semiannually.
Floating-Rate Bonds
The conventional bonds we have talked about in this chapter have fixed-dollar obliga-
tions because the coupon rate is set as a fixed percentage of the par value. Similarly, the
principal is set equal to the par value. Under these circumstances, the coupon payment and
principal are completely fixed.
With floating-rate bonds (floaters), the coupon payments are adjustable. The adjust-
ments are tied to an interest rate index such as the Treasury bill interest rate or the 30-year
Treasury bond rate.
The value of a floating-rate bond depends on exactly how the coupon payment adjust-
ments are defined. In most cases, the coupon adjusts with a lag to some base rate. For exam-
ple, suppose a coupon rate adjustment is made on June 1. The adjustment might be based
on the simple average of Treasury bond yields during the previous three months. In addition,
the majority of floaters have the following features:
1. The holder has the right to redeem his/her note at par on the coupon payment
date after some specified amount of time. This is called a put provision, and it is
discussed in the following section.
2. The coupon rate has a floor and a ceiling, meaning that the coupon is subject to
a minimum and a maximum. In this case, the coupon rate is said to be “capped,”
and the upper and lower rates are sometimes called the collar.
A particularly interesting type of floating-rate bond is an inflation-linked bond. Such
bonds have coupons that are adjusted according to the rate of inflation (the principal amount
may be adjusted as well). The U.S. Treasury began issuing such bonds in January of 1997.
The issues are sometimes called “TIPS,” or Treasury Inflation-Protected Securities. Other
countries, including Canada, Israel, and Britain, have issued similar securities.
Other Types of Bonds
Many bonds have unusual or exotic features. For example, at one time, Berkshire Hathaway,
the company run by the legendary Warren Buffett, issued bonds with a negative coupon.
The buyers of these bonds also received the right to purchase shares of stock in Berkshire
at a fixed price per share over the subsequent five years. Such a right, which is called a
warrant, would be very valuable if the stock price climbed substantially (a later chapter
discusses this subject in greater depth).
Bond features are really only limited by the imaginations of the parties involved.
Unfortunately, there are far too many variations for us to cover in detail here. We there-
fore close out this section by mentioning only a few of the more common types. A nearby
Finance Matters box has some additional discussion on more exotic bonds.
Income bonds are similar to conventional bonds, except that coupon payments are
dependent on company income. Specifically, coupons are paid to bondholders only if the
firm’s income is sufficient. This would appear to be an attractive feature, but income bonds
are not very common.
Official information
on U.S. inflation-
indexed bonds is at
www.treasurydirect.gov.
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A convertible bond can be swapped for a fixed number of shares of stock anytime before
maturity at the holder’s option. Convertibles are relatively common, but the number has
been decreasing in recent years.
A put bond allows the holder to force the issuer to buy the bond back at a stated price.
For example, International Paper Co. has bonds outstanding that allow the holder to force
International Paper to buy the bonds back at 100 percent of the face value given that cer-
tain “risk” events happen. One such event is a change in credit rating from investment
grade to lower than investment grade by Moody’s or S&P. The put feature is therefore just
the reverse of the call provision.
BEAUTY IS IN THE EYE OF THE BONDHOLDER
Many bonds have unusual or exotic features. One of the most common types is an asset-backed, or securitized, bond.
Mortgage-backed securities were big news in 2007. For several years, there had been rapid growth in so-called sub-
prime mortgage loans, which are mortgages made to individuals with less than top-quality credit. However, a combina-
tion of cooling (and in some places dropping) housing prices and rising interest rates caused mortgage delinquencies
and foreclosures to rise. This increase in problem mortgages caused a significant number of mortgage-backed securities
to drop sharply in value and created huge losses for investors. Bondholders of a securitized bond receive interest and
principal payments from a specific asset (or pool of assets) rather than a specific company. For example, at one point
rock legend David Bowie sold $55 million in bonds backed by future royalties from his albums and songs (that’s some
serious ch-ch-ch-change!). Owners of these “Bowie” bonds received the royalty payments, so if Bowie’s record sales fell,
there was a possibility the bonds could have defaulted. Other artists have sold bonds backed by future royalties, includ-
ing James Brown, Iron Maiden, and the estate of the legendary Marvin Gaye.
Mortgage-backs are the best known type of asset-backed security. With a mortgage-backed bond, a trustee pur-
chases mortgages from banks and merges them into a pool. Bonds are then issued, and the bondholders receive pay-
ments derived from payments on the underlying mortgages. One unusual twist with mortgage bonds is that if interest
rates decline, the bonds can actually decrease in value. This can occur because homeowners are likely to refinance at
the lower rates, paying off their mortgages in the process. Securitized bonds are usually backed by assets with long-term
payments, such as mortgages. However, there are bonds securitized by car loans and credit card payments, among
other assets, and a growing market exists for bonds backed by automobile leases.
The reverse convertible is a relatively new type of structured note. This type generally offers a high coupon rate, but
the redemption at maturity can be paid in cash at par value or paid in shares of stock. For example, one recent General
Motors (GM) reverse convertible had a coupon rate of 16 percent, which is a very high coupon rate in today’s interest rate
environment. However, at maturity, if GM’s stock declined sufficiently, bondholders would receive a fixed number of GM
shares that were worth less than par value. So, while the income portion of the bond return would be high, the potential
loss in par value could easily erode the extra return.
CAT bonds are issued to cover insurance companies against natural catastrophes. The type of natural catastrophe
is outlined in the bond’s indenture. For example, about 30 percent of all CAT bonds protect against a North Atlantic
hurricane. The way these issues are structured is that the borrowers can suspend payment temporarily (or even perma-
nently) if they have significant hurricane-related losses. These CAT bonds may seem like pretty risky investments, but to
date, only three such bonds have not made their scheduled payments, courtesy of the massive destruction caused by
Hurricane Katrina, the 2011 Japanese tsunami, and an unusually active 2011 tornado season.
Perhaps the most unusual bond (and certainly the most ghoulish) is the “death bond.” Companies such as Stone
Street Financial purchase life insurance policies from individuals who are expected to die within the next 10 years.
They then sell bonds that are paid off from the life insurance proceeds received when the policyholders pass away.
The return on the bonds to investors depends on how long the policyholders live. A major risk is that if medical treat-
ment advances quickly, it will raise the life expectancy of the policyholders, thereby decreasing the return to the
bondholder.
FINANCE MATTERS
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Structured notes are bonds that are based on stocks, bonds, commodities, or curren-
cies. One particular type of structured note has a return based on a stock market index.
At expiration, if the stock index has declined, the bond returns the principal. However,
if the stock index has increased, the bond will return a portion of the stock index return,
say 80 percent. Another type of structured note will return twice the stock index return, but
with the potential for loss of principal.
A given bond may have many unusual features. Two of the most recent exotic bonds are
CoCo bonds, which have a coupon payment, and NoNo bonds, which are zero coupon bonds.
CoCo and NoNo bonds are contingent convertible, putable, callable, subordinated bonds. The
contingent convertible clause is similar to the normal conversion feature, except the contingent
feature must be met. For example, a contingent feature may require that the company stock trade
at 110 percent of the conversion price for 20 out of the most recent 30 days. Valuing a bond
of this sort can be quite complex, and the yield to maturity calculation is often meaningless.
5.5 BOND MARKETS
Bonds are bought and sold in enormous quantities every day. You may be surprised to
learn that the trading volume in bonds on a typical day is many, many times larger than the
trading volume in stocks (by trading volume, we mean the amount of money that changes
hands). Here is a finance trivia question: What is the largest securities market in the world?
Most people would guess the New York Stock Exchange. In fact, the largest securities mar-
ket in the world in terms of trading volume is the U.S. Treasury market, with an average
daily volume over $500 billion.
How Bonds Are Bought and Sold
Most trading in bonds takes place over the counter, or OTC. Recall that this means that
there is no particular place where buying and selling occur. Instead, dealers around the
country (and around the world) stand ready to buy and sell. The various dealers are con-
nected electronically.
One reason the bond markets are so big is that the number of bond issues far exceeds the
number of stock issues. There are two reasons for this. First, a corporation would typically
have only one common stock issue outstanding (there are exceptions to this that we discuss in
our next chapter). However, a single large corporation could easily have a dozen or more note
and bond issues outstanding. Beyond this, federal, state, and local borrowing is enormous. For
example, even a small city would usually have a wide variety of notes and bonds outstanding,
representing money borrowed to pay for things like roads, sewers, and schools. When you
think about how many small cities there are in the United States, you begin to get the picture!
Because the bond market is almost entirely OTC, it has historically had little or no
transparency. A financial market is transparent if it is possible to easily observe its prices
and trading volume. On the New York Stock Exchange, for example, it is possible to see
the price and quantity for every single transaction. In contrast, in the bond market, it is
often not possible to observe either. Transactions are privately negotiated between parties,
and there is little or no centralized reporting of transactions.
Although the total volume of trading in bonds far exceeds that in stocks, only a very small
fraction of the total bond issues that exist actually trade on a given day. This fact, combined
with the lack of transparency in the bond market, means that getting up-to-date prices on
individual bonds can be difficult or impossible, particularly for smaller corporate or munici-
pal issues. Instead, a variety of sources of estimated prices exist and are very commonly used.
Bond Price Reporting
In 2002, transparency in the corporate bond market began to improve dramatically. Under
new regulations, corporate bond dealers are now required to report trade information
ExcelMaster
coverage online
www.mhhe.com/RossCore5e
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through what is known as the Trade Report and Compliance Engine (TRACE). By 2010,
transaction and price data were reported on more than 29,000 corporate bonds, which is
essentially all publicly traded corporate bonds.
TRACE bond quotes are available at http://finra-markets.morningstar.com/MarketData
/Default.jsp. We went to the site and entered “Deere” for the well-known manufacturer of
green tractors. We found a total of eight bond issues outstanding. Below you can see the
information we found for all of these bonds.
To learn more about
TRACE, visit www.finra
.org.
If you go to the website and click on a particular bond, you will get a lot of information
about the bond, including the credit rating, the call schedule, original issue information,
and trade information. For example, when we checked, the first bond listed had not traded
for two weeks.
As shown in Figure 5.3, the Financial Industry Regulatory Authority (FINRA) provides
a daily snapshot of the data from TRACE by reporting the most active issues. The infor-
mation reported is largely self-explanatory. Notice that the price of the first Apple bond
listed increased about 1.681 percent on this day. What do you think happened to the yield
to maturity for this bond? Figure 5.3 focuses on the most active bonds with investment-
grade ratings, but the most active high-yield and convertible bonds are also available on
the website.
As we mentioned before, the U.S. Treasury market is the largest securities market
in the world. As with bond markets in general, it is an OTC market, so there is limited
FIGURE 5.3 Sample TRACE Bond Quotations
Source: FINRA reported TRACE prices.
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transparency. However, unlike the situation with bond markets in general, trading in
Treasury issues, particularly recently issued ones, is very heavy. Each day, representative
prices for outstanding Treasury issues are reported.
Figure 5.4 shows a portion of the daily Treasury bond listings from the website wsj.com.
Examine the entry that begins “02/15/2026.” Reading from left to right, the “02/15/2026”
tells us that the bond’s maturity is February 15, 2026. The 1.625 is the bond’s coupon rate.
The next two pieces of information are the bid and asked prices. In general, in any OTC or
dealer market, the bid price represents what a dealer is willing to pay for a security, and the asked
price (or just “ask” price) is what a dealer is willing to take for it. The difference between the
two prices is called the bid-ask spread (or just “spread”), and it represents the dealer’s profit.
Treasury prices are quoted as a percentage of face value. The bid price, or what a dealer
is willing to pay, on the 02/15/2026 bond is 98.875. With a $1,000 face value, this quote
represents $988.75. The asked price, or the price at which the dealer is willing to sell the
bond, is 98.8906, or $988.906.
The next number quoted is the change in the asked price from the previous day, mea-
sured as a percentage of face value, so this issue’s asked price rose by .1172 percent, or
$1.172, in value from the previous day. Finally, the last number reported is the yield to
maturity, based on the asked price. Notice that this is a discount bond because it sells for
less than its face value. Not surprisingly, its yield to maturity (1.747 percent) is greater
than its coupon rate (1.625 percent).
The Federal Reserve
Bank of St. Louis main-
tains dozens of online
files containing macro-
economic data as well
as rates on U.S. Treasury
issues. Go to research
.stlouisfed.org/fred2/.
FIGURE 5.4
Sample Wall Street Journal
U.S. Treasury Bond Prices
Source: The Wall Street Journal,
February 19, 2016. 3/31/2016 2.375 100.1953 100.2109 -0.0313 0.34
1/31/2017 0.875 100.2813 100.2969 0.0078 0.558
4/15/2018 0.75 99.9219 99.9375 -0.0547 0.779
4/30/2018 0.625 99.6328 99.6484 -0.0703 0.787
5/15/2019 3.125 106.8984 106.9141 -0.0625 0.945
5/31/2020 1.375 100.8594 100.875 -0.0625 1.164
6/30/2021 2.125 104.1563 104.1719 0.0156 1.315
8/15/2022 7.25 135.8906 135.9063 -0.0313 1.429
8/15/2023 2.5 106.8125 106.8281 0.0625 1.531
11/15/2024 2.25 104.5078 104.5234 0.125 1.69
8/15/2025 6.875 145.0703 145.0859 0.0469 1.705
2/15/2026 1.625 98.875 98.8906 0.1172 1.747
2/15/2027 6.625 147.7656 147.8281 0.1094 1.804
8/15/2028 5.5 139.5156 139.5781 0.1406 1.919
2/15/2029 5.25 137.6094 137.6719 0.1328 1.951
5/15/2030 6.25 152.7344 152.7969 0.1641 1.975
2/15/2031 5.375 143.5625 143.625 0.2422 1.992
2/15/2036 4.5 138.2656 138.3281 0.3906 2.134
2/15/2037 4.75 142.6641 142.7266 0.3594 2.197
2/15/2038 4.375 136.2188 136.2813 0.4375 2.269
8/15/2039 4.5 138.0625 138.125 0.4688 2.373
5/15/2040 4.375 135.6797 135.7109 0.3984 2.419
11/15/2041 3.125 112.1641 112.1953 0.4766 2.481
8/15/2042 2.75 104.0234 104.0547 0.5156 2.539
5/15/2044 3.375 116.7656 116.7969 0.5859 2.538
8/15/2045 2.875 105.6484 105.6797 0.5781 2.598
11/15/2045 3 108.4844 108.5156 0.6016 2.588
2/15/2046 2.5 97.8281 97.8594 0.5391 2.603
Treasury Bonds
Coupon Bid Asked Chg
Asked
yieldMaturity
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SELECTED INTERNATIONAL GOVERNMENT
10-YEAR BOND YIELDS
YIELD (%)
Switzerland
Japan
Germany
United Kingdom
United States
Australia
Mexico
Brazil
Greece
–.36
.00
.20
1.41
1.75
2.43
3.96
6.87
10.25
Source: www.bloomberg.com, February 19, 2016.
The last bond listed, the 02/15/2046, is often called the “bellwether” bond. This bond’s
yield is the one that is usually reported in the evening news. So, for example, when you
hear that long-term interest rates rose, what is really being said is that the yield on this
bond went up (and its price went down).
If you examine the yields on the various issues in Figure 5.4, you will clearly see that
they vary by maturity. Why this occurs and what it might mean are some of the things we
discuss in our next section. Government (referred to as “sovereign”) bond yields also vary
by country of origin. Below we show the 10-year bond yields of several countries. The
yields vary according to default risks and foreign exchange risks (to be discussed later in
the text).
Current and historical
Treasury yield information
is available at www.
publicdebt.treas.gov/.
A Note on Bond Price Quotes
If you buy a bond between coupon payment dates, the price you pay is usually more than
the price you are quoted. The reason is that standard convention in the bond market is to
quote prices net of “accrued interest,” meaning that accrued interest is deducted to arrive
at the quoted price. This quoted price is called the clean price. The price you actually pay,
however, includes the accrued interest. This price is the dirty price, also known as the
“full” or “invoice” price.
An example is the easiest way to understand these issues. Suppose you buy a bond with a
12 percent annual coupon, payable semiannually. You actually pay $1,080 for this bond, so
$1,080 is the dirty, or invoice, price. Further, on the day you buy it, the next coupon is due
in four months, so you are between coupon dates. Notice that the next coupon will be $60.
Locate the Treasury issue in Figure 5.4 that matures on May 15, 2019. What is its coupon rate? What is its
bid price? What was the previous day’s asked price?
The bond listed as 05/15/2019 is the one we seek. Its coupon rate is 3.125 percent of face value.
The bid price is 106.8984, or 106.8984 percent of face value. The ask price is 106.9141, which is down
by .0625 from the previous day. This means that the ask price on the previous day was equal to
106.9141 + .0625 = 106.9766.
Treasury Quotes
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The accrued interest on a bond is calculated by taking the fraction of the coupon period
that has passed, in this case two months out of six, and multiplying this fraction by the
next coupon, $60. So, the accrued interest in this example is 2/6 × $60 = $20. The bond’s
quoted price (i.e., its clean price) would be $1,080 – 20 = $1,060.6
5.6 INFLATION AND INTEREST RATES
So far, we haven’t considered the role of inflation in our various discussions of interest
rates, yields, and returns. Because this is an important consideration, we discuss the impact
of inflation next.
Real versus Nominal Rates
In examining interest rates, or any other financial market rates such as discount rates, bond
yields, rates of return, and required returns, it is often necessary to distinguish between
real rates and nominal rates. Nominal rates are called nominal because they have not
been adjusted for inflation. Real rates are rates that have been adjusted for inflation.
To see the effect of inflation, suppose prices are currently rising by 5 percent per year.
In other words, the rate of inflation is 5 percent. An investment is available that will be
worth $115.50 in one year. It costs $100 today. Notice that with a present value of $100 and
a future value in one year of $115.50, this investment has a 15.5 percent rate of return. In
calculating this 15.5 percent return, we did not consider the effect of inflation, however, so
this is the nominal return.
What is the impact of inflation here? To answer, suppose pizzas cost $5 apiece at the
beginning of the year. With $100, we can buy 20 pizzas. Because the inflation rate is
5 percent, pizzas will cost 5 percent more, or $5.25, at the end of the year. If we take the
investment, how many pizzas can we buy at the end of the year? Measured in pizzas, what
is the rate of return on this investment?
Our $115.50 from the investment will buy us $115.50/5.25 = 22 pizzas. This is up from
20 pizzas, so our pizza rate of return is 10 percent. What this illustrates is that even though
the nominal return on our investment is 15.5 percent, our buying power goes up by only
10 percent because of inflation. Put another way, we are really only 10 percent richer. In
this case, we say that the real return is 10 percent.
Alternatively, we can say that with 5 percent inflation, each of the $115.50 nominal
dollars we get is worth 5 percent less in real terms, so the real dollar value of our investment
in a year is:
$115.50/1.05 = $110
What we have done is to deflate the $115.50 by 5 percent. Because we give up $100 in
current buying power to get the equivalent of $110, our real return is again 10 percent.
Because we have removed the effect of future inflation here, this $110 is said to be mea-
sured in current dollars.
The difference between nominal and real rates is important and bears repeating:
The nominal rate on an investment is the percentage change in the number of dollars
you have.
The real rate on an investment is the percentage change in how much you can buy with your
dollars, in other words, the percentage change in your buying power.
6 The way accrued interest is calculated actually depends on the type of bond being quoted, for example, Treasury or corporate. The differ-
ence has to do with exactly how the fractional coupon period is calculated. In our example above, we implicitly treated the months as having
exactly the same length (i.e., 30 days each, 360 days in a year), which is consistent with the way corporate bonds are quoted. In contrast,
for Treasury bonds, actual day counts are used.
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The Fisher Effect
Our discussion of real and nominal returns illustrates a relationship often called the
Fisher effect (after the great economist Irving Fisher). Because investors are ultimately
concerned with what they can buy with their money, they require compensation for infla-
tion. Let R stand for the nominal rate and r stand for the real rate. The Fisher effect tells
us that the relationship between nominal rates, real rates, and inflation can be written as:
1 + R = ( 1 + r ) × ( 1 + h ) [5.2]
where h is the inflation rate.
In the preceding example, the nominal rate was 15.50 percent and the inflation rate was
5 percent. What was the real rate? We can determine it by plugging in these numbers:
1 + .1550
=
(1 + r) × (1 + .05)
1 + r = 1.1550/1.05 = 1.10
r
=
.10, or 10%
This real rate is the same as we had before. If we take another look at the Fisher effect, we
can rearrange things a little as follows:
1 + R
= (1 + r) × (1 + h)
R
= r + h + r × h
[5.3]
What this tells us is that the nominal rate has three components. First, there is the real rate on
the investment, r. Next, there is the compensation for the decrease in the value of the money
originally invested because of inflation, h. The third component represents compensation for
the fact that the dollars earned on the investment are also worth less because of the inflation.
This third component is usually small, so it is often dropped. The nominal rate is then
approximately equal to the real rate plus the inflation rate:
R ≈ r + h [5.4]
Fisher’s thinking is that investors are not foolish. They know that inflation reduces pur-
chasing power, and therefore, they will demand an increase in the nominal rate before lend-
ing money. Fisher’s hypothesis, typically called the Fisher effect, can be stated as:
A rise in the rate of inflation causes the nominal rate to rise just enough so that the real rate
of interest is unaffected. In other words, the real rate is invariant to the rate of inflation.
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If investors require a 2 percent real rate of return, and the inflation rate is 8 percent, what must be the
approximate nominal rate? The exact nominal rate?
First of all, the nominal rate is approximately equal to the sum of the real rate and the inflation rate:
2 percent + 8 percent = 10 percent. From the Fisher effect, we have:
1 + R
=
(1 + r) × (1 + h)
= 1.02 × 1.08
=
1.1016
Therefore, the nominal rate will actually be closer to 10.16 percent. In this example, you can also see
how negative nominal interests can come about, e.g., in the unusual situation when inflation rates are
expected to be sufficiently negative.
The Fisher Effect
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It is important to note that financial rates, such as interest rates, discount rates, and rates of
return, are almost always quoted in nominal terms. To remind you of this, we will hence-
forth use the symbol R instead of r in most of our discussions about such rates.
5.7 DETERMINANTS OF BOND YIELDS
We are now in a position to discuss the determinants of a bond’s yield. As we will see,
the yield on any particular bond is a reflection of a variety of factors, some common to all
bonds and some specific to the issue under consideration.
The Term Structure of Interest Rates
At any point in time, short-term and long-term interest rates will generally be different.
Sometimes short-term rates are higher, sometimes lower. Figure 5.5 gives us a long-range
perspective on this by showing about two centuries of short- and long-term U.S. Treasury
interest rates. As shown, through time, the difference between short- and long-term rates has
ranged from essentially zero to up to several percentage points, both positive and negative.
The relationship between short- and long-term interest rates is known as the term
structure of interest rates. To be a little more precise, the term structure of interest rates
tells us what nominal interest rates are on default-free, pure discount bonds of all maturi-
ties. These rates are, in essence, “pure” interest rates because they involve no risk of default
and a single, lump-sum future payment. In other words, the term structure tells us the pure
time value of money for different lengths of time.
When long-term rates are higher than short-term rates, we say that the term structure is
upward sloping, and, when short-term rates are higher, we say it is downward sloping. The
term structure can also be “humped.” When this occurs, it is usually because rates increase
at first, but then begin to decline as we look at longer- and longer-term rates. The most
ExcelMaster
coverage online
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2
4
6
8
10
12
14
16
0
1800 1820 1840 1860 1880 1900
Year
In
te
re
st
ra
te
(%
)
1920 1940 1960 1980 2000
Long-term rates
Short-term rates
2020
FIGURE 5.5 U.S. Interest Rates: 1800–2015
Source: Jeremy J. Siegel, Stocks for the Long Run, 4th edition, © McGraw-Hill, 2008, updated by the authors.
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common shape of the term structure, particularly in modern times, is upward sloping, but
the degree of steepness has varied quite a bit.
What determines the shape of the term structure? There are three basic components.
The first two are the ones we discussed in our previous section, the real rate of interest
and the rate of inflation. The real rate of interest is the compensation investors demand for
forgoing the use of their money. You can think of it as the pure time value of money after
adjusting for the effects of inflation.
The real rate of interest is the basic component underlying every interest rate, regardless
of the time to maturity. When the real rate is high, all interest rates will tend to be higher,
and vice versa. Thus, the real rate doesn’t really determine the shape of the term structure;
instead, it mostly influences the overall level of interest rates.
In contrast, the prospect of future inflation very strongly influences the shape of the
term structure. Investors thinking about loaning money for various lengths of time recog-
nize that future inflation erodes the value of the dollars that will be returned. As a result,
investors demand compensation for this loss in the form of higher nominal rates. This extra
compensation is called the inflation premium.
If investors believe that the rate of inflation will be higher in the future, then long-term
nominal interest rates will tend to be higher than short-term rates. Thus, an upward-sloping
term structure may be a reflection of anticipated increases in inflation. Similarly, a downward-
sloping term structure probably reflects the belief that inflation will be falling in the future.
The third, and last, component of the term structure has to do with interest rate risk.
As we discussed earlier in the chapter, longer-term bonds have much greater risk of loss
resulting from changes in interest rates than do shorter-term bonds. Investors recognize
this risk, and they demand extra compensation in the form of higher rates for bearing it.
This extra compensation is called the interest rate risk premium. The longer the term
to maturity, the greater is the interest rate risk, so the interest rate risk premium increases
with maturity. However, as we discussed earlier, interest rate risk increases at a decreasing
rate, so the interest rate risk premium does as well.7
Putting the pieces together, we see that the term structure reflects the combined effect
of the real rate of interest, the inflation premium, and the interest rate risk premium.
Figure 5.6 shows how these can interact to produce an upward-sloping term structure (in
the top part of Figure 5.6) or a downward-sloping term structure (in the bottom part).
In the top part of Figure 5.6, notice how the rate of inflation is expected to rise gradually.
At the same time, the interest rate risk premium increases at a decreasing rate, so the com-
bined effect is to produce a pronounced upward-sloping term structure. In the bottom part of
Figure 5.6, the rate of inflation is expected to fall in the future, and the expected decline is
enough to offset the interest rate risk premium and produce a downward-sloping term struc-
ture. Notice that if the rate of inflation was expected to decline by only a small amount, we
could still get an upward-sloping term structure because of the interest rate risk premium.
We assumed in drawing Figure 5.6 that the real rate would remain the same. Actually,
expected future real rates could be larger or smaller than the current real rate. Also, for
simplicity, we used straight lines to show expected future inflation rates as rising or declin-
ing, but they do not necessarily have to look like this. They could, for example, rise and
then fall, leading to a humped yield curve.
Bond Yields and the Yield Curve:
Putting It All Together
Going back to Figure 5.4, recall that we saw that the yields on Treasury notes and bonds of
different maturities are not the same. Each day, in addition to the Treasury prices and yields
shown in Figure 5.4, the U.S Treasury Department website provides a plot of Treasury
Online yield curve infor-
mation is available at
www.bloomberg.com/
markets.
7 In days of old, the interest rate risk premium was called a “liquidity” premium. Today, the term liquidity premium has an altogether differ-
ent meaning, which we explore in our next section. Also, the interest rate risk premium is sometimes called a maturity risk premium. Our
terminology is consistent with the modern view of the term structure.
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156
yields relative to maturity. This plot is called the Treasury yield curve (or just the yield
curve). Figure 5.7 shows the yield curve as of February 2016. Note, the yield curve avail-
able on the U.S Treasury website will display both the nominal and real yield curves.
As you probably now suspect, the shape of the yield curve is a reflection of the term
structure of interest rates. In fact, the Treasury yield curve and the term structure of interest
rates are almost the same thing. The only difference is that the term structure is based on
pure discount bonds, whereas the yield curve is based on coupon bond yields. As a result,
Treasury yields depend on the three components that underlie the term structure—the real
rate, expected future inflation, and the interest rate risk premium.
Treasury notes and bonds have three important features that we need to remind you of:
they are default-free, they are taxable, and they are highly liquid. This is not true of bonds
in general, so we need to examine what additional factors come into play when we look at
bonds issued by corporations or municipalities.
The first thing to consider is credit risk, that is, the possibility of default. Investors
recognize that issuers other than the Treasury may or may not make all the promised pay-
ments on a bond, so they demand a higher yield as compensation for this risk. This extra
compensation is called the default risk premium. Earlier in the chapter, we saw how
bonds were rated based on their credit risk. What you will find if you start looking at bonds
of different ratings is that lower-rated bonds have higher yields.
To see the current
Treasury yield curve,
check out the Data and
Charts Center at: www.
treasury.gov.
FIGURE 5.6
The Term Structure of
Interest Rates
Time to maturity
Inflation
premium
Real rate
Interest rate
risk premium
Nominal
interest
rate
In
te
re
st
ra
te
A. Upward-sloping term structure
Nominal
interest
rate
Time to maturity
In
te
re
st
ra
te
B. Downward-sloping term structure
Inflation
premium
Interest rate
risk premium
Real rate
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An important thing to recognize about a bond’s yield is that it is calculated assuming
that all the promised payments will be made. As a result, it is really a promised yield, and
it may or may not be what you will earn. In particular, if the issuer defaults, your actual
yield will be lower, probably much lower. This fact is particularly important when it comes
to junk bonds. Thanks to a clever bit of marketing, such bonds are now commonly called
high-yield bonds, which has a much nicer ring to it; but now you recognize that these are
really high promised yield bonds.
Next, recall that we discussed earlier how municipal bonds are free from most taxes
and, as a result, have much lower yields than taxable bonds. Investors demand the extra
yield on a taxable bond as compensation for the unfavorable tax treatment. This extra com-
pensation is the taxability premium.
Finally, bonds have varying degrees of liquidity. As we discussed earlier, there are an
enormous number of bond issues, most of which do not trade on a regular basis. As a
result, if you wanted to sell quickly, you would probably not get as good a price as you
could otherwise. Investors prefer liquid assets to illiquid ones, so they demand a liquidity
premium on top of all the other premiums we have discussed. As a result, all else being
the same, less liquid bonds will have higher yields than more liquid bonds.
Conclusion
If we combine all of the things we have discussed regarding bond yields, we find that
bond yields represent the combined effect of no fewer than six things. The first is the
real rate of interest. On top of the real rate are five premiums representing compensation
for (1) expected future inflation, (2) interest rate risk, (3) default risk, (4) taxability, and
(5) lack of liquidity. As a result, determining the appropriate yield on a bond requires
careful analysis of each of these effects.
FIGURE 5.7 The
Treasury Yield Curve:
February 19, 2016Treasury Yield Curve
Month(s) Years
02/19/2015
02/19/2016
1 3 6 1 2 3 5 7 10 20 30
3.00%
2.00%
1.00%
0.00%
02/19/2016
Maturity
02/19/2015
Source: https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-Yield-Data-Visualization.
aspx, February 19, 2016.
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PART 2 Valuation and Capital Budgeting158
SUMMARY AND CONCLUSIONS
This chapter has explored bonds, bond yields, and interest rates. We saw that
1. Determining bond prices and yields is an application of basic discounted cash flow principles.
2. Bond values move in the direction opposite that of interest rates, leading to potential gains or losses for
bond investors.
3. Bonds have a variety of features spelled out in a document called the indenture.
4. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no risk of
default, whereas so-called junk bonds have substantial default risk.
5. A wide variety of bonds exist, many of which contain exotic or unusual features.
6. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result, bond
price and volume information can be difficult to find for some types of bonds.
7. Bond yields and interest rates reflect the effects of six different factors: the real interest rate and five
premiums that investors demand as compensation for inflation, interest rate risk, default risk, taxability,
and lack of liquidity.
CONCEPT QUESTIONS
1. Treasury Bonds Is it true that a U.S. Treasury security is risk free?
2. Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year
BB corporate bond?
3. Treasury Pricing With regard to bid and ask prices on a Treasury bond, is it possible for the bid price
to be higher? Why or why not?
4. Yield to Maturity Treasury bid and ask quotes are sometimes given in terms of yields, so there would
be a bid yield and an ask yield. Which do you think would be larger? Explain.
5. Call Provisions A company is contemplating a long-term bond issue. It is debating whether or not to
include a call provision. What are the benefits to the company from including a call provision? What are
the costs? How do these answers change for a put provision?
6. Coupon Rate How does a bond issuer decide on the appropriate coupon rate to set on its bonds?
Explain the difference between the coupon rate and the required return on a bond.
7. Real and Nominal Returns Are there any circumstances under which an investor might be more
concerned about the nominal return on an investment than the real return?
8. Bond Ratings Companies pay rating agencies such as Moody’s and S&P to rate their bonds, and the
costs can be substantial. However, companies are not required to have their bonds rated in the first
place; doing so is strictly voluntary. Why do you think they do it?
9. Bond Ratings Often, junk bonds are not rated. Why?
10. Term Structure What is the difference between the term structure of interest rates and the yield curve?
11. Crossover Bonds Looking back at the crossover bonds we discussed in the chapter, why do you think
split ratings such as these occur?
12. Municipal Bonds Why is it that municipal bonds are not taxed at the federal level but are taxable
across state lines? Why is it that U.S. Treasury bonds are not taxable at the state level? (You may need
to dust off the history books for this one.)
13. Bond Market What are the implications for bond investors of the lack of transparency in the bond market?
14. Treasury Market Take a look back at Figure 5.4. Notice the wide range of coupon rates. Why are they
so different?
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CHAPTER 5 Interest Rates and Bond Valuation 159
15. Rating Agencies A controversy erupted regarding bond-rating agencies when some agencies began
to provide unsolicited bond ratings. Why do you think this is controversial?
16. Bonds as Equity The 100-year bonds we discussed in the chapter have something in common with
junk bonds. Critics charge that, in both cases, the issuers are really selling equity in disguise. What are
the issues here? Why would a company want to sell “equity in disguise”?
17. Bond Prices versus Yields
a. What is the relationship between the price of a bond and its YTM?
b. Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What
do you know about the relationship between the coupon rate and the YTM for premium bonds?
What about for discount bonds? For bonds selling at par value?
c. What is the relationship between the current yield and YTM for premium bonds? For discount
bonds? For bonds selling at par value?
18. Interest Rate Risk All else being the same, which has more interest rate risk, a long-term bond or
a short-term bond? What about a low coupon bond compared to a high coupon bond? What about a
long-term, high coupon bond compared to a short-term, low coupon bond?
1. Valuing Bonds What is the dollar price of a zero coupon bond with 17 years to maturity, semiannual
compounding, and a par value of $1,000, if the YTM is
a. 4 percent
b. 10 percent
c. 14 percent
2. Valuing Bonds Microhard has issued a bond with the following characteristics:
Par: $1,000
Time to maturity: 23 years
Coupon rate: 7 percent
Semiannual payments
Calculate the price of this bond if the YTM is
a. 7 percent
b. 9 percent
c. 5 percent
3. Bond Yields Skolits Corp. issued 15-year bonds two years ago at a coupon rate of 5.1 percent. The
bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is
the YTM?
4. Coupon Rates Lydic Corporation has bonds on the market with 12.5 years to maturity, a YTM of 6.4
percent, a par value of $1,000, and a current price of $1,040. The bonds make semiannual payments.
What must the coupon rate be on these bonds?
5. Valuing Bonds Even though most corporate bonds in the United States make coupon payments
semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German
company has a bond outstanding with a par value of €1,000, 16 years to maturity, and a coupon rate of
4.7 percent paid annually. If the yield to maturity is 3.4 percent, what is the current price of the bond?
6. Bond Yields A Japanese company has a bond outstanding that sells for 103.25 percent of its
¥100,000 par value. The bond has a coupon rate of 4.9 percent paid annually and matures in 18 years.
What is the yield to maturity of this bond?
Basic
(Questions 1–15)
QUESTIONS AND PROBLEMS
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PART 2 Valuation and Capital Budgeting160
7. Calculating Real Rates of Return If Treasury bills are currently paying 4.8 percent and the inflation
rate is 2.7 percent, what is the approximate real rate of interest? The exact real rate?
8. Inflation and Nominal Returns Suppose the real rate is 1.8 percent and the inflation rate is
3.4 percent. What rate would you expect to see on a Treasury bill?
9. Nominal and Real Returns An investment offers a total return of 12.1 percent over the coming year.
Alan Wingspan thinks the total real return on this investment will be only 7.6 percent. What does Alan
believe the inflation rate will be over the next year?
10. Nominal versus Real Returns Say you own an asset that had a total return last year of 11.4 percent.
If the inflation rate last year was 3.9 percent, what was your real return?
11. Zero Coupon Bonds You find a zero coupon bond with a par value of $10,000 and 17 years to
maturity. If the yield to maturity on this bond if 4.9 percent, what is the dollar price of the bond?
Assume semiannual compounding periods.
12. Valuing Bonds Mycroft Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.9
percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8 percent.
What is the dollar price of the bond?
13. Valuing Bonds Union Local School District has bonds outstanding with a coupon rate of 3.7 percent
paid semiannually and 16 years to maturity. The yield to maturity on these bonds is 3.9 percent and the
bonds have a par value of $5,000. What is the price of the bonds?
14. Using Treasury Quotes Locate the Treasury bond in Figure 5.4 that matures in August 2028. What is its
coupon rate? What is its bid price? What was the previous day’s asked price? Assume a par value of $1,000.
15. Using Treasury Quotes Locate the Treasury bond in Figure 5.4 that matures in August 2039. Is this a
premium or a discount bond? What is its current yield? What is its yield to maturity? What is the bid-ask
spread in dollars? Assume a $1,000 par value.
16. Bond Price Movements Miller Corporation has a premium bond making semiannual payments.
The bond has a coupon rate of 8.2 percent, a YTM of 6.2 percent, and 13 years to maturity. The
Modigliani Company has a discount bond making semiannual payments. This bond has a coupon
rate of 6.2 percent, a YTM of 8.2 percent, and also has 13 years to maturity. If interest rates remain
unchanged, what do you expect the price of these bonds to be 1 year from now assuming both bonds
have a par value of $1,000? In 3 years? In 8 years? In 12 years? In 13 years? What’s going on here?
Illustrate your answers by graphing bond prices versus time to maturity.
17. Interest Rate Risk Laurel, Inc., and Hardy Corp. both have 6.5 percent coupon bonds outstanding,
with semiannual interest payments, and both are currently priced at the par value of $1,000. The
Laurel, Inc., bond has 4 years to maturity, whereas the Hardy Corp. bond has 23 years to maturity. If
interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the
price of these bonds be then? Illustrate your answers by graphing bond prices versus YTM. What does
this problem tell you about the interest rate risk of longer-term bonds?
18. Interest Rate Risk The Faulk Corp. has a bond with a coupon rate of 5.7 percent outstanding. The
Gonas Company has a bond with a coupon rate of 12.3 percent outstanding. Both bonds have 14 years
to maturity, make semiannual payments, and have a YTM of 9 percent. If interest rates suddenly
rise by 2 percent, what is the percentage change in the price of these bonds? What if interest rates
suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower
coupon bonds?
19. Bond Yields Bonino Software has 6.4 percent coupon bonds on the market with 11 years to maturity.
The bonds make semiannual payments and currently sell for 108 percent of par. What is the current
yield on the bonds? The YTM? The effective annual yield?
20. Bond Yields Hagelin Co. wants to issue new 20-year bonds for some much-needed expansion
projects. The company currently has 6.4 percent coupon bonds on the market that sell for $1,121.80,
Intermediate
(Questions 16–26)
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CHAPTER 5 Interest Rates and Bond Valuation 161
make semiannual payments, and mature in 20 years. What coupon rate should the company set on its
new bonds if it wants them to sell at par? Both bonds have a par value of $1,000.
21. Accrued Interest You purchase a bond with an invoice price of $945. The bond has a coupon rate of
6.8 percent, and there are two months to the next semiannual coupon date. What is the clean price of
the bond?
22. Accrued Interest You purchase a bond with a coupon rate of 7.6 percent and a clean price of $1,060.
If the next semiannual coupon payment is due in four months, what is the invoice price?
23. Finding the Bond Maturity Cavo Corp. has 6.3 percent coupon bonds making annual payments with
a YTM of 7.14 percent. The current yield on these bonds is 6.95 percent. How many years do these
bonds have left until they mature?
24. Using Bond Quotes Suppose the following bond quote for IOU Corporation appears in the financial
page of today’s newspaper. Assume the bond has a face value of $1,000 and the current date is
April 15, 2016. What is the yield to maturity of the bond? What is the current yield?
COMPANY (T ICKER) COUPON MATURITY LAST PRICE LAST YIELD EST VOL (000s)
IOU (IOU) 5.400 Apr 15, 2029 104.355 ?? 1,827
25. Finding the Maturity You’ve just found a 10 percent coupon bond on the market that sells for par
value. What is the maturity on this bond?
26. Components of Bond Returns Bond P is a premium bond with a coupon of 8.4 percent. Bond D has
a coupon rate of 5.6 percent and is currently selling at a discount. Both bonds make annual payments,
have a YTM of 7 percent, and have eight years to maturity. What is the current yield for Bond P? For
Bond D? If interest rates remain unchanged, what is the expected capital gains yield over the next
year for Bond P? For Bond D? Explain your answers and the interrelationship among the various types
of yields.
27. Holding Period Yield You will earn the YTM on a bond if you hold the bond until maturity and if
interest rates don’t change. If you actually sell the bond before it matures, your realized return is
known as the holding period yield (HPY).
a. Suppose that today you buy a bond with an annual coupon rate of 5.5 percent for $865. The bond
has 21 years to maturity. What rate of return do you expect to earn on your investment?
b. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What
price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM
when you first bought the bond. Why are they different?
28. Valuing Bonds The Grimm Corporation has two different bonds currently outstanding. Bond M has
a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years,
then pays $800 every six months over the subsequent eight years, and finally pays $1,000 every six
months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years;
it makes no coupon payments over the life of the bond. If the required return on both these bonds is
5.9 percent compounded semiannually, what is the current price of Bond M? Of Bond N?
29. Valuing the Call Feature At one point, some Treasury bonds were callable. Consider the prices on
the following three Treasury issues as of February 24, 2016:
5.50
7.60
8.40
May 20
May 20
May 20
106.32150
103.12000
107.98750
106.37500
103.50000
108.21875
–.406
–.094
–.406
5.28
5.24
5.32
The bond in the middle is callable in February 2017. What is the implied value of the call feature? (Hint:
Is there a way to combine the two noncallable issues to create an issue that has the same coupon as
the callable bond?)
Challenge
(Questions 27–34)
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PART 2 Valuation and Capital Budgeting162
30. Treasury Bonds The following Treasury bond quote appeared in The Wall Street Journal on
May 11, 2004:
9.125 May 09 100:03 100:04 . . . –2.15
Why would anyone buy this Treasury bond with a negative yield to maturity? How is this possible?
31. Real Cash Flows An engineer earned $22,400 per year when he began his career. Thirty years
later, his annual salary was $97,500. The inflation index over this same period grew from 415.23 to
1,021.39. What was his real annual salary increase? What is his current salary in real terms?
32. Real Cash Flows When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh
flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of
fresh flowers that the former baseball player thought appropriate for the star cost about $5. Based
on actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died. Assume that
the EAR is 5.5 percent. Also, assume that the price of the flowers will increase at 2.9 percent per year,
when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value
of this commitment? Joe began purchasing flowers the week after Marilyn died.
33. Real Cash Flows You are planning to save for retirement over the next 30 years. To save for
retirement, you will invest $700 per month in a stock account in real dollars and $325 per month
in a bond account in real dollars. The effective annual return of the stock account is expected to be
12 percent, and the bond account will have an annual return of 7 percent. When you retire, you will
combine your money into an account with an effective annual return of 8 percent. The inflation rate
over this period is expected to be 4 percent. How much can you withdraw each month from your
account in real terms assuming a 25-year withdrawal period? What is the nominal dollar amount of
your last withdrawal?
34. Real Cash Flows Paul Adams owns a health club in downtown Los Angeles. He charges his
customers an annual fee of $800 and has an existing customer base of 525. Paul plans to raise the
annual fee by 6 percent every year and expects the club membership to grow at a constant rate of
3 percent for the next five years. The overall expenses of running the health club are $80,000 a year
and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul plans to buy
a luxury boat for $400,000, close the health club, and travel the world in his boat for the rest of his
life. What is the annual amount that Paul can spend while on his world tour if he will have no money
left in the bank when he dies? Assume Paul has a remaining life of 25 years and earns 9 percent on
his savings.
WHAT’S ON THE WEB?
1. Bond Quotes You can find current bond prices at finra-markets.morningstar.com/MarketData/Default
.jsp. You want to find the bond prices and yields for bonds issued by Georgia Pacific. You can enter the
ticker symbol “GP” to do a search. What is the shortest maturity bond issued by Georgia Pacific that is
outstanding? What is the longest maturity bond? What is the credit rating for Georgia Pacific’s bonds? Do
all of the bonds have the same credit rating? Why do you think this is?
2. Yield Curves You can find information regarding the most current bond yields at money.cnn.com. Find
the yield curve for U.S. Treasury bonds. What is the general shape of the yield curve? What does this
imply about expected future inflation? Now graph the yield curve for AAA, AA, and A rated corporate
bonds. Is the corporate yield curve the same shape as the Treasury yield curve? Why or why not?
3. Default Premiums The Federal Reserve Bank of St. Louis has files listing historical interest rates on
its website www.stlouisfed.org. Find the link for “FRED” data. You will find listings for Moody’s Seasoned
Aaa Corporate Bond Yield and Moody’s Seasoned Baa Corporate Bond Yield. A default premium can be
calculated as the difference between the Aaa bond yield and the Baa bond yield. Calculate the default
premium using these two bond indexes for the most recent 36 months. Is the default premium the same
for every month? Why do you think this is?
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CHAPTER 5 Interest Rates and Bond Valuation 163
EXCEL MASTER IT ! PROBLEM
Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated
portfolio because the proceeds of the portfolio are dedicated to the future liability. In such a case, the port-
folio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the
coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at
a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if
interest rates increase, the portfolio value at maturity will be higher than needed.
Suppose Ice Cubes, Inc., has the following liability due in five years. The company is going to buy five-year
bonds today to meet the future obligation. The liability and current YTM are below:
Amount of liability:
Current YTM:
$100,000,000
8%
a. At the current YTM, what is the face value of the bonds the company has to purchase today to meet
its future obligation? Assume that the bonds in the relevant range will have the same coupon rate as
the current YTM and these bonds make semiannual coupon payments.
b. Assume the interest rates remain constant for the next five years. Thus, when the company reinvests
the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in five years?
c. Assume that immediately after the company purchases the bonds, interest rates either rise or fall by
1 percent. What is the value of the portfolio in five years under these circumstances?
One way to eliminate reinvestment risk is called immunization. Rather than buying bonds with the same maturity
as the liability, the company instead buys bonds with the same duration as the liability. If you think about the ded-
icated portfolio, if the interest rate falls, the future value of the reinvested coupon payments decreases. However,
as interest rates fall, the price of bonds increases. These effects offset each other in an immunized portfolio.
Another advantage of using duration to immunize a portfolio is that the duration of a portfolio is the
weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a portfo-
lio, you simply take the weight of each asset multiplied by its duration and then sum the results.
d. What is the duration of the liability for Ice Cubes, Inc.?
e. Suppose the two bonds shown below are the only bonds available to immunize the liability. What
face amount of each bond will the company need to purchase to immunize the portfolio?
FINANCING EAST COAST YACHTS’ EXPANSION PLANS
WITH A BOND ISSUE
After Dan’s EFN analysis for East Coast Yachts (see the Closing Case in Chapter 3), Larissa has decided to expand
the company’s operations. She has asked Dan to enlist an underwriter to help sell $45 million in new 30-year
bonds to finance new construction. Dan has entered into discussions with Renata Harper, an underwriter from
the firm of Crowe & Mallard, about which bond features East Coast Yachts should consider and also what coupon
CLOSING CASE
BOND A BOND B
Settlement
Maturity
Coupon rate
YTM
Coupons per year
1/1/2000
1/1/2003
7.00%
7.50%
2
1/1/2000
1/1/2008
8.00%
9.00%
2
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PART 2 Valuation and Capital Budgeting164
rate the issue will likely have. Although Dan is aware of bond features, he is uncertain as to the costs and
benefits of some of them, so he isn’t clear on how each feature would affect the coupon rate of the bond issue.
1. You are Renata’s assistant, and she has asked you to prepare a memo to Dan describing the effect of
each of the following bond features on the coupon rate of the bond. She would also like you to list any
advantages or disadvantages of each feature.
a. The security of the bond, that is, whether or not the bond has collateral.
b. The seniority of the bond.
c. The presence of a sinking fund.
d. A call provision with specified call dates and call prices.
e. A deferred call accompanying the above call provision.
f. A make-whole call provision.
g. Any positive covenants. Also, discuss several possible positive covenants East Coast Yachts might
consider.
h. Any negative covenants. Also, discuss several possible negative covenants East Coast Yachts might
consider.
i. A conversion feature (note that East Coast Yachts is not a publicly traded company).
j. A floating rate coupon.
Dan is also considering whether to issue coupon-bearing bonds or zero coupon bonds. The YTM on either
bond issue will be 5.5 percent. The coupon bond would have a 5.5 percent coupon rate. The company’s
tax rate is 35 percent.
2. How many of the coupon bonds must East Coast Yachts issue to raise the $45 million? How many of the
zeroes must it issue?
3. In 30 years, what will be the principal repayment due if East Coast Yachts issues the coupon bonds?
What if it issues the zeroes?
4. What are the company’s considerations in issuing a coupon bond compared to a zero coupon bond?
5. Suppose East Coast Yachts issues the coupon bonds with a make-whole call provision. The make-whole
call rate is the Treasury rate plus .40 percent. If East Coast calls the bonds in seven years when the
Treasury rate is 4.8 percent, what is the call price of the bond? What if it is 6.2 percent?
6. Are investors really made whole with a make-whole call provision?
7. After considering all the relevant factors, would you recommend a zero coupon issue or a
regular coupon issue? Why? Would you recommend an ordinary call feature or a make-whole call
feature? Why?
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CHAPTER 6 Stock Valuation 165
6
OPENING
CASE
Stock Valuation
When the stock market closed on February 19, 2016, the common stock of heavy equip-
ment manufacturer Caterpillar was selling for $65.40 per share. On that same day, Marriott
International, the well-known hotel company, closed at $65.71 per share, and software com-
pany Red Hat closed at $65.90. Since the stock prices of these three companies were so
similar, you might expect that they would be offering similar dividends to their stockholders,
but you would be wrong. In fact, Caterpillar’s annual dividend was $3.01 per share, Marriott’s
was $.95 per share, and Red Hat paid no dividends at all!
As we will see in this chapter, dividends currently being paid are one of the primary factors
we look at when attempting to value common stocks. However, it is obvious from looking at
Red Hat that current dividends are not the end of the story. This chapter explores dividends,
stock values, and the connection between the two.
Please visit us at corecorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
In our previous chapter, we introduced you to bonds and bond valuation. In this chapter,
we turn to the other major source of financing for corporations, common and preferred
stock. We first describe the cash flows associated with a share of stock and then go
on to develop a very famous result, the dividend growth model. From there, we move
on to examine various important features of common and preferred stock, focusing on
shareholder rights. We close out the chapter with a discussion of how shares of stock
are traded and how stock prices and other important information are reported in the
financial press.
6.1 THE PRESENT VALUE OF COMMON STOCKS
Dividends versus Capital Gains
Our goal in this section is to value common stocks. We learned in Chapter 5 that an asset’s
value is determined by the present value of its future cash flows. Investing in a stock can
provide two kinds of cash flows. First, many stocks pay dividends on a regular basis.
Second, the stockholder receives the sale price when she sells the stock. Thus, in order to
value common stocks, we need to answer an interesting question: Is the value of a stock
equal to:
1. The discounted present value of the sum of next period’s dividend plus next
period’s stock price, or
2. The discounted present value of all future dividends?
This is the kind of question that students would love to see on a multiple-choice exam, because
both (1) and (2) are right.
ExcelMaster
coverage online
www.mhhe.com/RossCore5e
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166
To see that (1) and (2) are the same, let’s start with an individual who will buy the stock
and hold it for one year. In other words, she has a one-year holding period. In addition, she
is willing to pay P0 for the stock today. That is, she calculates:
P 0 =
Div 1 _____
1 + R
+ P 1 _____
1 + R
[6.1]
Div1 is the dividend paid at year’s end and P1 is the price at year’s end. P0 is the present
value of the common stock investment. The term in the denominator, R, is the appropriate
discount rate for the stock.
That seems easy enough, but where does P1 come from? P1 is not pulled out of thin air.
Rather, there must be a buyer at the end of Year 1 who is willing to purchase the stock for
P1. This buyer determines the price by:
P 1 =
Div 2 _____
1 + R
+ P 2 _____
1 + R
[6.2]
Substituting the value of P1 from Equation 6.2 into Equation 6.1 yields:
P 0 =
1 ____
1 + R
[ Div 1 + (
Div 2 + P 2 ________
1 + R
) ]
[6.3]
= Div 1 ____
1 + R
+ Div 2 _______
(1 + R) 2
+ P 2 _______
(1 + R) 2
We can ask a similar question for Formula 6.3: Where does P2 come from? An investor
at the end of Year 2 is willing to pay P2 because of the dividend and stock price at Year 3.
This process can be repeated ad nauseam.1 At the end, we are left with:
P 0 =
Div 1 _____
1 + R
+ Div 2 ________
(1 + R) 2
+ Di v 3 ________
(1 + R) 3
+ . . . = ∑
t=1
*
Di v t _______
(1 + R) t
[6.4]
Thus the value of a firm’s common stock to the investor is equal to the present value of all
of the expected future dividends.
This is a very useful result. A common objection to applying present value analysis to
stocks is that investors are too shortsighted to care about the long-run stream of dividends.
These critics argue that an investor will generally not look past his or her time horizon.
Thus, prices in a market dominated by short-term investors will reflect only near-term
dividends. However, our discussion shows that a long-run dividend discount model holds
even when investors have short-term time horizons. Although an investor may want to cash
out early, she must find another investor who is willing to buy. The price this second inves-
tor pays is dependent on dividends after his date of purchase.
Valuation of Different Types of Stocks
The above discussion shows that the value of the firm is the present value of its future
dividends. How do we apply this idea in practice? Equation 6.4 represents a very general
model and is applicable regardless of whether the level of expected dividends is growing,
fluctuating, or constant. The general model can be simplified if the firm’s dividends are
expected to follow some basic patterns: (1) zero growth, (2) constant growth, and (3) dif-
ferential growth. These cases are illustrated in Figure 6.1.
1 This procedure reminds us of the physicist lecturing on the origins of the universe. He was approached by an elderly gentleman in the
audience who disagreed with the lecture. The attendee said that the universe rests on the back of a huge turtle. When the physicist asked
what the turtle rested on, the gentleman said another turtle. Anticipating the physicist’s objections, the attendee said, “Don’t tire yourself
out, young fellow. It’s turtles all the way down.”
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CASE 1 (ZERO GROWTH) The value of a stock with a constant dividend is given by:
P 0 =
Div 1 ____
1 + R
+ Div 2 _______
(1 + R) 2
+ . . . = Div ____
R
Here it is assumed that Div1 = Div2 = . . . = Div. This is just an application of the perpetu-
ity formula from a previous chapter.
CASE 2 (CONSTANT GROWTH) Dividends grow at rate g, as follows:
End of Year
D iv idend
1 2 3 4 . . .
Div Div(1 + g) Div(1 + g)2 Div(1 + g)3
Note that Div is the dividend at the end of the first period.
FIGURE 6.1
Zero Growth, Constant
Growth, and Differential
Growth Patterns
Di�erential growth
Constant growth
High growth
g1
Low growth
g2
g1 > g2
Zero growth
g = 0
Years
Dividend growth models
Zero growth: P0 =
Div
R
1 10
D
iv
id
en
ds
p
er
s
ha
re
2 3 4 5 6 7 8 9
Constant growth: P0 =
Div
R – g
Di�erential growth: P0 = Σ +
t = 1
T Div(1 + g1)t
(1 + R)t
R – g 2
(1 + R)T
DivT + 1
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.1
Hampshire Products will pay a dividend of $4 per share a year from now. Financial analysts believe that
dividends will rise at 6 percent per year for the foreseeable future. What is the dividend per share at the
end of each of the first five years?
End of Year
Div idend
1 2 3 4 5
$4.00 $4 × (1.06)
= $4.24
$4 × (1.06)2
= $4.4944
$4 × (1.06)3
= $4.7641
$4 × (1.06)4
= $5.0499
Projected Dividends
(continued )
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168
The assumption of steady dividend growth might strike you as peculiar. Why would the
dividend grow at a constant rate? The reason is that, for many companies, steady growth
in dividends is an explicit goal. For example, in 2016, Procter & Gamble, the Cincinnati-
based maker of personal care and household products, increased its annual dividend by
about 1 percent to $2.68 per share; this increase was notable because it was the 60th in a
row. The subject of dividend growth falls under the general heading of dividend policy, so
we will defer further discussion of it to a later chapter.
CASE 3 (DIFFERENTIAL GROWTH) In this case, an algebraic formula would be too unwieldy.
Instead, we present examples.
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.2
Suppose an investor is considering the purchase of a share of the Utah Mining Company. The stock will
pay a $3 dividend a year from today. This dividend is expected to grow at 10 percent per year (g = 10%)
for the foreseeable future. The investor thinks that the required return (R) on this stock is 15 percent,
given her assessment of Utah Mining’s risk. (We also refer to R as the discount rate of the stock.) What is
the value of a share of Utah Mining Company’s stock?
Using the constant growth formula of Case 2, we assess the value to be $60:
$60 =
$3
________
.15 − .10
P0 is quite dependent on the value of g. If g had been estimated to be 12.5 percent, the value of the
share would have been:
$120 = $3 _________
.15 − .125
The stock price doubles (from $60 to $120) when g only increases 25 percent (from 10 percent to
12.5 percent). Because of P0’s dependency on g, one must maintain a healthy sense of skepticism when
using this constant growth of dividends model.
Furthermore, note that P0 is equal to infinity when the growth rate, g, equals the discount rate, R.
Because stock prices do not grow infinitely, an estimate of g greater than R implies an error in
estimation. More will be said of this point later.
Stock Valuation
The value of a common stock with dividends growing at a constant rate is:
P 0 =
Div
____
1 + R +
Div (1 + g)
________
(1 + R) 2
+ Div (1 + g)
2
_________
(1 + R) 3
+ Div (1 + g)
3
_________
(1 + R) 4
+ . . . = Div ____
R − g
where g is the growth rate. Div is the dividend on the stock at the end of the first period. This is the
formula for the present value of a growing perpetuity, which we derived in a previous chapter.
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Consider the stock of Elixir Drug Company, which has a new back-rub ointment and is enjoying rapid
growth. The dividend for a share of stock a year from today will be $1.15. During the next four years, the
dividend will grow at 15 percent per year (g1 = 15%). After that, growth (g2) will be equal to 10 percent
per year. Can you calculate the present value of the stock if the required return (R) is 15 percent?
Figure 6.2 displays the growth in the dividends. We need to apply a two-step process to discount
these dividends. We first calculate the present value of the dividends growing at 15 percent per annum.
That is, we first calculate the present value of the dividends at the end of each of the first five years.
Second, we calculate the present value of the dividends beginning at the end of Year 6.
Differential Growth
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Calculate Present Value of First Five Dividends The present value of dividend payments in Years 1
through 5 is as follows:
FUTURE
YEAR
GROWTH
RATE (g 1)
EXPECTED
DIVIDEND
PRESENT
VALUE
1 .15 $1.1500 $1
2 .15 1.3225 1
3 .15 1.5209 1
4 .15 1.7490 1
5 .15 2.0114 1
Years 1–5 The present value of dividends = $5
The growing annuity formula of the previous chapter could normally be used in this step. However, note
that dividends grow at 15 percent, which is also the discount rate. Since g = R, the growing annuity for-
mula cannot be used in this example.
Calculate Present Value of Dividends Beginning at End of Year 6 This is the procedure for deferred
perpetuities and deferred annuities that we mentioned in a previous chapter. The dividends beginning at
the end of Year 6 are:
End of Year
Div idend
6 7 8 9
Div5 × (1 + g2)
$2.0114 × 1.10
= $2.2125
Div5 × (1 + g2)2
$2.0114 × (1.10)2
= $2.4338
Div5 × (1 + g2)3
$2.0114 × (1.10)3
= $2.6771
Div5 × (1 + g2)4
$2.0114 × (1.10)4
= $2.9448
As stated in the previous chapter, the growing perpetuity formula calculates present value as of one year
prior to the first payment. Because the payment begins at the end of Year 6, the present value formula
calculates present value as of the end of Year 5.
The price at the end of Year 5 is given by:
P 5 =
Div 6 _____
R − g 2
= $2.2125 ________
.15 − .10 = $44.25
FIGURE 6.2 Growth in Dividends for Elixir Drug Company
D
iv
id
en
ds
End of year
15% growth rate
$1.15
$1.3225
$1.5209
$1.7490
$2.0114 $2.2125
$2.4338
$2.6772
$2.9449
10% growth rate
9 1087654321
(continued )
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170
6.2 ESTIMATES OF PARAMETERS IN THE
DIVIDEND DISCOUNT MODEL
The value of the firm is a function of its growth rate, g, and its discount rate, R. How does
one estimate these variables?
Where Does g Come From?
The previous discussion on stocks assumed that dividends grow at the rate g. We now want
to estimate this rate of growth. This section extends the discussion of growth contained in
Chapter 3. Consider a business whose earnings next year are expected to be the same as
earnings this year unless a net investment is made. This situation is likely to occur, because
net investment is equal to gross, or total, investment less depreciation. A net investment of
zero occurs when total investment equals depreciation. If total investment is equal to depre-
ciation, the firm’s physical plant is maintained, consistent with no growth in earnings.
Net investment will be positive only if some earnings are not paid out as dividends, that
is, only if some earnings are retained.2 This leads to the following equation:
Earnings
next
year
= Earnings
this
year
+ Retained
earnings
this year
× Return on
retained
earnings
Increase in earnings
The increase in earnings is a function of both the retained earnings and the return on the
retained earnings.
We now divide both sides of Equation 6.5 by earnings this year, yielding:
Earnings next year ________________
Earnings this year
= Earnings this year _______________
Earnings this year
+ Retained earnings this year _______________________
Earnings this year
[6.6]
× Return on retained earnings
The left-hand side of Equation 6.6 is one plus the growth rate in earnings, which we write
as 1 + g. The ratio of retained earnings to earnings is called the retention ratio. Thus, we
can write:
1 + g = 1 + Retention ratio × Return on retained earnings [6.7]
It is difficult for a financial analyst to determine the return to be expected on currently
retained earnings, because the details on forthcoming projects are not generally public
information. However, it is frequently assumed that the projects selected in the current year
have an anticipated return equal to returns from projects in other years. Here, we can esti-
mate the anticipated return on current retained earnings by the historical return on equity
or ROE. After all, ROE is the return on the firm’s entire equity, which is the return on the
cumulation of all the firm’s past projects.
[6.5]
The present value of P5 at the end of Year 0 is:
P 5 _______
(1 + R ) 5
= $44.25 _______
(1.15 ) 5
= $22
The present value of all dividends as of the end of Year 0 is $27 (= $22 + 5).
2 We ignore the possibility of the issuance of stocks or bonds in order to raise capital. These possibilities are considered in later chapters.
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From Equation 6.7, we have a simple way to estimate growth:
Formula for Firm’s Growth Rate :
g = Retention ratio × Return on retained earnings (ROE) [6.8]
Previously g referred to growth in dividends. However, the growth in earnings is equal to
the growth rate in dividends in this context, because as we will presently see, the ratio of
dividends to earnings is held constant. In fact, as you have probably figured out, g is the
sustainable growth rate we introduced in Chapter 3.
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Pagemaster Enterprises just reported earnings of $2 million. It plans to retain 40 percent of its earnings.
The historical return on equity (ROE) has been 16 percent, a figure that is expected to continue into the
future. How much will earnings grow over the coming year?
We first perform the calculation without reference to Equation 6.8. Then we use [6.8] as a check.
Calculation without Reference to Equation 6.8 The firm will retain $800,000 (= 40% × $2 million).
Assuming that historical ROE is an appropriate estimate for future returns, the anticipated increase in
earnings is:
$800, 000 × .16 = $128, 000
The percentage growth in earnings is:
Change in earnings
________________
Total earnings
= $128, 000 _________
$2 million
= .064
This implies that earnings in one year will be $2,128,000 (= $2,000,000 × 1.064).
Check Using Equation 6.8 We use g = Retention ratio × ROE. We have:
g = .4 × .16 = .064
Earnings Growth
Where Does R Come From?
Thus far, we have taken the required return, or discount rate R, as given. We will have quite
a bit to say on this subject in later chapters. For now, we want to examine the implications
of the dividend growth model for this required return. Earlier, we calculated P0 as:
P 0 = Div / (R − g)
Now let’s assume we know P0. If we rearrange this equation to solve for R, we get:
R − g
= Div / P 0
R
= Div / P 0 + g
[6.9]
This tells us that the total return, R, has two components. The first of these, Div/P0,
is called the expected dividend yield. Because this is calculated as the expected cash
dividend divided by the current price, it is conceptually similar to the current yield on
a bond.
The second part of the total return is the growth rate, g. As we will verify shortly, the
dividend growth rate is also the rate at which the stock price grows. Thus, this growth
rate can be interpreted as the capital gains yield, that is, the rate at which the value of the
investment grows.
To illustrate the components of the required return, suppose we observe a stock selling
for $20 per share. The next dividend will be $1 per share. You think that the dividend will
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172
grow by 10 percent per year more or less indefinitely. What return does this stock offer you
if this is correct?
The dividend growth model calculates total return as:
R
= Dividend yield + Capital gains yield
R = Div / P 0 + g
In this case, total return works out to be:
R
= $1/20 + 10%
= 5 % + 10%
= 15%
This stock, therefore, has an expected return of 15 percent.
We can verify this answer by calculating the price in one year, P1, using 15 percent as
the required return. Based on the dividend growth model, this price is:
P 1
= Div × (1 + g) / (R − g)
= $1 × 1.10/ (.15 − .10)
= $1.10/ .05
Notice that this $22 is $20 × 1.1, so the stock price has grown by 10 percent as it should. If
you pay $20 for the stock today, you will get a $1 dividend at the end of the year, and you
will have a $22 − 20 = $2 gain. Your dividend yield is thus $1/20 = 5 percent. Your capital
gains yield is $2/20 = 10 percent, so your total return would be 5 percent + 10 percent
= 15 percent.
To get a feel for actual numbers in this context, consider that, according to the 2016
Value Line Investment Survey, Procter & Gamble’s dividends were expected to grow by
4 percent over the next 5 or so years, compared to a historical growth rate of 8.5 percent
over the preceding 5 years and 10 percent over the preceding 10 years. In 2016, the
projected dividend for the coming year was given as $2.75. The stock price at that time
was about $82 per share. What is the return investors require on P&G? Here, the dividend
yield is 3.4 percent and the capital gains yield is 4 percent, giving a total required return of
7.4 percent on P&G stock.
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Pagemaster Enterprises, the company examined in the previous example, has 1,000,000 shares of stock
outstanding. The stock is selling at $10. What is the required return on the stock?
Because the retention ratio is 40 percent, the payout ratio is 60 percent (= 1 − Retention ratio). The
payout ratio is the ratio of dividends/earnings. Because earnings a year from now will be $2,128,000
(=$2,000,000 × 1.064), dividends will be $1,276,800 (=60 × $2,128,000). Dividends per share will
be $1.28 (=$1,276,800/1,000,000). Given our previous result that g =.064, we calculate R from [6.9]
as follows:
.192 = $1.28 ______
10.00
+ .064
Calculating the Required Return
A Healthy Sense of Skepticism
It is important to emphasize that our approach merely estimates g; our approach does not
determine g precisely. We mentioned earlier that our estimate of g is based on a number
of assumptions. For example, we assume that the return on reinvestment of future retained
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CHAPTER 6 Stock Valuation 173
earnings is equal to the firm’s past ROE. We assume that the future retention ratio is equal
to the past retention ratio. Our estimate for g will be off if these assumptions prove to be
wrong. 3D Systems, a 3-D printer manufacturer, is an example of a firm whose historical
growth rate will not equal future growth rates. The company had total revenues of about
$112.8 million in 2009 compared to about $663 million in 2015. That works out to a
growth rate of a remarkable 34.3 percent per year! How likely is it that the company can
continue to grow at this rate? If it did, it would have revenues of about $17 trillion in just
11 years, which is about the same as the gross domestic product (GDP) of the United States.
Obviously, 3D Systems’ growth rate will slow substantially in the next several years.
Unfortunately, the determination of R is highly dependent on g. In the Pagemaster
Enterprises example, if g is estimated to be 0, R equals 12.8 percent (=$1.28/10.00). If g is
estimated to be 12 percent, R equals 24.8 percent (=$1.28/10.00 + 12%). Thus, one should
view estimates of R with a healthy sense of skepticism.
Because of the preceding, some financial economists generally argue that the estima-
tion error for R for a single security is too large to be practical. Therefore, they suggest
calculating the average R for an entire industry. This R would then be used to discount the
dividends of a particular stock in the same industry.
One should be particularly skeptical of two polar cases when estimating R for individual
securities. First, consider a firm currently paying no dividend. The stock price will be
above zero because investors believe that the firm may initiate a dividend at some point or
the firm may be acquired at some point. However, when a firm goes from no dividends to a
positive number of dividends, the implied growth rate is infinite. Thus, Equation 6.9 must
be used with extreme caution here, if at all—a point we emphasize later in this chapter.
Second, we mentioned earlier that the value of the firm is infinite when g is equal
to R. Because prices for stocks do not grow infinitely, an analyst whose estimate of g for a
HOW FAST IS TOO FAST?
Growth rates are an important tool for evaluating a company and, as we have seen, an important part of valuing a com-
pany’s stock. When you’re thinking about (and calculating) growth rates, a little common sense goes a long way. For
example, in 2015, retailing giant Walmart had about 777 million square feet of stores, distribution centers, and so forth in
the U.S. The company expected to increase its square footage by about 4 percent over the next year. This doesn’t sound
too outrageous, but can Walmart grow its square footage at 4 percent indefinitely?
Using the compound growth calculation we discussed in an earlier chapter, see if you agree that if Walmart grows at
4 percent per year over the next 300 years, the company will have more than 100 trillion square feet under roof, which
is about the total land mass of the entire United States! In other words, if Walmart keeps growing at 4 percent, the entire
country will eventually be one big Walmart. Scary.
What about growth in cash flow? As of its fiscal year-end in September 2015, Apple had grown its operating cash flow
at an annual rate of about 41.4 percent for the previous six years. The company generated about $81.3 billion in cash
flow for 2015. If the company were to grow its cash flow at that same rate for the next nine years, it would generate over
$1.83 trillion per year, which is greater than total amount of U.S. currency in the world.
As these examples show, growth rates shouldn’t just be extrapolated into the future. It is fairly easy for a small com-
pany to grow very fast. If a company has $100 in sales, it only has to increase sales by another $100 to have a 100 percent
increase in sales. If the company’s sales are $10 billion, it has to increase sales by another $10 billion to achieve the same
100 percent increase. So, long-term growth rate estimates must be chosen very carefully. As a rule of thumb, for really long-
term growth rate estimates, you should probably assume that a company will not grow much faster than the economy as a
whole, which is probably noticeably less than 5 percent (inflation adjusted).
FINANCE MATTERS
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particular firm is equal to or above R must have made a mistake. Most likely, the analyst’s
high estimate for g is correct for the next few years. However, firms cannot maintain an
abnormally high growth rate forever. The analyst’s error was to use a short-run estimate of
g in a model requiring a perpetual growth rate. A nearby Finance Matters box discusses
the consequences of long-term growth at unrealistic rates.
The No-Payout Firm
Students frequently ask the following question: If the dividend discount model is correct,
why aren’t no-payout stocks selling at zero? This is a good question and gets at the goals
of the firm. A firm with many growth opportunities is faced with a dilemma. The firm can
pay out cash now, or it can forgo cash payments now so that it can make investments that
will generate even greater payouts in the future.3 This is often a painful choice, because a
strategy of deferment may be optimal yet unpopular among certain stockholders.
Many firms choose to pay no cash to stockholders—and these firms sell at positive
prices. For example, many Internet firms, such as Alphabet, pay no cash to stockholders.
Rational shareholders believe that they will either receive a payout at some point or they
will receive something just as good. That is, the firm will be acquired in a merger, with the
stockholders receiving either cash or shares of stock at that time.
Of course, the actual application of the dividend discount model is difficult for firms of
this type. Clearly, the model for constant growth of payouts does not exactly apply. Though
the differential growth model can work in theory, the difficulties of estimating the date of
the first payout, the growth rate of payouts after that date, and the ultimate merger price
make application of the model quite difficult in reality.
Empirical evidence suggests that firms with high growth rates are likely to have lower pay-
outs, a result consistent with the above analysis. For example, consider Microsoft Corporation.
The company started in 1975 and grew rapidly for many years. It paid its first dividend in
2003, though it was a billion-dollar company (in both sales and market value of stockholders’
equity) prior to that date. Why did it wait so long to pay a dividend? It waited because it had
so many positive growth opportunities, that is, new software products, to take advantage of.
6.3 COMPARABLES
So far in this chapter, we have valued stocks by discounting dividends (or total payouts). In
addition to this approach, practitioners commonly value stocks by comparables. The com-
parables approach is similar to valuation in real estate. If your neighbor’s home just sold
for $200,000 and it has similar size and amenities to your home, your home is probably
worth around $200,000 also. In the stock market, comparable firms are assumed to have
similar multiples. To see how the comparables approach works, let’s look at perhaps the
most common multiple, the price-to-earnings (PE) multiple, or PE ratio.
Price-to-Earnings Ratio
Recall that a stock’s price-to-earnings ratio is the ratio of the stock’s price to its earn-
ings per share. For example, if the stock of Sun Aerodynamic Systems (SAS) is selling at
$27.00 per share and its earnings per share over the last year was $4.50, SAS’s PE ratio
would be 6 (= $27/4.50).
It is generally assumed that similar firms have similar PE ratios. For example, imagine
the average price-to-earnings (PE) ratio across all publicly traded companies in the specialty
retail industry is 12 and a particular company in the industry has earnings of $10 million.
If this company is judged to be similar to the rest of the industry, one might estimate that
company’s value to be $120 million (= 12 × $10 million).
3 A third alternative is to issue stock so that the firm has enough cash both to pay dividends and to invest. This possibility is explored in a
later chapter.
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Valuation via PE certainly looks easier than valuation via discounted cash flow (DCF),
since the DCF approach calls for estimates of future cash flows. But is the PE approach
better? That depends on the similarity across comparables.
On February 19, 2016, Alphabet’s stock price was $701 and its EPS was $23.59, imply-
ing a PE ratio of about 29.7.4 On the same day, Hewlett-Packard’s PE was 10.2, Microsoft’s
was 36.7, and Apple’s was 10.2. Why would stocks in the same industry trade at different
PE ratios?
The dividend discount model (in Examples 6.1 and 6.2) implies that the PE ratio is
related to growth opportunities.5 As an example, consider two firms, each having just
reported earnings per share of $1. However, one firm has many valuable growth opportuni-
ties, while the other firm has no growth opportunities at all. The firm with growth oppor-
tunities should sell at a higher price, because an investor is buying both current income of
$1 and growth opportunities. Suppose that the firm with growth opportunities sells for $16
and the other firm sells for $8. The $1 earnings per share number appears in the denomina-
tor of the PE ratio for both firms. Thus, the PE ratio is 16 for the firm with growth oppor-
tunities, but only 8 for the firm without the opportunities.
There are at least two additional factors explaining the PE ratio. The first is the discount
rate, R. Since R appears in the denominator of the dividend discount model, the formula
implies that the PE ratio is negatively related to the firm’s discount rate. We have already
suggested that the discount rate is positively related to the stock’s risk or variability. Thus,
the PE ratio is negatively related to the stock’s risk. To see that this is a sensible result, con-
sider two firms, A and B, behaving as cash cows. The stock market expects both firms to have
annual earnings of $1 per share forever. However, the earnings of Firm A are known with
certainty while the earnings of Firm B are quite variable. A rational stockholder is likely to
pay more for a share of Firm A because of the absence of risk. If a share of Firm A sells at a
higher price and both firms have the same EPS, the PE ratio of Firm A must be higher.
The second additional factor concerns the firm’s accounting method. As an example,
consider two identical firms, C and D. Firm C uses LIFO and reports earnings of $2 per
share.6 Firm D uses the less conservative accounting assumptions of FIFO and reports
earnings of $3 per share. The market knows that both firms are identical and prices both
at $18 per share. The price–earnings ratio is 9 (= $18/2) for Firm C and 6 (= $18/3) for
Firm D. Thus, the firm with the more conservative principles has the higher PE ratio.
In conclusion, we have argued that a stock’s PE ratio is likely a function of three factors:
1. Growth opportunities. Companies with significant growth opportunities are
likely to have high PE ratios.
2. Risk. Low-risk stocks are likely to have high PE ratios.
3. Accounting practices. Firms following conservative accounting practices will
likely have high PE ratios.
4 We just calculated PE as the ratio of current price to last year’s EPS. Alternatively, PE can be computed as the ratio of current price to
projected EPS over the next year.
5 We can also use the constant growth version of the dividend discount model to solve for the price–earnings ratio.
Recall that
Price per share = Div ____
R − g
If Div can be expressed as EPS1 × (1 − b), where EPS1 is earnings per share in time 1 and b is the plowback ratio (where 1 − b is the dividend
payout ratio), and EPS0 (1 + g) 5 EPS1, then
Price per share = EP S 0 (1 + g)(1 − b) ________________
R − g
dividing by EPS0 yields
Price per share __________
EP S 0
=
(1 + g)(1 − b)
_________
R − g
6 Recall from your accounting courses that in an inflationary environment, FIFO (first-in, first-out) accounting understates the true cost of
inventory and hence inflates reported earnings. Inventory is valued according to more recent costs under LIFO (last-in, first-out), implying
that reported earnings are lower here than they would be under FIFO. Thus, LIFO inventory accounting is a more conservative method than
FIFO. Similar accounting leeway exists for construction costs (completed contracts versus percentage-of-completion methods) and deprecia-
tion (accelerated depreciation versus straight-line depreciation).
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176
Which of these factors is most important in the real world? The consensus among
finance professionals is that growth opportunities typically have the biggest impact on
PE ratios. For example, high-tech companies generally have higher PE ratios than, say,
utilities, because utilities have fewer opportunities for growth, even though utilities
typically have lower risk. And, within industries, differences in growth opportunities
also generate the biggest differences in PE ratios. In our example at the beginning of
this section, Alphabet’s high PE is almost certainly due to its growth opportunities, not
its low risk or its accounting conservatism. In fact, due to its relative youth, the risk of
Alphabet is likely higher than the risk of many of its competitors. Hewlett-Packard’s
PE is lower than Alphabet’s PE because Hewlett-Packard’s growth opportunities are
a small fraction of its existing business lines. However, Hewlett-Packard had a much
higher PE decades ago, when it had huge growth opportunities but little in the way of
existing business.
Thus, while multiples such as the PE ratio can be used to price stocks, care must be
taken. Firms in the same industry are likely to have different multiples if they have differ-
ent growth rates, risk levels, and accounting treatments. Average multiples should not be
calculated across all firms in any industry. Rather, an average multiple should be calculated
only across those firms in an industry with similar characteristics.
Enterprise Value Ratios
The PE ratio is an equity ratio. That is, the numerator is the price per share of stock and the
denominator is the earnings per share of stock. In addition, practitioners often use ratios
involving both equity and debt. Perhaps the most common is the enterprise value (EV) to
EBITDA ratio. Enterprise value is equal to the market value of the firm’s equity plus the
market value of the firm’s debt minus cash. Recall, EBITDA stands for earnings before
interest, taxes, depreciation, and amortization.
For example, imagine that Illinois Food Products Co. (IFPC) has equity worth $800 million,
debt worth $300 million, and cash of $100 million. The enterprise value here is $1 billion
(= $800 + 300 − 100). Further imagine the firm has the following income statement:
ILL INOIS FOOD PRODUCTS CO.
Income Statement ($ in mi l l ions)
Revenue $700.00
Cost of goods sold −500.00
Earnings before interest, taxes, depreciation, and amortization $200.00
(EBITDA)
Depreciation and amortization −100.00
Interest − 24.00
Pretax income 76.00
Taxes (@ 30%) − 22.80
Profit after taxes $ 53.20
The EV to EBITDA ratio is 5 (= $1 billion/200 million). Note that all the items in the income
statement below EBITDA are ignored when calculating this ratio.
As with PE ratios, it is generally assumed that similar firms have similar EV/EBITDA
ratios. For example, imagine that the average EV/EBITDA ratio in an industry is 6. If
QRT Corporation, a firm in the industry with EBITDA of $50 million, is judged to be
similar to the rest of the industry, its enterprise value might be estimated at $300 million
(= 6 × $50). Now imagine that QRT has $75 million of debt and $25 million of cash.
Given our estimate of QRT’s enterprise value, QRT’s stock would be worth $250 million
(= $300 − 75 + 25).
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A number of questions arise with value ratios:
1. Is there any advantage to the EV/EBITDA ratio over the PE ratio? Yes.
Companies in the same industry may differ by leverage, i.e., the ratio of debt
to equity. As you will learn in Chapter 14, leverage increases the risk of equity,
impacting the discount rate, R. Thus, while firms in the same industry may be
otherwise comparable, they are likely to have different PE ratios if they have dif-
ferent degrees of leverage. Since enterprise value includes debt and equity, the
impact of leverage on the EV/EBITDA ratio is less.7
2. Why is EBITDA used in the denominator? The numerator and denominator of
a ratio should be consistent. Since the numerator of the PE ratio is the price of
a share of stock, it makes sense that the denominator is the earnings per share
(EPS) of stock. That is, interest is specifically subtracted before EPS is calculated.
By contrast, since EV involves the sum of debt and equity, it is sensible that the
denominator is unaffected by interest payments. This is the case with EBITDA
since, as its name implies, earnings are calculated before interest is taken out.
3. Why does the denominator ignore depreciation and amortization? Many practi-
tioners argue that, since depreciation and amortization are not cash flows, earn-
ings should be calculated before taking out depreciation and amortization. In
other words, depreciation and amortization merely reflect the sunk cost of a pre-
vious purchase. However, this view is by no means universal. Others point out
that depreciable assets will eventually be replaced in an ongoing business. Since
depreciation charges reflect the cost of future replacement, it can be argued that
these charges should be considered in a calculation of income.
4. What other denominators are used in value ratios? Among others, practitioners
may use EBIT (earnings before interest and taxes), EBITA (earnings before
interest, taxes, and amortization), and free cash flow.
5. Why is cash subtracted out? Many firms seem to hold amounts of cash well in
excess of what is needed. For example, Microsoft held tens of billions of dol-
lars in cash and short-term investments throughout the last decade, far more
than many analysts believed was optimal. Since an enterprise value ratio should
reflect the ability of productive assets to create earnings or cash flow, cash
should be subtracted out when calculating the ratio. However, the viewpoint that
all cash should be ignored can be criticized. Some cash holdings are necessary
to run a business, and this amount of cash should be included in EV.
6.4 VALUING STOCKS USING FREE CASH FLOWS
So far in this chapter, we have discounted cash payouts to value a single share of stock and
used the method of comparables. As an alternative, one can value stocks by discounting
their cash flows using a “top down” approach.
As an example, consider Global Harmonic Control Systems (GHCS). Revenues, which
are forecasted to be $500 million in one year, are expected to grow at 10 percent per year
for the two years after that, 8 percent per year for the next two years, and 6 percent per
year after that. Expenses including depreciation are 60 percent of revenues. Net invest-
ment, including net working capital and capital spending less depreciation, is 10 percent
of revenues. Because all costs are proportional to revenues, net cash flow (sometimes
referred to as free cash flow) grows at the same rate as do revenues. GHCS is an all-equity
firm with 12 million shares outstanding. A discount rate of 16 percent is appropriate for
a firm of GHCS’s risk.
7 However, leverage does impact the ratio of EV to EBITDA to some extent. As we discuss in Chapter 14, leverage creates a tax shield,
increasing EV. Since leverage should not impact EBITDA, the ratio should increase with leverage.
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The relevant numbers for the first five years, rounded to two decimals, are:
YEAR ($000,000) 1 2 3 4 5
Revenues 500.00 550.00 605.00 653.40 705.67
Expenses 300.00 330.00 363.00 392.04 423.40
Earnings before taxes 200.00 220.00 242.00 261.36 282.27
Taxes (40%) 80.00 88.00 96.80 104.54 112.91
Earnings after taxes 120.00 132.00 145.20 156.82 169.36
Net investment 50.00 55.00 60.50 65.34 70.57
Net cash flow 70.00 77.00 84.70 91.48 98.79
Since net cash flow grows at 6 percent per year after Year 5, net cash flow in Year 6 is
forecasted to be $104.72 (= $98.79 × 1.06). Using the growing perpetuity formula, we can
calculate the present value as of Year 5 of all future cash flows to be $1,047.22 million
[= $104.72/(.16 − .06)].
The present value as of today of that terminal value is:
$1, 047.22 × 1 _______
(1.16) 5
= $498.59 million
The present value of the net cash flows during the first five years is:
$70 _____
1.16
+ $77 _______
(1.16) 2
+ $84.7 _______
(1.16) 3
+ $91.48 _______
(1.16) 4
+ $98.79 _______
(1.16) 5
= $269.39 million
Adding in the terminal value, today’s value of the firm is $767.98 million (= $269.39
+ 498.59). Given the number of shares outstanding, the price per share is $64.00
(= $767.98/12).
The above calculation assumes a growing perpetuity after Year 5. However, we pointed
out in the previous section that stocks are often valued by multiples. An investor might
estimate the terminal value of GHCS via a multiple, rather than the growing perpetuity for-
mula. For example, suppose that the price–earnings ratio for comparable firms in GHCS’s
industry is 7.
Since earnings after tax in Year 5 are $169.36. Using the PE multiple of 7, the value of
the firm at Year 5 would be estimated as $1,185.52 million (= $169.36 × 7).
The firm’s value today is:
$70 _____
1.16
+ $77 _______
(1.16) 2
+ $84.7 _______
(1.16) 3
+ $91.48 _______
(1.16) 4
+ $98.79 _______
(1.16) 5
+ $1,185.52 _________
(1.16) 5
= $833.83
With 12 million shares outstanding, the price per share of GHCS would be $69.49
(= $833.83/12).
Now we have two estimates of the value of a share of equity in GHCS. The differ-
ent estimates reflect the different ways of calculating terminal value. Using the constant
growth discounted cash flow method for terminal value, our estimate of the equity value
per share of GHCS is $64; using the PE comparable method, our estimate is $69.49. There
is no best method. If the comparable firms were all identical to GHCS, perhaps the PE
method would be best. Unfortunately, firms are not identical. On the other hand, if we
were very sure of the terminal date and the growth in subsequent cash flows, perhaps the
constant growth method would be best. In practice, both methods are used.
Conceptually, the dividend discount model, the comparables method, and the free cash
flow model are mutually consistent and can be used to determine the value of a share
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of stock. In practice, the dividend discount model is especially useful for firms paying
very steady dividends and the comparables method is useful for firms with similar growth
opportunities. The free cash flow model is helpful for non-dividend-paying firms with
external financing needs.
6.5 SOME FEATURES OF COMMON AND
PREFERRED STOCKS
In discussing common stock features, we focus on shareholder rights and dividend pay-
ments. For preferred stock, we explain what the “preferred” means, and we also debate
whether preferred stock is really debt or equity.
Common Stock Features
The term common stock means different things to different people, but it is usually applied
to stock that has no special preference either in receiving dividends or in bankruptcy.
SHAREHOLDER RIGHTS The conceptual structure of the corporation assumes that sharehold-
ers elect directors who, in turn, hire management to carry out their directives. Shareholders,
therefore, control the corporation through the right to elect the directors. Generally, only
shareholders have this right.
Directors are elected each year at an annual meeting. Although there are exceptions
(discussed next), the general idea is “one share, one vote” (not one shareholder, one vote).
Corporate democracy is thus very different from our political democracy. With corporate
democracy, the “golden rule” prevails absolutely.8
Directors are elected at an annual shareholders’ meeting by a vote of the holders of a
majority of shares who are present and entitled to vote. However, the exact mechanism
for electing directors differs across companies. The most important difference is whether
shares must be voted cumulatively or voted straight.
To illustrate the two different voting procedures, imagine that a corporation has two share-
holders: Smith with 20 shares and Jones with 80 shares. Both want to be a director. Jones
does not want Smith, however. We assume there are a total of four directors to be elected.
The effect of cumulative voting is to permit minority participation.9 If cumulative vot-
ing is permitted, the total number of votes that each shareholder may cast is determined
first. This is usually calculated as the number of shares (owned or controlled) multiplied by
the number of directors to be elected.
With cumulative voting, the directors are elected all at once. In our example, this means
that the top four vote getters will be the new directors. A shareholder can distribute votes
however he/she wishes.
Will Smith get a seat on the board? If we ignore the possibility of a five-way tie, then the
answer is yes. Smith will cast 20 × 4 = 80 votes, and Jones will cast 80 × 4 = 320 votes. If
Smith gives all his votes to himself, he is assured of a directorship. The reason is that Jones
can’t divide 320 votes among four candidates in such a way as to give all of them more than
80 votes, so Smith will finish fourth at worst.
In general, if there are N directors up for election, then 1/(N + 1) percent of the stock plus
one share will guarantee you a seat. In our current example, this is 1/(4 + 1) = 20 percent. So
the more seats that are up for election at one time, the easier (and cheaper) it is to win one.
With straight voting, the directors are elected one at a time. Each time, Smith can cast
20 votes and Jones can cast 80. As a consequence, Jones will elect all of the candidates.
8 The golden rule: Whosoever has the gold makes the rules.
9 By minority participation, we mean participation by shareholders with relatively small amounts of stock.
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The only way to guarantee a seat is to own 50 percent plus one share. This also guarantees
that you will win every seat, so it’s really all or nothing.
As we’ve illustrated, straight voting can “freeze out” minority shareholders; that is the
reason many states have mandatory cumulative voting. In states where cumulative voting
is mandatory, devices have been worked out to minimize its impact.
One such device is to stagger the voting for the board of directors. With staggered elec-
tions, only a fraction of the directorships are up for election at a particular time. Thus, if
only two directors are up for election at any one time, it will take 1/(2 + 1) = 33.33 percent
of the stock plus one share to guarantee a seat.
Overall, staggering has two basic effects:
1. Staggering makes it more difficult for a minority to elect a director when there is
cumulative voting because there are fewer directors to be elected at one time.
2. Staggering makes takeover attempts less likely to be successful because it makes
it more difficult to vote in a majority of new directors.
We should note that staggering may serve a beneficial purpose. It provides “institutional
memory,” that is, continuity on the board of directors. This may be important for corpora-
tions with significant long-range plans and projects.
PROXY VOTING A proxy is the grant of authority by a shareholder to someone else to vote
his/her shares. For convenience, much of the voting in large public corporations is actually
done by proxy.
As we have seen, with straight voting, each share of stock has one vote. The owner of
10,000 shares has 10,000 votes. Large companies have hundreds of thousands or even mil-
lions of shareholders. Shareholders can come to the annual meeting and vote in person, or
they can transfer their right to vote to another party.
Obviously, management always tries to get as many proxies as possible transferred to it.
However, if shareholders are not satisfied with management, an “outside” group of share-
holders can try to obtain votes via proxy. They can vote by proxy in an attempt to replace
management by electing enough directors. The resulting battle is called a proxy fight.
CLASSES OF STOCK Some firms have more than one class of common stock. Often, the
classes are created with unequal voting rights. The Ford Motor Company, for example, has
Class B common stock, which is not publicly traded (it is held by Ford family interests and
trusts). This class has 40 percent of the voting power, even though it represents less than
10 percent of the total number of shares outstanding.
There are many other cases of corporations with different classes of stock. For example,
Adolph Coors Class B shares, which were owned by the public, had no votes at all except
in the case of a merger. (Adolph Coors later merged with Molson.) The CEO of cable TV
giant Comcast, Brian Roberts, owned about .4 percent of the company’s equity, but he
Stock in JRJ Corporation sells for $20 per share and features cumulative voting. There are 10,000 shares
outstanding. If three directors are up for election, how much does it cost to ensure yourself a seat on
the board?
The question here is how many shares of stock it will take to get a seat. The answer is 2,501, so
the cost is 2,501 × $20 = $50,020. Why 2,501? Because there is no way the remaining 7,499 votes
can be divided among three people to give all of them more than 2,501 votes. For example, sup-
pose two people receive 2,502 votes and the first two seats. A third person can receive at most
10,000 − 2,502 − 2,502 − 2,501 = 2,495, so the third seat is yours.
Buying the Election
E
X
A
M
P
L
E
6
.6
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had a third of all the votes, thanks to a special class of stock. Another good example is
Alphabet, formerly Google. Alphabet initially had two classes of common stock, A and B
(it has recently added a third class). The Class A shares are held by the public, and each
share has one vote. The Class B shares are held by company insiders, and each Class B
share has 10 votes. As a result, Google’s founders and management control the company.
Historically, the New York Stock Exchange did not allow companies to create classes of
publicly traded common stock with unequal voting rights. Exceptions (e.g., Ford) appear to
have been made. In addition, many non-NYSE companies have dual classes of common stock.
A primary reason for creating dual or multiple classes of stock has to do with control
of the firm. If such stock exists, management of a firm can raise equity capital by issuing
nonvoting or limited-voting stock while maintaining control.
The subject of unequal voting rights is controversial in the United States, and the idea
of one share, one vote has a strong following and a long history. Interestingly, however,
shares with unequal voting rights are quite common in the United Kingdom and elsewhere
around the world.
OTHER RIGHTS The value of a share of common stock in a corporation is directly related
to the general rights of shareholders. In addition to the right to vote for directors, share-
holders usually have the following rights:
1. The right to share proportionally in dividends paid.
2. The right to share proportionally in assets remaining after liabilities have been
paid in a liquidation.
3. The right to vote on stockholder matters of great importance, such as a merger.
Voting is usually done at the annual meeting or a special meeting.
In addition, stockholders sometimes have the right to share proportionally in any new stock
sold. This is called the preemptive right.
Essentially, a preemptive right means that a company that wishes to sell stock must first
offer it to the existing stockholders before offering it to the general public. The purpose
is to give a stockholder the opportunity to protect his/her proportionate ownership in the
corporation.
DIVIDENDS A distinctive feature of corporations is that they have shares of stock on
which they are authorized by law to pay dividends to their shareholders. Dividends paid
to shareholders represent a return on the capital directly or indirectly contributed to the
corporation by the shareholders. The payment of dividends is at the discretion of the board
of directors.
Some important characteristics of dividends include the following:
1. Unless a dividend is declared by the board of directors of a corporation, it is
not a liability of the corporation. A corporation cannot default on an undeclared
dividend. As a consequence, corporations cannot become bankrupt because of
nonpayment of dividends. The amount of the dividend and even whether it is
paid are decisions based on the business judgment of the board of directors.
2. The payment of dividends by the corporation is not a business expense.
Dividends are not deductible for corporate tax purposes. In short, dividends are
paid out of the corporation’s aftertax profits.
3. Dividends received by individual shareholders are taxable. However, corporations
that own stock in other corporations are permitted to exclude 70 percent of the
dividend amounts they receive and are taxed only on the remaining 30 percent.10
10 For the record, the 70 percent exclusion applies when the recipient owns less than 20 percent of the outstanding stock In a corporation.
If a corporation owns more than 20 percent but less than 80 percent, the exclusion is 80 percent. If more than 80 percent is owned, the
corporation can file a single “consolidated” return and the exclusion is effectively 100 percent.
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182
Preferred Stock Features
Preferred stock differs from common stock because it has preference over common stock
in the payment of dividends and in the distribution of corporation assets in the event of
liquidation. Preference means only that the holders of the preferred shares must receive
a dividend (in the case of an ongoing firm) before holders of common shares are entitled
to anything.
Preferred stock is a form of equity from a legal and tax standpoint. It is important to
note, however, that holders of preferred stock sometimes have no voting privileges.
STATED VALUE Preferred shares have a stated liquidating value, usually $100 per share.
The cash dividend is described in terms of dollars per share. For example, a Ford “$5 pre-
ferred” easily translates into a dividend yield of 5 percent of stated value.
CUMULATIVE AND NONCUMULATIVE DIVIDENDS A preferred dividend is not like interest
on a bond. The board of directors may decide not to pay the dividends on preferred shares,
and their decision may have nothing to do with the current net income of the corporation.
Dividends payable on preferred stock are either cumulative or noncumulative; most are
cumulative. If preferred dividends are cumulative and are not paid in a particular year, they
will be carried forward as an arrearage. Usually, both the accumulated (past) preferred
dividends and the current preferred dividends must be paid before the common sharehold-
ers can receive anything.
Unpaid preferred dividends are not debts of the firm. Directors elected by the common
shareholders can defer preferred dividends indefinitely. However, in such cases, common share-
holders must also forgo dividends. In addition, holders of preferred shares are sometimes
granted voting and other rights if preferred dividends have not been paid for some time.
IS PREFERRED STOCK REALLY DEBT? A good case can be made that preferred stock is
really debt in disguise, a kind of equity bond. Preferred shareholders receive a stated
dividend only, and if the corporation is liquidated, preferred shareholders get a stated
value. Often, preferred stocks carry credit ratings much like those of bonds. Furthermore,
preferred stock is sometimes convertible into common stock, and preferred stocks are
often callable.
In addition, many issues of preferred stock have obligatory sinking funds. The exis-
tence of such a sinking fund effectively creates a final maturity because it means that
the entire issue will ultimately be retired. For these reasons, preferred stock seems to be
a lot like debt. However, for tax purposes, preferred dividends are treated like common
stock dividends.
In the 1990s, firms began to sell securities that look a lot like preferred stock but are
treated as debt for tax purposes. The new securities were given interesting acronyms like
TOPrS (trust-originated preferred securities, or toppers), MIPS (monthly income preferred
securities), and QUIPS (quarterly income preferred securities), among others. Because of
various specific features, these instruments can be counted as debt for tax purposes, mak-
ing the interest payments tax deductible. Payments made to investors in these instruments
are treated as interest for personal income taxes for individuals. Until 2003, interest pay-
ments and dividends were taxed at the same marginal tax rate. When the tax rate on divi-
dend payments was reduced, these instruments were not included, so individuals must still
pay their higher income tax rate on dividend payments received from these instruments.
6.6 THE STOCK MARKETS
Stock markets consist of a primary market and a secondary market. In the primary, or
new-issue market, shares of stock are first brought to the market and sold to investors. In
the secondary market, existing shares are traded among investors.
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CHAPTER 6 Stock Valuation 183
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In the primary market, companies sell securities to raise money. We will discuss this pro-
cess in detail in a later chapter. We therefore focus mainly on secondary market activity in this
section. We conclude with a discussion of how stock prices are quoted in the financial press.
Dealers and Brokers
Because most securities transactions involve dealers and brokers, it is important to under-
stand exactly what is meant by the terms dealer and broker. A dealer maintains an inven-
tory and stands ready to buy and sell at any time. In contrast, a broker brings buyers and
sellers together, but does not maintain an inventory. Thus, when we speak of used car deal-
ers and real estate brokers, we recognize that the used car dealer maintains an inventory,
whereas the real estate broker does not.
In the securities markets, a dealer stands ready to buy securities from investors wishing
to sell them and sell securities to investors wishing to buy them. Recall from our previous
chapter that the price the dealer is willing to pay is called the bid price. The price at which
the dealer will sell is called the ask price (sometimes called the asked, offered, or offer-
ing price). The difference between the bid and ask prices is called the spread, and it is the
basic source of dealer profits.
Dealers exist in all areas of the economy, not just the stock markets. For example, your
local college bookstore is probably both a primary and a secondary market textbook dealer.
If you buy a new book, this is a primary market transaction. If you buy a used book, this is
a se
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