BU 22003 Troy University Intermediate Financial Management Template

2FM/SGF/DMP/17
SCHOOL OF BUSINESS
2FM – Intermediate Financial Management
Solutions to Revision Questions
1.
Taxco Ltd
Capital Allowance Computation
£
Cost
Yr 1 WDA @ 25%
£ allowance
1,000,000
(250,000)
750,000
(187,500)
562,500
(140,625)
421,875
(105,468)
316,407
(200,000)
116,407
Yr 2 WDA @ 25%
Yr 3 WDA @ 25%
Yr 4 WDA @ 25%
Yr 5 proceeds
Yr 5 balancing allowance
250,000
187,500
140,625
105,468
116,407
800,000
Tax Computations
Taxable cashflow
Sales – cost of sales
Consultant fees
Capital allowances
Taxable profit/(loss)
Tax @ 50%
Yr 1
Yr 2
Yr 3
Yr 4
Yr 5
75
(150)
(75)
(250)
(325)
(162.5)
300
300
(187.5)
(112.5)
56.250
550
550
(140.625)
409.375
204.687
600
600
(105.648)
494.352
247.176
600
600
(116.407)
483.593
241.796
Project Evaluation
Year
Equipment
0
1
2
3
4
5
6
(1,000,000)
200,000
Operations
(75,000)
300,000
550,000
600,000
600,000
Therefore go ahead with the project.
Tax
Net
PV Factor
at 10%
PV
162,500
(56,250)
(204,687)
(247,176)
(241,796)
(1,000,000)
(75,000)
462,500
493,750
395,313
552,734
(241,796)
1.0
0.909
0.826
0.751
0.683
0.621
0.564
(1,000,000)
(68,175)
382,025
370,806
269,999
343,248
(136,373)
161,530
2.
(a)
(b)
(c)
WACC = 0.1
1 Year 235 days
IRR by quadratic equation:
Let (1+r) = X
(500,000) + 275,000 + 350,000
X
X2
=0
(500,000)X² + 275,000X + 350,000 = 0
X=
-275   (275)² – 4(-500) (350)
2 x (–-500)
X=
–275   75625 + 700,000
–1000
X=
275  880.7 = 1.1557 or –0.6057
1000
1 + r = 1.1557
(d)
r = 0.1557 or 15.57%
NPV = (500,000) + 275,000 + 350,000
1.1
(1.1)²
NPV = (500,000) + 250,000 + 289,256 = 39,256
Therefore accept the project.
3.
Inflatable Tyres
Year
Investment
Sales
Labour
Material A
Material B
Total
0
(250,000)
–
–
10,000
–
(240,000)
1
(50,000)
200,000
(30,000)
–
(75,000)
45,000
2
–
224,000
(66,000)
(21,000)
28,250
3
–
250,880
(72,600)
(22,050)
4
–
280,985
(79,860)
(23,152)
(78,750)
(30,000)
(82,687)
(30,000)
(86,822)
5
10,000
314,704
(87,846)
(224,310)
(91,163)
121,385
NB Depreciation and overheads are irrelevant costs.
(140,000) + 45,000 + 28,250 + 43,543 + (91,151) + 121,385
1.1
(1.1)²
(1.1)³
(1.1)4
(1.1)5
= (240,000) + 40,909 + 23,347 + 32,715 + 62,257 + 75,370 = (5402)
Therefore reject.
43,543
91,151
4.
(i)
Po
(ii)
Po
(iii)
(iv)
Po
D1994
D1995
D1996
D1997
D1998
=
D1 + P1
1+r
=
10 + 210
1.1
=
£200
=
D
r
=
4
0.1
=
£40
=
D0 (1 + g)
(r-g)
=
D1
r-g
=
8
0.1-0.05
=
£160
= £4
= 4 (1.2) = £4.80
= 4 (1.2)² = £5.76
= 1 (1.2)³ = £6.91
– growing at 6%
Price
i. Present value of the first four years.
= 4.00 + 4.80 + 5.76 + 6.91
1.1
1.21 1.331 1.4641
= £16.65
ii.
Present value of dividend from year five onwards.
P4 = 6.91 (1.06)
0.1 – 0.06
= 183.12
Price =
5.
(ii)
16.65 + 183.12 = £141.71
(1.1)4
Hyper Ltd
0
1
2
3
Price
200,000
400,000
Materials
(40,000)
(40,000 x 1.2)
(40,000 x (1.2)2)
Labour
(6,500)
(65,000 x 1.15)
(65,000 x (1.15)2)
Equipment
(200,000)
50,000
Annual Cashflow
(40,000)
(113,000)
(132,350)
364,037
0
1
2
3
Cumulative Cashflow
(40,000)
(153,000)
(285,350)
+ 78,687
1023
(iii) NPV
@ 15% = +1023
@ 16% = -2548
x
15%
16%
X – 15/1023 = 16%-15%/1023-254
X – 15 = 1023/3571
X = 15.286%
(iv)
Payback:- 2 years and ( 285350/(285350 + 78687) )x 12 = 2 years and 9.4 months
(v)
NPV of project @ 10% = + 21399
Thus, Hyper Ltd should accept the contract.
6.(a)
WACC
Ordinary shares
50p
/£2.50 =
0.07
Debentures
/0.75 =
20.00%
9.33%
(250,000/400,000 )x 20% + (150,000/400,000 )x 9.33% = 16%
(b)
Project
Year 0
A
B
C
D
E
F
(250,000)
(70,000)
(110,000)
(210,000)
(170,000)
(135,000)
(a)
Life
Years
6
5
3
8
4
5
10
Annuity
Amount
£72,500
£30,000
£45,000
£57,000
£70,000
£30,000
£20,000
Annuity Factor
3.685
3.685-0.862
2.246
4.344
2.798
3.274
5.575-3.274
Accept D, E, B and F. Total NPV £87,398. Outlay £585,000
NPV
17162
14690
(8930)
37608
25860
9240
Ranking
3
4
1
2
5
(b)
Payback
A
B
C
D
E
F
3 years
3 years
2 years
3 years
2 years
4 years
5 months
4 months
5 months
8 months
5 months
6 months
Therefore accept C and E.
7.
NPV
Probabilities
-206611.00
41322.31
0.10
0.40
-20661.10
16528.93
4.3E+09
6.8E+08
-115702.00
49586.77
214876.00
0.06
0.09
0.15
-6942.15
4462.81
32231.40
8.0+E+08
2.2E+08
6.9E.09
57851.23
223140.40
388428.70
0.04
0.14
0.02
1
2314.05
31239.67
7768.60
66942.15
1.3E+08
7.0E+09
3.0E+09
2.0E+09
E(NPV) = 66942.15
SD(NPV) = 136173.10
8.
Expected Return on Portfolio = W1 IRR1+ W2 IR R2
=
=
0.5 (0.12) + 0.5 (0.10)
0.11 or 11%
Risk of Portfolio =
VARIANCE
VAR(p) = (0.5)(0.08) + (0.5)(0.02) + 2 (.5) (.5)(6.00) =
STANDARD DEVIATION =
9.
0.0255
WP
0.15
0.20
ER
SDR
Cov
=
=
-0.5 x 0.2 x 0.1
-0.01
E(Rp)
=
=
0.6 (0.15) + 0.4 (0.06)
0.114 or 11.4%
=
0.0255
0.1597 or 15.97%
LO
0.06
0.10
VAR(p) =
=
(0.6)2(0.2)2 + (0.4)2(0.1)2 + 2 (0.6)(0.4)(-0.01)
0.0112
SD(p)
0.10 58 = 10.58%
=
10.
Month
2
£
1
£
Collections
Old system
New system
Discount 1.25% x £675,000
Interest saved: 15/12% x £(67,00045,000 = 22,500)
45,000
67,500
843.75
281.25
3
£
30,000
7,500
15,000
15,000
The proposal therefore is not justified.
11.
E NPV for each project
Project A
NPV
Project B
Prob
EV
£000
NPV
Prob
£000
£000
EV
£000
-20
0.15
(3.00)
5
0.2
1.0
10
0.20
2.00
15
0.3
4.5
25
0.35
8.75
20.
0.4
8.0
40
0.30
12.00
25
0.1
2.5
ENPV = 19.75
ENPV = 16.0
Project A has a higher ENPV, but what about the “risks”.
The standard deviation, SD, can be calculated as
Project A X = 19.75
X
P
£000
x-X
Project B X = 16.0
P(x-X)
2
£000
X
P
P(x-X)2
x-X
£000
£000
-20
0.15
-39.75
237.01
5
0.2
-11
24.2
10
0.20
-9.75
19.01
15
0.3
-1
-.3
20
0.35
5.25
9.65
20.
0.4
+4
6.4
40
0.30
20.25
123.02
25
+9
8.1
0.1
388.69
SD = 388.69
= 19.72
i.e.£19,720 approx
39.0
SD = 39.0
= 6.24
i.e. £6,240 approx
Although Project A has a higher ENPV, it also has a bigger deviation of NPV, and so has greater
business risk associated with it.
Project selection clearly depends on the attitude of the company’s management to business risk:
(a)
If management is prepared to take the risk of a lower NPV and go for the possibility of a
higher NPV, they will opt for Project A;
(b)
If the management is “risk-averse” and prefer to play it safe, they will opt for the much less
risky Project B.
12.
Average debtors
Reduction in Working Capital
(a) Interest Savings (15%)
Current Policy
800,000
–
Option 1
600,000
200,000
30,000
Option 2
400,000
400,000
60,000
144,000
–
96,000
48,000
48,000
96,000
–
78,000
156,000
(6,000)
72,000
(160,000)
(£4,000)
Bad Debt Losses
(b) Reduction in losses
Benefits of each Option
(a) and (b)
Extra Costs of Debt
Collection
Net Benefit/(loss) from option
Conclusion: Option 1 is preferable to the current policy, but Option 2 is more costly.
Note:
When reducing working capital average debtors should always be based on sales and not the variable
cost on sales as the former is the opportunity cost of the reduction. When increasing working capital
however it is always the cost of sales that should be used.
13.
The change in credit policy would be justifiable, in the context of this question, if the rate of return on
the additional investment in working capital exceeds 20%.
Extra profit:
Contribution/sales ratio
Increase in sales revenue
Increase in contribution and profit
(a)
15%
£600,000
£90,000
Extra investment, if only the new debtors take 2 months credit:
Increase in debtors (2/12 of £600,000 x 0.85)
Increase in stocks
Increase in creditors
Net increase in working capital investment
Return on extra investment £90,000/£165,000 = 54.5%
£
85,000
100,000
185,000
(20,000)
165,000
14. Shannon
250,000
Moderate
Weak
100,000
0.7
0.2
Strong
550,000
0.3
Moderate
35,000
Moderate
C
0.7
Strong
350,00
0
0.3
250,000
Moderate
Good
B
250,00
200,000
0.5
Invest
A
D
E
0.7
300,000
0.3
Strong
350,000
F
0.3
Don’t
A
B
C
D
E
F
E(NPV)=£35.680
PROB
NPVxPROB
NPV2xPROB
-86.4
-6.7
2.8
82.6
92.1
171.9
0.14
0.06
0.35
0.15
0.21
0.09
-12.100
-0.402
0.980
12.390
19.341
15.471
35.680
1047.515
2.693
2.744
1023.414
1781.306
2659.465
6517.137
SDNPV =
P(NPV) < 0 P(z) 0 − 35.68 = 72.401 < NPV 6517.137 − (35.68) 2 = £72.401 -0.4928 From tables = 31.21% If "Weak" in YR1 PV1 = 250 Abandon If "Moderate" in YR1 PV1 = 250 Abandon If "Strong" in YR1 PV1 = 250 Abandon Increase in E(NPV) 262,000-250,000 = £10,000 Q15 SUIR Additional Costs Raw Materials Direct Labour Overheads 700000 x 0.20 = 700,000 x 0.35 = 700,000 x 0.15 = 140,000 245,000 105,000 W/C Requirement Stock of RM: WIP Mat Lab O/H 140000 x 2/52 140000 x 4/52 245000 x 4/52 x 1/2 105000 x 4/52 x 1/2 490000 x 3/52 700000 x 8/52 140000 x 4/52 FG Debtors Creditors 5385 10769 9423 4038 24230 28269 107692 (10769) 154507 (ii) Evaluating Option Proposed Debtors Current Debtors Increase in Debtors Financing Cost @ 12% 1725000 x 60/365 1500000 x 30/365 Increase in contribution 15% x 1500000 x 0.4 = Bad debts New Old 725000 x 0.04 1500000x 0.01 283562 123288 160274 x0.12 (19233) 90000 69000 15000 Admin Costs (iii) Changing the Credit Terms (1+2/98) 360/30 - 1 = 27.43% Supplies will change as 27.43% if we don't pay after 10 days (54000) (5000) 11767 16. Ballyvaden E(Rx) = 0.3(0.30) + 0.4(0.25) + 0.3(0.20) = 0.25 E(Rx) = 0.2(0.50) + 0.6(0.30) + 0.2(0.10) = 0.30 VARx = 0.3(0.30-0.25)2 + 0.4 (0.25-0.25)2 + 0.3(0.20-0.25)2 = 0.0015 VARy = 0.2(0.50-0.30)2 + 0.6 (0.30-0.30)2 + 0.2(0.10-0.30)2 = 0.0240 SDx = 0.0015 = 0.039 SDy = 0.0240 = 0.155 COV (Rx Ry) = 0.006 E(Rp) = 0.6(0.25) + 0.4(0.30) = 0.27 VAR(p) = 0.62 (0.0015) + 0.42 (0.024) + 2(0.6)(0.4)(0.006) = SDp 0.00726 0.00726 = = 0.0852 or 8.52% 17. Hilliard (i) E(IRRp) = WA E(IRRA) + WB E(IRRB) + WC E(IRRc) = 0.5 (0.1) + 0.3(0.2) + 0.2(0.4) = 0.19 or 19% = WA2VARA + WB2VARB + WC2VARC + + 2WA WB COVAB + 2 WAWCCOVAC + 2WBWCCOVBC VAR(IRRP) = (0.5)2(0.05)2+(0.3)2 (0.15)2 + (0.2)2(0.2)2 + 2(0.5)(0.3)(-0.0075) + 2(0.5)(0.2)(0.0100) + 2(0.3) (0.2)(0.0180) = 0.00616 0.00616 = 0.0785 or 7.85% SDIRR = (ii) It depends upon the risk- return trade off Return of portfolio is higher that A but lower than C and B Risk of portfolio is higher than A but lower than C and B (iii) Alternative strategy might just focus on A and B Since the correlation between these two is -1.0 Q 18 (i) (ii) After-tax cost of debt = PV(Leasing) = PV (Purchase) = Therefore Lease. (iii) NPV @15% = -£112915 Therefore reject the project 0.167 x (1-0.4) =0.10 -£221891 -£348665 19. Conroy fav Expand -200 1040+900 0.2 Unfav Favourable 800 320+900 0.2 0.5 Fav Not 800+800 0.8 Unfav -1500 200+800 0.2 1040+900 Fav Expand -200 Small Plant 0.4 320 + 900 unfav Unfavourable 200 0.6 0.5 fav Not 800 + 800 0.4 unfav 200+800 0.6 fav Contract 150 Large Plant 1040+900 0.8 unfav Favourable 1300 320 + 900 0.2 1300+1000 Fav 0.5 Not 0.8 unfav 100 + 1000 0.2 -2000 Fav Contract 150 0.4 Unfav Unfavourable 1040+900 320+900 0.6 100 0.5 Fav Not 1300+1000 0.4 Unfav 0.6 100+1000 7AU Fav +Expand 1940 1 1220 2 0.8 600 0.5 Unfav -1500 1600 Fav 0.4 Unfav + No Expand 200 Small Unfav 4 1000 Fav Large Fav+No.Contraction 3 2300 A 1100 B 0.8 1300 0.5 Unfav 0.2 -2000 Fav Unfav + Contraction C 1940 0.4 250 0.5 Unfav D 1220 0.6 SMALL PLANT NPV 1 648.76 0.4 NPVxProb 259.50 NPV2xProb 168356 Prob 2 53.75 0.1 5.37 289 3 4.13 0.2 0.83 3 4 -491.74 0.3 -147.52 72541 118.18 241189 E(NPV) = 118.18 Sdenpv = = 476.68 241189 − (118.18) 2 LARGE PLANT NPV Prob NPV2 x Prob NPVxProb A 1082.65 0.4 433.06 468848 B 90.91 0.1 9.09 826 C -169.42 0.2 -33.88 5741 D -764.46 0.3 -229.34 175321 178.93 650736 E(NPV) = 178.93 SDpv = 650736 − (178.93) 2 = 786.59 Other factors 1. high standard of deviation of outcomes for LARGE plant 2. high prob. Of obtaining negative NPV of LARGE plant. Q20 Glenroe (i) (ii) Draw the Decision tree Work out the ENPV NPV A -300 + B -300 + C -300 + D -300 + E -300 + F -300 + G -300 + H -300 + I -300 + i. E(NPV) = £44.524 ii. SDnpv = 100 1.1 100 1.1 100 1.1 200 1.1 200 1.1 200 1.1 300 1.1 300 1.1 300 1.1 + + + + + + + + + 0 (1.1)² 100 (1.1)² 100 (1.1)² 100 (1.1)² 200 (1.1)² 300 (1.1)² 200 (1.1)² 300 (1.1)² 350 (1.1)² 192.3E8 − (44.524) = £131347.7 2 Prob NPVxProb NPV²xProb = 209.090 0.0625 -13.068 2.7E = -126.446 0.1250 -15.806 2.0E = -43.802 0.0625 -2.738 1.2E8 = 35.537 0.0625 -4.442 1.6E8 = 47.107 0.1250 11.777 5.5E8 = 129.752 0.0625 16.219 2.1E9 = 138.017 0.0625 8.626 1.2E9 = 280.661 0.1250 27.583 6.1E9 261.938 0.0625 1.00 16.374 44.525 4.3E9 192.3E8 = iii. Prob NPV < 0 From tables p= 36.7% iv. Abandon project if PV1 of year 2 cash flows < 150,000 If cashflow in yr 1 = 100,000 PV2 = 1/4(o) + 1/2(100,000) + 1/4(200,000) = 90,909 1.1 1.1 If cashflow in yr 1 = 200,000 PV2 = 1/4(100,000) + 1/2(200,000) + 1/4(300,000) = 181818 1.1 1.1 1.1 If cashflow in yr 1 = 300,000 PV2 = 1/4(200,000) + 1/2(300,000) + 1/4(300,000) = 261363 1.1 1.1 1.1 Abandon the site if cashflow in yr1 = £100,000 21 E(Rx) = 0.25 E(Rx) = 0.32 VARx = 0.0015 VARy = 0.0246 SDx = 0.039 SDy = 0.157 COV (Rx Ry) = -0.006 E(Rp) = 0.278 VAR(p) = 0.0016 SDp 22. (b) (c) = 0.04 or 4% Lower limit Spread Upper limit Return Point = = = = EOQ Average Cash Balance Number of transactions Total Cost £40,000 £230,952 £270,952 £116,984 = = = = £35,000 £17,500 7 £175+£175 = £350 23 2FM/SGF/DMP/17 SCHOOL OF SOCIAL SCIENCES 2FM - INTERMEDIATE FINANCIAL MANAGEMENT Revision Questions 1. Taxco Ltd Taxco Ltd is deciding whether to proceed with a project that will attract capital allowances of 25% reducing balance. The project requires an initial investment of £1 million, will last for five years and have a resale value of £200,000 in five years time. The following profit estimates have been produced by the company: £000 Sales Cost of Sales Depreciation Consultant Fees (tax allowable) Year 1 Year 2 Year 3 Year 4 Year 5 100 25 160 150 400 100 160 700 150 160 750 150 160 800 200 160 (235) 140 390 440 440 The company pays tax at 50% with a one year lag. If the company's cost of capital is 10% advise the company on whether to accept the project. 2. Rubber Duck Ltd Rubber Duck Ltd produces novelties for the bathroom and is considering whether to produce a new product, the singing mermaid. For purposes of investment appraisal, the company use their equity and debt holders weighted average cost of capital. The company has in issue two million ordinary shares of 25p each with a current market price of 50p. The dividend declared is 5½p per share. Also in issue are 312,500 4.8% debentures with a current price of 80 pence. The singing mermaid project is estimated to have the following cash flows: Year 0 Year 1 Year 2 (500,000) 275,000 350,000 You are required to: a) b) c) d) Calculate the cost of capital to be used in investment appraisal. Calculate the payback period to the nearest day. Calculate the IRR of the project using similar triangles and quadratic equations. Advise the company whether to accept the project 2 3. Inflatable Tyres Inflatable Tyres Ltd is deciding on whether or not to go ahead with a new inflator system. The new system would require an investment of £250,000 now and £50,000 in one year's time. It will last for five years and be worth £10,000 in scrap at that time. 1. Sales Sales are forecast to be £200,000 in the first year and will rise in line with the retail price index which is expected to increase at a rate of 12% pa. 2. Labour Labour required will be 20,000 man hours per year. The current wage rate which has just been agreed for the current year is £3 per hour. It is anticipated that wage increases will be 10% pa for the foreseeable future. The men are currently on short time working, working only half time at the moment. This is expected to last for this year only. 3. Material A There is currently 20,000 kilos in stock and if the project is not undertaken it will cost £10,000 to dispose of it now. The new system will require 10,000 kilos per annum. The current price just introduced is £2 per kilo. 4. Material B Annual usage will be 15,000 kilos. The current price is £5 per kilo. In years 2 and 3 there will be a shortage of material B and if used elsewhere could earn a contribution of £2 per kilo. Material prices for both A and B will increase by 5% pa. 5. Depreciation Depreciation is charged at 20% reducing balance. 6. Overheads The overheads will be £50,000 pa which are the same as with the current system. The company uses a cost of capital of 10% for investment appraisal purposes. Cashflows occur at the end of the year unless otherwise stated. Ignore tax. You are required to advise the company whether to proceed with the project. 4. On 1 January 1996 Mr Smith sought your advice on determining the prices of the shares of the following companies in his portfolio: i) Company W is expected to pay a dividend in December 1996, of £10 per share, after which the share price is expected to be £210. ii) Company X is expected to pay an annual dividend each December of £4 per share indefinitely. iii) Company Y's dividend per share is expected to grow by 5% a year for the foreseeable future. The dividend is expected to be £8 per share in December 1996. iv) Company Z is expected to pay a dividend of £4 per share in December of this year. Short term prospects for the company are excellent and a 20% annual growth rate is expected for the next three years (1995-97). At the end of three years the growth rate is expected to decline to a more normal 6%. The current rate of return required, which is expected to remain unchanged, is 10% per annum. 3 5. Advise Mr Smith. Hyper Ltd Hyper Ltd has an authorised ordinary share capital of 2 million shares of £1 each and an issued ordinary share capital of 1 million shares of £1 each. It also has 800,000 £1 8% debentures. The market price of the shares is £1.60 per share and the debentures are valued at par. Dividends and interest are paid annually. An ordinary dividend has just been paid of £176,000 and the debenture interest has also just been paid. Hyper Ltd has been asked to consider a contract of £600,000 to manufacture six Itzabargain machines. Manufacturing would take place over three years commencing immediately on 1 June 1996. The contract price would be payable in two instalments, one-third on 1 June 1996 and the final two-thirds on 31 May 1999. Two machines would be manufactured each year. The following details are relevant: 1) Raw Materials There is one raw material, the Cheepie, which will be used on the contract. One year's supply of Cheepie currently costs £40,000. Materials are purchased and paid for annually in advance. Material values and prices are expected to increase at an annual compound rate of 20%. 2) Labour Labour in the first year will cost £65,000. Wage rates are expected to increase at a compound rate of 15%. 3) Equipment Equipment for the contract will be purchased and paid for now at a cost of £200,000 and will be sold at the end of the contract for £50,000. Assume that all payments arise on the last day of the year to which they relate unless otherwise stated. Input prices change annually at midnight on 31 May. Required i) Calculate the weighted average cost of capital. ii) Calculate the payback period to the nearest month. iii) Calculate the internal rate of return of the contract (in the range of 14% to 18%). iv) Using a cost of capital of 10%, advise Hyper Ltd whether to accept the contract. 6. Sleigh Manufacturing Ltd a) Sleigh Manufacturing has 100,000 50p ordinary shares in issue with a current value of £2.50 per share. They are also 200,000 7% £1 debentures in issue which have a current market value of 75p per debenture. The current dividend per share is 50p. You are required to show that Sleigh Manufacturing Ltd's weighted average cost of capital is 16%. b) You have been asked to advise on the current year's investment proposals for Sleigh Manufacturing Ltd. The proposed projects shown below are not mutually exclusive. They are: A) To replace the existing data processing equipment. Initial cost £250,000. Expected life of new equipment 6 years. Expected annual after tax cash inflow £72,500. B) To develop a new type of sleigh costing £70,000 where all the cost is to be incurred immediately. The expected life of the product is 5 years. Expected annual after tax cash inflow for each year £30,000. The inflows will commence in year 2. 4 C) To install safety equipment at an initial cost of £110,000. Expected life three years. Expected annual after tax cash inflow £45,000. D) To construct a new factory building. Initial cost of £210,000. Expected life 8 years. Expected annual after tax cash inflow £57,000. E) To extend the existing loading equipment. Initial cost of £170,000. Expected life 4 years. Expected annual after tax cash inflow £70,000. F) To purchase patent rights to a new process. Initial cost £135,000. Expected life 15 years. Expected annual after tax cash inflows £30,000 for the first five years and £20,000 for the next ten years. With the exception of project B, all cash inflows commence in the current year, and are always received on the last day of the year. Tax is paid when the inflow is received. The company's cost of capital is 16%. The company is, however, in a capital rationing situation and estimates it will only have £600,000 to invest in the current year. The company normally adopts a payback period of 3 years for its investment appraisal. Required a) Recommend to the company, using the NPV method of investment appraisal, which projects to undertake, bearing in mind its £600,000 spending limit. Give reasons for your choice. 7. b) Calculate to the nearest month which projects the company would accept using its payback period of within 3 years. c) Explain why your choice is different from the company's choice under its normal investment appraisal method. A firm is considering an investment that requires an initial outlay of £1m and will yield the resultant cashflows for the next two years. During the first year there are three possible outcomes. Cash Flows Possibility Outcome 1 Outcome 2 Outcome 3 £600,000 0.5 £700,000 0.3 £800,000 0.2 In year two the following possible cash inflows may arise: If Outcome 1 Cash flow = 600,000 If Outcome 2 Cash flow = 700,000 If Outcome 3 Cash flow = 800,000 Then Cash Flow £300,000 £600,000 Then Cash Flow £300,000 £500,000 £700,000 Then Cash Flow £400,000 £600,000 £800,000 Prob 0.2 0.8 Prob 0.2 0.3 0.5 Prob 0.2 0.7 0.1 Find the Expected NPV and Standard Deviation of NPV for the project if the cost of capital is 10%. 5 8. The following are the variances and the covariance for the returns of two different shares A and B. VAR A VAR B COV (A,B) = = = 0.08 0.02 0.001 If an investor holds 50% of his wealth in A and 50% of his wealth in B find the Expected Return and Risk of this portfolio if: E (RA) E (RB) = = 0.12 0.10 9. Ms M Audrey is considering investing in two shares. The first - WP - is expected to earn a return of 15% over the next year and the standard deviation of the expected returns is 20%. The second - LO -is expected to earn a return of 6% and the standard deviation of the expected returns is estimated at 10%. If the correlation between the expected returns is - 0.5 estimate the expected return and standard deviation of returns for a portfolio with 60% of wealth invested in WP and 40% of wealth invested in LO. 10. X Ltd has monthly sales of £90,000. About half of its customers pay their accounts within the month of invoicing, one third in the following month, and the remainder during the second month after invoicing. It has been decided to offer 1¼% discount for payment within the month of invoicing. During the first six months of the new policy, collections are improved so that on average three-quarters of the customers pay in the first month, this improvement coming entirely from those customers who had previously paid in the month after invoicing. The current cost of capital is 15% a year. Ignoring any additional clerical costs is the change in policy financially justified? 11. Frame plc is considering which of two mutually exclusive projects, A or B, to undertake. There is some uncertainty about the running costs with each project, and a probability distribution of the NPV for each has been estimated, as follows: NPV £000 -20 +10 +25 +40 Project A Probability NPV £000 +5 +15 +20 +25 0.15 0.20 0.35 0.30 Project B Probability 0.2 0.3 0.4 0.1 Which project should the company choose, if any? 12. Couttes Purse Ltd requires advice on its debt collection policy. Should the current policy be discarded in favour of Option 1 or Option 2? Current Policy Option 1 Option 2 £240,000 £300,000 £400,000 Bad debt losses (% of sales) 3% 2% 1% Average collection period 2 months 1½ months 1 month Expenditure on debt collection procedures, per annum Current sales are £4.8 million per annum, and the variable cost of sales is 90% of sales value. The company requires a 15% return on its investments. 6 13. Russian Beard Ltd is considering a change in its credit policy which will result in a slowing down in the average collection period from one to two months. The relaxation in credit standards is expected to produce an increase in sales in each year amounting to 25% of the current sales volume. Sales price per unit Variable cost per unit Current sales per annum £10 £8.50 £2.4 million The required rate of return on investment is 20%. Assume that the 25% increase in sales would result in additional stocks of £100,000 and additional creditors of £20,000. Advise the company on whether or not to extend the credit period offered to customers if existing customers do not change they payment habits, and only the new customers take a full 2 months' credit. 14. (a) Outline the main advantages and disadvantages of the decision tree approach to evaluating the riskiness of a capital investment proposal. (b) Shannon plc is considering a two-year investment with an initial outlay of £375,000. The estimated net cash flows and probabilities in year 1 are as follows: Economic Conditions Weak Moderate Good Net Cash Flows in Year 1 Probability 0.2 0.5 0.3 Cash Flow (£) 100,000 200,000 300,000 At the end of year 1, economic conditions in year 2 are forecast to be either moderate or good and the cash flows (and probabilities) associated with these conditions are predicted to be as follows: Economic Conditions Moderate Good Net Cash Flows in Year 2 Probability 0.7 0.3 Cash Flow (£) 250,000 350,000 Required (i) Represent the problem as a decision tree. (ii) Calculate the Expected Net Present Value and Standard Deviation of the Net Present Value of the investment. (iii) Estimate the probability of obtaining a negative Net Present Value. (iv) If the company has the option to abandon the project at the end of the first year and sell the plant and equipment for £262,000, calculate the increase in net present value associated with this option. 7 15. (a) Mrs B Suir, a recently appointed finance director of a large divisionalised water company, seeks your advice in dealing with capital issues raised by financial controllers at three of the company’s divisions: (i) The Corrib division which makes hose pipes has budgeted sales of £700,000 per annum. Its costs as a percentage of sales are as follows: Raw Materials 20%: Direct Labour 35%; Overheads 15%. The division carries raw materials in stock for two weeks, while finished goods are held in stock for three weeks before sale. Production takes four weeks. The division takes four weeks’ credit from suppliers and gives eight weeks’ credit to its customers. Both overheads and production costs are incurred evenly throughout the year and work in progress is normally 100% complete with respect to material costs but only 50% complete with regards to labour and overheads. Required Calculate the total working capital requirement for the Corrib division. (ii) The Erin division which makes sprinkler systems, has current sales of £1.5m per year. Cost of sales is 75% of sales and bad debts are 1% of sales. The manager of the division reports that 80% of these costs are variable while 20% are fixed. The division currently allows customers 30 days credit but is considering increasing this to 60days, in order to increase sales. It has been estimated that this change in policy will increase sales by 15% while bad debts will rise from 1% to 4%. It is expected that this change in policy will result in an increase of £5,000 in administration costs while creditors and stock will remain unchanged. Required If the division’s cost of capital is 12% should they proceed with the change in credit policy? (iii) The Derg division is considering taking a discount of 2% from their suppliers if they pay within 10 days. If the discount is not taken, payment will occur after 40 days. Required If the division’s cost of capital is 12% and assuming 360 days in the year, advise Mrs Suir on whether the discount should be taken. 16. (a) Ballyvaden plc is considering two different investment projects with the following return possibilities: Project X State 1 2 3 Return (%) 30 25 20 Project Y Probability 0.3 0.4 0.3 Return (%) 50 30 10 Probability 0.3 0.4 0.3 The financial director of the firm is unsure about which opportunity or which combination of opportunities, to choose and seeks your advice. Required (i) Calculate the expected return and standard deviation of return for each project. (ii) Calculate the covariance between the returns offered by this pair of projects. (iii) Consider whether a portfolio comprising 60% of project X and 40% of project Y might offer the firm a more attractive combination of risk and return if fractions of the projects can be undertaken. 8 17. (a) Comment on whether standard deviation is an appropriate measure of risk in investment appraisal in the light of the views expressed in March and Shapira (1986). (b) Hilliard plc is considering investing in three projects with the following characteristics: Project A B C E(IRR) 0.10 0.20 0.40 SD (IRR) 0.05 0.15 0.20 where E (IRR) is the expected IRR of the project and SD (IRR) is the standard deviation of the IRR. In addition, the financial director of the company has ascertained that the covariance between the IRRs of projects A and B is –0.0075 while the correlation between the IRRs of projects B and C is 1.0 and between the IRRs of projects A and C is 0.2. Required (i) Estimate the E (IRR) and SD (IRR) of a portfolio of these projects if the £1m available for investment is spent as follows: A = £500,000 B = £300,000 C = £200,000 (ii) Comment on whether Hilliard plc would wish to proceed with this portfolio of projects and identify what further information might help the directors in making their decision. (iii) Suggest an alternative investment strategy which would reduce the risk faced by the company when deciding to invest in some or all of these projects. 18. Leasco plc is deciding on how to finance the purchase of a new machine costing £500,000 which will have a useful life of 4 years. It can either be purchased with a loan where the pre-tax interest rate is 16.67% or it can be leased. If it is leased, four annual lease payments of £100,000 would have to be paid in advance to the leasing firm. The machine is needed to produce the following product which can be sold at the following costs over the next four years: Year 1 2 3 4 Quantity 50,000 60,000 40,000 30,000 Price £5 £6 £4 £4 Variable Cost £3 £4 £3 £3 In addition, fixed annual costs of £20,000 would be incurred in the production process. Required (i) (ii) (iii) If the tax rate is 40% and if a 25% writing down allowance is available on the purchase of the machine, advise the firm on whether the machine should be purchased or leased? Work out the after-tax cash flows associated with the production output from the machine. Calculate the NPV from the investment decision associated with the machine if the after-tax WACC is 15%. 9 19 (a) “Real Options commonly occurred and were generally significant in determining how decision makers regard an investment.” (Busby and Pitts, 1997) Outline the various real options which management believed to be useful when making investment decisions. (b) Conroy plc has to decide what size of new plant to build. A large plant will provide economies of scale but is also likely to lead to a reduced selling price. The capital costs and annual fixed and variable costs for two different size plants are as follows: Capacity (millions of units) 0.4 0.8 Investment (£000) 1500 2000 Annual Fixed Costs (£000) 200 300 Unit Cost (£) 2.00 1.80 Conroy plc believes that market conditions will either be favourable or unfavourable and that both of these conditions are equally likely to occur. Depending upon these conditions, the following unit prices are expected to be obtained for the product. Quality Sold (millions of units) Price Per Unit (£) Favourable £5.00 £3.80 0.4 0.8 Unfavourable £3.00 £2.30 After the first year Conroy plc can adjust to market conditions. If they build a 400,000 unit plant and conditions prove favourable they can expand by building an extra 200,000 unit plant at a cost of £300,000. This expansion would increase the sales price, variable costs and fixed costs. Alternatively, if the company builds the 800,000 unit plant, they can reduce the capacity of the larger plant by 200,000 units releasing £150,000 immediately and changing prices, variable costs and fixed costs. For an output of 600,000 units the follow data apply: Units Annual Fixed Cost (£) Variable Cost per Unit (£) 600,000 220,000 1.90 Price per unit Favourable Unfavourable £4.00 £2.80 If demand in year 1 is favourable there is an 80 per cent chance that it will remain favourable while if demand is unfavourable in year 1 there is a 60 per cent chance that it will remain unfavourable in year two. At the end of year two, the plant will be sold to another firm for the following amounts: Capacity 400,000 600,000 800,000 Sale Price in year two (£) 800,000 900,000 1,000,000 Required (i) Draw a decision tree for this problem. (ii) Calculate the Expected Present Value of the small plant and of the large plant if the company’s cost of capital is 10 per cent. (iii) Calculate the Standard Deviation of the Expected Net Present Value of both plants. (iv) Advise the management of Conroy plc which plant they should build based on your answers to (ii) and (iii) and highlight what other information might help management in 10 making their decision. 20. (a) Comment on the usefulness of standard deviation as a measure of risk. (b) Glenroe plc is considering a project involving the outlay of £300,000 which it estimates will generate cash flows over its two-year life at the probabilities shown in the following table: Cash flows for project Year 1 Cash flow £ 100,000 200,000 300,000 If cash flow in Year 1 is: £ 100,000 200,000 Probability 0.25 0.50 0.25 1.00 Year 2 There is a probability of: 0.25 0.50 0.25 1.00 0.25 0.50 0.25 1.00 That cash flow in Year 2 will be: £ NIL 100,000 200,000 100,000 200,000 300,000 300,000 0.25 200,000 0.50 300,000 0.25 350,000 1.00 Note: All cash flows should be treated as being received at the end of the year. Glenroe plc has a choice of undertaking this project at either of two sites (A or B) whose costs are identical and are included in the above outlay. In terms of the technology of the project itself, the location will have no effect on the outcome. If the company chooses Site B it has the facility to abandon the project at the end of the first year and to sell the site to an interested purchaser for £150,000. This facility is not available at Site A. The company’s cost of capital for this type of project is 10%. Its policy would be to abandon the project on Site B and to sell the site at the end of year 1 if its expected future cash flows for year 2 were less than the disposal value. Required (i) Construct a probability tree representing the possible outcomes for the project on Site A. (ii) Calculate the Expected Net Present Value and Standard Deviation of Expected Net Present Value for the project at Site A. (iii) Estimate the probability that the Expected Net Present Value of the project on Site A 11 (iv) (v) will be negative. Explain, based on the data given, the specific circumstances in which the company would abandon the project on Site B. Calculate the increase in Expected Net Present Value. 12 21 Ballykay plc is considering two different investment projects with the following return possibilities: Project X State 1 2 3 Return (%) 20 25 30 Project Y Probability 0.3 0.4 0.3 Return (%) 50 35 10 Probability 0.3 0.4 0.3 The financial director of the firm is unsure about which opportunity or which combination of opportunities, to choose and seeks your advice. Required (i) Calculate the expected return and standard deviation of return for each project. 22. (ii) Calculate the covariance between the returns offered by this pair of projects. (iii) Consider whether a portfolio comprising 60% of project X and 40% of project Y might offer the firm a more attractive combination of risk and return if fractions of the projects can be undertaken. Explain your answer. (a) Compare and contrast the Baumol and Miller-Orr models for cash management and discuss whether these models offer companies useful guides to managing their cash resources. (b) The treasurer of Callmack plc on reviewing past cash flow patterns has estimated the standard deviation of the company's cash flows to be £50000. The cost of converting marketable securities into cash is £20 and the average annual rate of return on marketable securities is currently 3% per annum. Management policy is to maintain a safety margin for cash of £40,000. Required Determine the target level cash balance, the upper cash limit and the average cash balance for Callmack plc according to the Miller-Orr model. Explain what the company should do to manage its cash balances. (c) The financial controller of Shangarry plc estimates that the average interest rate for the coming year will be 1%. In addition, when Shangarry plc sells securities it incurs a cost of £25, while funds are placed on deposit until they are needed. Required If the company is likely to demand £245,000 in cash over the coming year, estimate the optimal quantity of cash to withdraw from marketable securities each time the cash balance reduces to zero and calculate the number of transactions which will take place each year. What is the total cost (per annum) of this approach to managing cash outflows? 13 23. Alphabeta Company, an unlisted company based in Scotland, has been manufacturing electrical parts used in mobility vehicles for people with disabilities and the elderly, for many years. These parts are exported to various manufacturers worldwide but at present there are no local manufacturers of mobility vehicles in Scotland. Retailers in Scotland normally import mobility vehicles and sell them at an average price of £4,000 each. Alphabeta Company wants to manufacture mobility vehicles locally and believes that it can sell vehicles of equivalent quality locally at a discount of 37.5% to the current average retail price. Although this is a completely new venture for the company, it will be in addition to the company’s core business. Alphabeta Company’s directors expect to develop the project for a period of four years and then sell it for £16 million to a private equity firm. A feasibility study commissioned by the directors, at a cost of £250,000, has produced the following information: 1. The initial cost of acquiring suitable premises will be £11 million, and plant and machinery used in the manufacture will cost £3 million. Acquiring the premises and installing the machinery is a quick process and manufacturing can commence almost immediately. 2. It is expected that in the first year 1,300 units will be manufactured and sold. Unit sales will grow by 40% in each of the next two years before falling to an annual growth rate of 5% for the final year. After the first year the selling price per unit is expected to increase by 3% per year. 3. In the first year, it is estimated that the total direct material, labour and variable overheads costs will be £1,200 per unit produced. After the first year, the direct costs are expected to increase by an annual inflation rate of 8%. 4. Annual fixed overhead costs will be £2.5 million of which 60% are centrally allocated overheads. The fixed overhead costs will increase by 5% per year after the first year. 5. Alphabeta Company will need to make working capital available of 15% of the anticipated sales revenue for the year, at the beginning of each year. The working capital is expected to be released at the end of the fourth year when the project is sold. Alphabeta Company’s tax rate is 25% per year on taxable profits. Tax is payable in the same year as when the profits are earned. Capital allowances of 25% are available on the plant and machinery on a straight line basis. It is anticipated that the value attributable to the plant and machinery after four years is £400,000. This value is included in the price at which the directors expect to sell the project at the end of four years. Alphabeta Company uses 8% as its discount rate for new projects but feels that this rate may not be appropriate for this new type of investment. Although no other companies produce mobility vehicles in Scotland, Deltagamma Company, a listed company, produces electrical-powered vehicles using similar technology to that required for the mobility vehicles. DeltaGamma Company’s cost of capital is estimated to be 10%. Required: (a) Evaluate, on financial grounds, whether Alphabeta Company should proceed with the project. (b) Discuss the appropriateness of the evaluation method used and explain any assumptions made in part (a) above. School of Social Sciences University of Dundee School of Business INTERMEDIATE FINANCIAL MANAGEMENT MODULE 2FM – BU22003 APRIL/MAY 2019 TWO HOURS ANSWER THREE QUESTIONS – ONE FROM EACH OF SECTION A, SECTION B AND SECTION C PRESENT VALUE AND ANNUITY TABLES ARE SUPPLIED AT THE END OF THE QUESTION PAPER The use of approved calculators (CASIO FX83, FX85 or FX115) is permitted in this examination Dictionaries are not permitted in this examination BU22003 Page 1 of 10 SECTION A ANSWER ONE QUESTION FROM THIS SECTION 1. Greenfingers Ltd is a wholesaler of lawn mowers which is keen to explore the financial implications of making a significant investment in equipment and the development of a website. Due to the fast-changing nature of the equipment and the internet software, Greenfingers management has set a project lifetime of three years – that is, the equipment will be replaced at the end of 2022 and a new website designed. £60,000 would be paid for the new equipment on 31 December 2019. The supplier has agreed to pay £10,000 as a trade-in price in December 2022. The estimated final sales for the current accounting year (which ends on 31 December 2019) are £1,200,000. The company’s costs behave in such a way that its contribution to sales ratio for 2019 is expected to be 40% and its net margin 10%. A considerable proportion of Greenfingers total fixed costs are marketing expenses. The proposed project will lead to savings in this area. So, in 2020, fixed costs (at 31 December 2020 prices) will total £316,800. Sales estimates are shown below: Total sales if no investment (at 31 December 2019 prices) £ Year to 31 December 2020 1,240,000 Year to 31 December 2021 1,265,000 Year to 31 December 2022 1,290,000 Total sales with investment (at 31 December 2019 prices) £ 1,288,000 1,325,000 1,362,000 From 1 January 2020, inflation will have the following effects on Greenfingers operations: (i) (ii) Sales prices will increase by 5% per annum; and All costs (variable and fixed) will increase by 10% per annum. The increase in sales will mean that Greenfingers will carry an investment in working capital as follows (all at 31 December 2019 prices): 2019 2020 2021 2022 Initially Increase of Decrease of Decrease of £20,000 £10,000 £15,000 £15,000 This investment will also be affected by inflation from 1 January 2020, at the same annual rate as the variable and fixed costs. The website would be designed and installed during the first four months of 2020. It will cost £150,000 (at 2020 prices) payable at the end of 2020. The suppliers will be paid a retaining/advisory fee of £10,000 in both 2021 and 2022. These are 31 December 2020 prices and it is anticipated that, due to inflation, they will increase at the same rate as all other costs. Greenfingers has a nominal cost of capital of 10% and pays tax at an annual rate of 30% in the year profits are earned. It can claim capital allowances on a 25% reducing balance basis. Question continued on next page BU22003 Page 2 of 10 Required: (a) Advise the management of Greenfingers whether it should proceed with the proposed investment. Your recommendation should be supported by relevant workings and a calculation of Net Present Value (NPV). (28) (b) Explain the differences between real rates of return and nominal rates of return. (6) (c) Discuss the advantages and disadvantages of the payback method of investment appraisal. (6) (40) BU22003 Page 3 of 10 2. Bella Bunny has invested £220,000 over the past two years in the development of a fluffy toy bunny. The bunny is designed for busy individuals wishing to reduce their stress levels. Market research that was commissioned earlier in the year at a cost of £45,000 suggests that the price for the fluffy toy bunny should be £22 per unit and that the expected life of the product is four years. In order to produce the fluffy toy bunny, the business must purchase immediately specialist machinery and equipment at a cost of £300,000. This machinery and equipment has an expected life of four years and will have no residual value at the end of this period. The machinery and equipment can produce a maximum of 15,000 fluffy toy bunnies per year over four years. To ensure that the maximum output is achieved, the business will spend £50,000 a year in advertising the product over the next four years. Based on the maximum output of 15,000 units per year, the fluffy toy bunny has the following expected costs per unit: Notes £ Materials 1 6.50 Labour 2 5.50 Overheads 3 8.50 20.50 Notes: (1) The materials figure above includes a charge of £2 for fur that is currently in stock and can be used for this project. Each fluffy toy bunny requires 200 grammes of the fur and the charge is based on the original cost of £1 per 100 grammes for the fur. It is a material that is currently used in other areas of the business and the cost of replacing the fur is £1.50 per 100 grammes. The fur could easily be sold at a price of £1.25 per 100 grammes. (2) The labour costs relate to payments made to employees that will be directly involved in producing the fluffy toy bunnies. These employees have no work at present and, if the fluffy toy bunny is not produced, they will be made redundant immediately at a cost of £230,000. However, if the project goes ahead, the employees are likely to be found other work at the end of the four year period and so no redundancy costs will be incurred. (3) The figure includes a depreciation charge for the new machinery and equipment. The policy of the business is to depreciate non-current assets in equal instalments over their expected life. All other overheads included in the above figure are incurred in the production of the new product. Bella Bunny has an authorised share capital of 10,000,000 shares of £1 each and an issued share capital of 5,000,000 shares of £1 each. The company also has 3,000,000 10% preference shares of £1 each. There are also 2,000,000 £1 6% debentures in issue. The market price of the ordinary shares is 50p per share and the debentures are currently trading at a value of 120%. The preference shares are currently valued at par. An ordinary dividend has just been paid of 10p per share. Ignore taxation. Question continued on next page BU22003 Page 4 of 10 Required: (a) Advise Bella Bunny on the cost of capital that should be used for capital budgeting purposes. (6) (b) Calculate the Net Present Value (NPV) of the project. (15) (c) Calculate the Internal Rate of Return (IRR) of the project using the similar triangles method. Use your answer from (a) and a rate of 32%. (6) (d) Discuss your findings in (b) and (c) above. (2) (e) Discuss the advantages and disadvantages of the Accounting Rate or Return (ARR) and Internal Rate of Return methods of investment appraisal. (11) (40) BU22003 Page 5 of 10 SECTION B ANSWER ONE QUESTION FROM THIS SECTION 3. (a) Jet 3 Ltd is a new company formed to provide an executive flying service from Dundee to London. The founder thinks that there will be a demand for the service from business however she is unsure about what the actual cash flows will be. There is a 40% chance that demand in the first year will be low. If it is, there is a 60% chance that it will remain low in subsequent years. On the other hand if the initial demand is high, there is an 80% chance that it will remain high. The immediate problem is to decide what kind of plane to buy. A brand new Jet Engine plane costs £400m. A second hand Propeller plane costs £260m but has less capacity and customer appeal. The Year 1 cash flows associated with each option are as follows (all figures are in £m): Year 1 Demand Jet Engine Propeller High 150 100 Low 30 50 In addition the present value (at time 2) of future cash flows for the Jet Engine from Year 2 onwards are: Year 2 demand is high Year 2 demand is low if Year 1 demand is High Low 1,000 900 200 100 An analyst also provides you with estimates of the present value (at time 2) of future cash flows for the Propeller from Year 2 onwards: Year 2 demand is high Year 2 demand is low if Year 1 demand is High Low 400 200 200 100 Required: (i) Represent this problem as a decision tree. (4) (ii) If the cost of capital for the company is 10% advise the firm on whether they should proceed with the project and, if so, which plane they should purchase. (10) (iiii) Jet 3 has discovered that if they purchase the Propeller plane and demand is higher in Year 1, they can expand by purchasing another second-hand Propeller plane for £150m. If demand is low, the company can sit tight. If they do expand and demand turns out to be high, the present value in Year 2 of all future cash flows will be £800m, while if demand is low, the present value in Year 2 will only be £100m. Estimate the increase in expected net present value and reduction in risk from including this expansion option. (13) (b) Outline the different types of options which need to be considered in expected net present value calculations and comment on the difficulty of incorporating such options into the analysis. (13) (40) BU22003 Page 6 of 10 4. (a) Autoz Plc is planning to set up a business to sell model cars on credit to shops throughout Scotland. The product is budgeted to have the following price/cost structure per unit: Selling price £20.00 Manufacturing Costs Variable: Direct material Direct labour £7.00 £2.00 Fixed: Overhead £2.00 Profit per unit £11.00 £9.00 Sales of model cars are expected to be 20,000 units per annum and to be uniform throughout the year. It is expected that debtors will take four weeks to pay on average. The vetting of intended customers means that bad debts will not be expected. Required: (i) Show the expected level of debtors in the Statement of Financial Position of Autoz Plc assuming a 50-week year. (5) (ii) Assuming that the company’s cost of capital is 10% per annum, calculate the annual financing cost of increasing the credit period from four to six weeks if sales levels rise by 5% as a result. (8) (iii) Estimate the saving in financing costs that would result from reducing the credit period from four weeks to one week if sales levels decline by 20% as a result. (6) (iv) If Autoz Plc requires cash of £240,000 and can sell Gilts to raise cash at a fixed cost of £30, estimate the optimum level of cash that the firm should hold, and the total cost of this cash management policy, when sales are 20,000 units per annum. (9) (b) Outline the benefits and costs of having a trade credit policy. (12) (40) BU22003 Page 7 of 10 SECTION C ANSWER ONE QUESTION FROM THIS SECTION 5. “Economists are frequently asked to measure the effects of an economic event on the value of firms. On the surface, this seems like a difficult task, but a measure can be constructed easily using an event study. Using financial market data, an event study measures the impact of a specific event on the value of a firm. The usefulness of such a study comes from the fact that, given rationality in the marketplace, the effects of an event will be reflected immediately in security prices.” (MacKinlay, 1997) Explain the event study method and critically evaluate its usefulness for determining the economic effects of an event on a firm. (20) 6. “Principal-agent conflicts can affect any of a firm’s core functions – its investment, operating or financial policies …. Therefore, it is important that investors understand the types of agency problems that may exist in a corporate setting.” (Byrd et al., 1998) Describe the principal-agent problems which Byrd et al. (1998) highlight and illustrate how these problems may be overcome by various corporate mechanisms. (20) END OF QUESTIONS BU22003 Page 8 of 10 Table 1 Present value of 1 at compound interest : (1 + r)-n Periods Interest rates (%) (n) 1 2 1 0.9901 0.9804 2 0.9803 0.9612 3 0.9706 0.9423 4 0.9610 0.9238 5 0.9515 0.9057 6 0.9420 0.8880 7 0.9327 0.8706 8 0.9235 0.8535 9 0.9143 0.8368 10 0.9053 0.8203 11 0.8963 0.8043 12 0.8874 0.7885 13 0.8787 0.7730 15 0.8613 0.7430 16 0.8528 0.7284 17 0.8444 0.7142 18 0.8360 0.7002 19 0.8277 0.6864 20 0.8195 0.6730 25 0.7795 0.6095 30 0.7419 0.5521 35 0.7059 0.5000 40 0.6717 0.4529 45 0.6391 0.4102 50 0.6080 0.3715 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 16 0.8621 0.7432 0.6407 0.5523 0.4761 0.4104 0.3538 0.3050 0.2630 0.2267 0.1954 0.1685 0.1452 0.1252 0.1079 0.0930 0.0802 0.0691 0.0596 0.0514 0.0245 0.0116 0.0055 0.0026 0.0013 0.0006 BU22003 17 0.8547 0.7305 0.6244 0.5337 0.4561 0.3898 0.3332 0.2848 0.2434 0.2080 0.1778 0.1520 0.1299 0.1110 0.0949 0.0811 0.0693 0.0592 0.0506 0.0433 0.0197 0.0090 0.0041 0.0019 0.0009 0.0004 3 0.9709 0.9426 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 0.7224 0.7014 0.6611 0.6419 0.6232 0.6050 0.5874 0.5703 0.5537 0.4776 0.4120 0.3554 0.3066 0.2644 0.2281 4 0.9615 0.9246 0.8990 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.5775 0.5553 0.5339 0.5134 0.4936 0.4746 0.4564 0.3751 0.3083 0.2534 0.2083 0.1712 0.1407 5 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5051 0.4810 0.4581 0.4363 0.4155 0.3957 0.3769 0.2953 0.2314 0.1813 0.1420 0.1113 0.0872 6 0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4423 0.4173 0.3936 0.3714 0.3503 0.3305 0.3118 0.2330 0.1741 0.1301 0.0972 0.0727 0.0543 7 0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 0.4751 0.4440 0.3878 0.3624 0.3387 0.3166 0.2959 0.2765 0.2584 0.1842 0.1314 0.0937 0.0668 0.0476 0.0339 8 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3405 0.3152 0.2919 0.2703 0.2502 0.2317 0.2145 0.1460 0.0994 0.0676 0.0460 0.0313 0.0213 9 0.9174 0.8417 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 0.3875 0.3555 0.2992 0.2745 0.2519 0.2311 0.2120 0.1945 0.1784 0.1160 0.0754 0.0490 0.0318 0.0207 0.0134 10 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2633 0.2394 0.2176 0.1978 0.1799 0.1635 0.1486 0.0923 0.0573 0.0356 0.0221 0.0137 0.0085 11 0.9009 0.8116 0.7312 0.6587 0.6935 0.5346 0.4817 0.4339 0.3909 0.3522 0.3173 0.2858 0.2320 0.2090 0.1883 0.1696 0.1528 0.1377 0.1240 0.0736 0.0437 0.0259 0.0154 0.0091 0.0054 12 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 0.2875 0.2567 0.2046 0.1827 0.1631 0.1456 0.1300 0.1161 0.1037 0.0588 0.0334 0.0189 0.0107 0.0061 0.0035 13 0.8850 0.7831 0.6931 0.6133 0.5428 0.4803 0.4251 0.3762 0.3329 0.2946 0.2607 0.2307 0.1807 0.1599 0.1415 0.1252 0.1108 0.0981 0.0868 0.0471 0.0256 0.0139 0.0075 0.0041 0.0022 14 0.8772 0.7695 0.6750 0.5921 0.5194 0.4556 0.3996 0.3506 0.3075 0.2697 0.2366 0.2076 0.1597 0.1401 0.1229 0.1078 0.0946 0.0829 0.0728 0.0378 0.0196 0.0102 0.0053 0.0027 0.0014 15 0.8696 0.7561 0.6575 0.5718 0.4972 0.4323 0.3759 0.3269 0.2843 0.2472 0.2149 0.1869 0.1413 0.1229 0.1069 0.0929 0.0808 0.0703 0.0611 0.0304 0.0151 0.0075 0.0037 0.0019 0.0009 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 25 30 35 40 45 50 18 0.8475 0.7182 0.6086 0.5158 0.4371 0.3704 0.3139 0.2660 0.2255 0.1911 0.1619 0.1372 0.1163 0.0985 0.0835 0.0708 0.0600 0.0508 0.0431 0.0365 0.0160 0.0070 0.0030 0.0013 0.0006 0.0003 19 0.8403 0.7062 0.5934 0.4987 0.4190 0.3521 0.2959 0.2487 0.2090 0.1756 0.1476 0.1240 0.1042 0.0876 0.0736 0.0618 0.0520 0.0437 0.0367 0.0308 0.0129 0.0054 0.0023 0.0010 0.0004 0.0002 20 0.8333 0.6944 0.5787 0.4823 0.4019 0.3349 0.2791 0.2326 0.1938 0.1615 0.1346 0.1122 0.0935 0.0779 0.0649 0.0541 0.0451 0.0376 0.0313 0.0261 0.0105 0.0042 0.0017 0.0007 0.0003 0.0001 21 0.8264 0.6830 0.5645 0.4665 0.3855 0.3186 0.2633 0.2176 0.1799 0.1486 0.1228 0.1015 0.0839 0.0693 0.0573 0.0474 0.0391 0.0323 0.0267 0.0221 0.0085 0.0033 0.0013 0.0005 0.0002 0.0001 22 0.8197 0.6719 0.5507 0.4514 0.3700 0.3033 0.2486 0.2038 0.1670 0.1369 0.1122 0.0920 0.0754 0.0618 0.0507 0.0415 0.0340 0.0279 0.0229 0.0187 0.0069 0.0026 0.0009 0.0004 0.0001 0.0000 23 0.8130 0.6610 0.5374 0.4369 0.3552 0.2888 0.2348 0.1909 0.1552 0.1262 0.1026 0.0834 0.0678 0.0551 0.0448 0.0364 0.0296 0.0241 0.0196 0.0159 0.0057 0.0020 0.0007 0.0003 0.0001 0.0000 24 0.8065 0.6504 0.5245 0.4230 0.3411 0.2751 0.2218 0.1789 0.1443 0.1164 0.0938 0.0757 0.0610 0.0492 0.0397 0.0320 0.0258 0.0208 0.0168 0.0135 0.0046 0.0016 0.0005 0.0002 0.0001 0.0000 25 0.8000 0.6400 0.5120 0.4096 0.3277 0.2621 0.2097 0.1678 0.1342 0.1074 0.0859 0.0687 0.0550 0.0440 0.0352 0.0281 0.0225 0.0180 0.0144 0.0115 0.0038 0.0012 0.0004 0.0001 0.0000 0.0000 26 0.7937 0.6299 0.4999 0.3968 0.3149 0.2499 0.1983 0.1574 0.1249 0.0992 0.0787 0.0625 0.0496 0.0393 0.0312 0.0248 0.0197 0.0156 0.0124 0.0098 0.0031 0.0010 0.0003 0.0001 0.0000 0.0000 27 0.7874 0.6200 0.4882 0.3844 0.3027 0.2383 0.1877 0.1478 0.1164 0.0916 0.0721 0.0568 0.0447 0.0352 0.0277 0.0218 0.0172 0.0135 0.0107 0.0084 0.0025 0.0008 0.0002 0.0001 0.0000 0.0000 28 0.7812 0.6104 0.4768 0.3725 0.2910 0.2274 0.1776 0.1388 0.1084 0.0847 0.0662 0.0517 0.0404 0.0316 0.0247 0.0193 0.0150 0.0118 0.0092 0.0072 0.0021 0.0006 0.0002 0.0001 0.0000 0.0000 29 0.7752 0.6009 0.4658 0.3611 0.2799 0.2170 0.1682 0.1304 0.1011 0.0784 0.0607 0.0471 0.0365 0.0283 0.0219 0.0170 0.0132 0.0102 0.0079 0.0061 0.0017 0.0005 0.0001 0.0000 0.0000 0.0000 30 0.7692 0.5917 0.4552 0.3501 0.2693 0.2072 0.1594 0.1226 0.0943 0.0725 0.0558 0.0429 0.0330 0.0254 0.0195 0.0150 0.0116 0.0089 0.0068 0.0053 0.0014 0.0004 0.0001 0.0000 0.0000 0.0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 Page 9 of 10 Table 2 Present value of an annuity of 1: 1 − (1 + r ) − n r Periods Interest rates (%) (n) 1 2 1 0.9901 0.9804 2 1.9704 1.9416 3 2.9410 2.8839 4 3.9020 3.8077 5 4.8534 4.7135 6 5.7955 5.6014 7 6.7282 6.4720 8 7.6517 7.3255 9 8.5660 8.1622 10 9.4713 8.9826 11 10.3676 9.7868 12 11.2551 10.5753 13 12.1337 11.3484 14 13.0037 12.1062 15 13.8651 12.8493 16 14.7179 13.5777 17 15.5623 14.2919 18 16.3983 14.9920 19 17.2260 15.6785 20 18.0456 16.3514 25 22.0232 19.5235 30 25.8077 22.3965 35 29.4086 24.9986 40 32.8347 27.3555 45 36.0945 29.4902 50 39.1961 31.4236 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 16 0.8621 1.6052 2.2459 2.7982 3.2743 3.6847 4.0386 4.3436 4.6065 4.8332 5.0286 5.1971 5.3423 5.4675 5.5755 5.6685 5.7487 5.8178 5.8775 5.9288 6.0971 6.1772 6.2153 6.2335 6.2421 6.2463 BU22003 17 0.8547 1.5852 2.2096 2.7432 3.1993 3.5892 3.9224 4.2072 4.4506 4.6586 4.8364 4.9884 5.1183 5.2293 5.3242 5.4053 5.4746 5.5339 5.5845 5.6278 5.7662 5.8294 5.8582 5.8713 5.8773 5.8801 3 0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775 17.4131 19.6004 21.4872 23.1148 24.5187 25.7298 4 0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 15.6221 17.2920 18.6646 19.7928 20.7200 21.4822 5 0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 14.0939 15.3725 16.3742 17.1591 17.7741 18.2559 6 0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 10.1059 10.4773 10.8276 11.1581 11.4699 12.7834 13.7648 14.4982 15.0463 15.4558 15.7619 7 0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 7.4987 7.9427 8.3577 8.7455 9.1079 9.4466 9.7632 10.0591 10.3356 10.5940 11.6536 12.4090 12.9477 13.3317 13.6055 13.8007 8 0.9259 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 7.1390 7.5361 7.9038 8.2442 8.5595 8.8514 9.1216 9.3719 9.6036 9.8181 10.6748 11.2578 11.6546 11.9246 12.1084 12.2335 9 0.9174 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 6.8052 7.1607 7.4869 7.7862 8.0607 8.3126 8.5436 8.7556 8.9501 9.1285 9.8226 10.2737 10.5668 10.7574 10.8812 10.9617 10 0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 9.0770 9.4269 9.6442 9.7791 9.8628 9.9148 11 0.9009 1.7125 2.4437 3.1024 3.6959 4.2305 4.7122 5.1461 5.5370 5.8892 6.2065 6.4924 6.7499 6.9819 7.1909 7.3792 7.5488 7.7016 7.8393 7.9633 8.4217 8.6938 8.8552 8.9511 9.0079 9.0417 12 0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.8431 8.0552 8.1755 8.2438 8.2825 8.3045 13 0.8850 1.6681 2.3612 2.9745 3.5172 3.9975 4.4226 4.7988 5.1317 5.4262 5.6869 5.9176 6.1218 6.3025 6.4624 6.6039 6.7291 6.8399 6.9380 7.0248 7.3300 7.4957 7.5856 7.6344 7.6609 7.6752 14 0.8772 1.6467 2.3216 2.9137 3.4331 3.8887 4.2883 4.6389 4.9464 5.2161 5.4527 5.6603 5.8424 6.0021 6.1422 6.2651 6.3729 6.4674 6.5504 6.6231 6.8729 7.0027 7.0700 7.1050 7.1232 7.1327 15 0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.4641 6.5660 6.6166 6.6418 6.6543 6.6605 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 18 0.8475 1.5656 2.1743 2.6901 3.1272 3.4976 3.8115 4.0776 4.3030 4.4941 4.6560 4.7932 4.9095 5.0081 5.0916 5.1624 5.2223 5.2732 5.3162 5.3527 5.4669 5.5168 5.5386 5.5482 5.5523 5.5541 19 0.8403 1.5465 2.1399 2.6386 3.0576 3.4098 3.7057 3.9544 4.1633 4.3389 4.4865 4.6105 4.7147 4.8023 4.8759 4.9377 4.9897 5.0333 5.0700 5.1009 5.1951 5.2347 5.2512 5.2582 5.2611 5.2623 20 0.8333 1.5278 2.1065 2.5887 2.9906 3.3255 3.6046 3.8372 4.0310 4.1925 4.3271 4.4392 4.5327 4.6106 4.6755 4.7296 4.7746 4.8122 4.8435 4.8696 4.9476 4.9789 4.9915 4.9966 4.9986 4.9995 21 0.8264 1.5095 2.0739 2.5404 2.9260 3.2446 3.5079 3.7256 3.9054 4.0541 4.1769 4.2784 4.3624 4.4317 4.4890 4.5364 4.5755 4.6079 4.6346 4.6567 4.7213 4.7463 4.7559 4.7596 4.7610 4.7616 22 0.8197 1.4915 2.0422 2.4936 2.8636 3.1669 3.4155 3.6193 3.7863 3.9232 4.0354 4.1274 4.2028 4.2646 4.3152 4.3567 4.3908 4.4187 4.4415 4.4603 4.5139 4.5338 4.5411 4.5439 4.5449 4.5452 23 0.8130 1.4740 2.0114 2.4483 2.8035 3.0923 3.3270 3.5179 3.6731 3.7993 3.9018 3.9852 4.0530 4.1082 4.1530 4.1894 4.2190 4.2431 4.2627 4.2786 4.3232 4.3391 4.3447 4.3467 4.3474 4.3477 24 0.8065 1.4568 1.9813 2.4043 2.7454 3.0205 3.2423 3.4212 3.5655 3.6819 3.7757 3.8514 3.9124 3.9616 4.0013 4.0333 4.0591 4.0799 4.0967 4.1103 4.1474 4.1601 4.1644 4.1659 4.1664 4.1666 25 0.8000 1.4400 1.9520 2.3616 2.6893 2.9514 3.1611 3.3289 3.4631 3.5705 3.6564 3.7251 3.7801 3.8241 3.8593 3.8874 3.9099 3.9279 3.9424 3.9539 3.9849 3.9950 3.9984 3.9995 3.9998 3.9999 26 0.7937 1.4235 1.9234 2.3202 2.6351 2.8850 3.0833 3.2407 3.3657 3.4648 3.5435 3.6059 3.6555 3.6949 3.7261 3.7509 3.7705 3.7861 3.7985 3.8083 3.8342 3.8424 3.8450 3.8458 3.8460 3.8461 27 0.7874 1.4074 1.8956 2.2800 2.5827 2.8210 3.0087 3.1564 3.2728 3.3644 3.4365 3.4933 3.5381 3.5733 3.6010 3.6228 3.6400 3.6536 3.6642 3.6726 3.6943 3.7009 3.7028 3.7034 3.7036 3.7037 28 0.7812 1.3916 1.8684 2.2410 2.5320 2.7594 2.9370 3.0758 3.1842 3.2689 3.3351 3.3868 3.4272 3.4587 3.4834 3.5026 3.5177 3.5294 3.5486 3.5458 3.5640 3.5693 3.5708 3.5712 3.5714 3.5714 29 0.7752 1.3761 1.8420 2.2031 2.4830 2.7000 2.8682 2.9986 3.0997 3.1781 3.2388 3.2859 3.3224 3.3507 3.3726 3.3896 3.4028 3.4130 3.4210 3.4271 3.4423 3.4466 3.4478 3.4481 3.4482 3.4483 30 0.7692 1.3609 1.8161 2.1662 2.4356 2.6427 2.8021 2.9247 3.0190 3.0915 3.1473 3.1903 3.2233 3.2487 3.2682 3.2832 3.2948 3.3037 3.3105 3.3158 3.3286 3.3321 3.3330 3.3332 3.3333 3.3333 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 Page 10 of 10 2FM/SGF/DMP/17 SCHOOL OF BUSINESS 2FM - Intermediate Financial Management Solutions to Revision Questions 1. Taxco Ltd Capital Allowance Computation £ Cost Yr 1 WDA @ 25% £ allowance 1,000,000 (250,000) 750,000 (187,500) 562,500 (140,625) 421,875 (105,468) 316,407 (200,000) 116,407 Yr 2 WDA @ 25% Yr 3 WDA @ 25% Yr 4 WDA @ 25% Yr 5 proceeds Yr 5 balancing allowance 250,000 187,500 140,625 105,468 116,407 800,000 Tax Computations Taxable cashflow Sales - cost of sales Consultant fees Capital allowances Taxable profit/(loss) Tax @ 50% Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 75 (150) (75) (250) (325) (162.5) 300 300 (187.5) (112.5) 56.250 550 550 (140.625) 409.375 204.687 600 600 (105.648) 494.352 247.176 600 600 (116.407) 483.593 241.796 Project Evaluation Year Equipment 0 1 2 3 4 5 6 (1,000,000) 200,000 Operations (75,000) 300,000 550,000 600,000 600,000 Therefore go ahead with the project. Tax Net PV Factor at 10% PV 162,500 (56,250) (204,687) (247,176) (241,796) (1,000,000) (75,000) 462,500 493,750 395,313 552,734 (241,796) 1.0 0.909 0.826 0.751 0.683 0.621 0.564 (1,000,000) (68,175) 382,025 370,806 269,999 343,248 (136,373) 161,530 2. (a) (b) (c) WACC = 0.1 1 Year 235 days IRR by quadratic equation: Let (1+r) = X (500,000) + 275,000 + 350,000 X X2 =0 (500,000)X² + 275,000X + 350,000 = 0 X= -275   (275)² - 4(-500) (350) 2 x (–-500) X= –275   75625 + 700,000 –1000 X= 275  880.7 = 1.1557 or –0.6057 1000 1 + r = 1.1557 (d) r = 0.1557 or 15.57% NPV = (500,000) + 275,000 + 350,000 1.1 (1.1)² NPV = (500,000) + 250,000 + 289,256 = 39,256 Therefore accept the project. 3. Inflatable Tyres Year Investment Sales Labour Material A Material B Total 0 (250,000) - - 10,000 - (240,000) 1 (50,000) 200,000 (30,000) - (75,000) 45,000 2 - 224,000 (66,000) (21,000) 28,250 3 - 250,880 (72,600) (22,050) 4 - 280,985 (79,860) (23,152) (78,750) (30,000) (82,687) (30,000) (86,822) 5 10,000 314,704 (87,846) (224,310) (91,163) 121,385 NB Depreciation and overheads are irrelevant costs. (140,000) + 45,000 + 28,250 + 43,543 + (91,151) + 121,385 1.1 (1.1)² (1.1)³ (1.1)4 (1.1)5 = (240,000) + 40,909 + 23,347 + 32,715 + 62,257 + 75,370 = (5402) Therefore reject. 43,543 91,151 4. (i) Po (ii) Po (iii) (iv) Po D1994 D1995 D1996 D1997 D1998 = D1 + P1 1+r = 10 + 210 1.1 = £200 = D r = 4 0.1 = £40 = D0 (1 + g) (r-g) = D1 r-g = 8 0.1-0.05 = £160 = £4 = 4 (1.2) = £4.80 = 4 (1.2)² = £5.76 = 1 (1.2)³ = £6.91 - growing at 6% Price i. Present value of the first four years. = 4.00 + 4.80 + 5.76 + 6.91 1.1 1.21 1.331 1.4641 = £16.65 ii. Present value of dividend from year five onwards. P4 = 6.91 (1.06) 0.1 - 0.06 = 183.12 Price = 5. (ii) 16.65 + 183.12 = £141.71 (1.1)4 Hyper Ltd 0 1 2 3 Price 200,000 400,000 Materials (40,000) (40,000 x 1.2) (40,000 x (1.2)2) Labour (6,500) (65,000 x 1.15) (65,000 x (1.15)2) Equipment (200,000) 50,000 Annual Cashflow (40,000) (113,000) (132,350) 364,037 0 1 2 3 Cumulative Cashflow (40,000) (153,000) (285,350) + 78,687 1023 (iii) NPV @ 15% = +1023 @ 16% = -2548 x 15% 16% X – 15/1023 = 16%-15%/1023-254 X – 15 = 1023/3571 X = 15.286% (iv) Payback:- 2 years and ( 285350/(285350 + 78687) )x 12 = 2 years and 9.4 months (v) NPV of project @ 10% = + 21399 Thus, Hyper Ltd should accept the contract. 6.(a) WACC Ordinary shares 50p /£2.50 = 0.07 Debentures /0.75 = 20.00% 9.33% (250,000/400,000 )x 20% + (150,000/400,000 )x 9.33% = 16% (b) Project Year 0 A B C D E F (250,000) (70,000) (110,000) (210,000) (170,000) (135,000) (a) Life Years 6 5 3 8 4 5 10 Annuity Amount £72,500 £30,000 £45,000 £57,000 £70,000 £30,000 £20,000 Annuity Factor 3.685 3.685-0.862 2.246 4.344 2.798 3.274 5.575-3.274 Accept D, E, B and F. Total NPV £87,398. Outlay £585,000 NPV 17162 14690 (8930) 37608 25860 9240 Ranking 3 4 1 2 5 (b) Payback A B C D E F 3 years 3 years 2 years 3 years 2 years 4 years 5 months 4 months 5 months 8 months 5 months 6 months Therefore accept C and E. 7. NPV Probabilities -206611.00 41322.31 0.10 0.40 -20661.10 16528.93 4.3E+09 6.8E+08 -115702.00 49586.77 214876.00 0.06 0.09 0.15 -6942.15 4462.81 32231.40 8.0+E+08 2.2E+08 6.9E.09 57851.23 223140.40 388428.70 0.04 0.14 0.02 1 2314.05 31239.67 7768.60 66942.15 1.3E+08 7.0E+09 3.0E+09 2.0E+09 E(NPV) = 66942.15 SD(NPV) = 136173.10 8. Expected Return on Portfolio = W1 IRR1+ W2 IR R2 = = 0.5 (0.12) + 0.5 (0.10) 0.11 or 11% Risk of Portfolio = VARIANCE VAR(p) = (0.5)(0.08) + (0.5)(0.02) + 2 (.5) (.5)(6.00) = STANDARD DEVIATION = 9. 0.0255 WP 0.15 0.20 ER SDR Cov = = -0.5 x 0.2 x 0.1 -0.01 E(Rp) = = 0.6 (0.15) + 0.4 (0.06) 0.114 or 11.4% = 0.0255 0.1597 or 15.97% LO 0.06 0.10 VAR(p) = = (0.6)2(0.2)2 + (0.4)2(0.1)2 + 2 (0.6)(0.4)(-0.01) 0.0112 SD(p) 0.10 58 = 10.58% = 10. Month 2 £ 1 £ Collections Old system New system Discount 1.25% x £675,000 Interest saved: 15/12% x £(67,00045,000 = 22,500) 45,000 67,500 843.75 281.25 3 £ 30,000 7,500 15,000 15,000 The proposal therefore is not justified. 11. E NPV for each project Project A NPV Project B Prob EV £000 NPV Prob £000 £000 EV £000 -20 0.15 (3.00) 5 0.2 1.0 10 0.20 2.00 15 0.3 4.5 25 0.35 8.75 20. 0.4 8.0 40 0.30 12.00 25 0.1 2.5 ENPV = 19.75 ENPV = 16.0 Project A has a higher ENPV, but what about the "risks". The standard deviation, SD, can be calculated as Project A X = 19.75 X P £000 x-X Project B X = 16.0 P(x-X) 2 £000 X P P(x-X)2 x-X £000 £000 -20 0.15 -39.75 237.01 5 0.2 -11 24.2 10 0.20 -9.75 19.01 15 0.3 -1 -.3 20 0.35 5.25 9.65 20. 0.4 +4 6.4 40 0.30 20.25 123.02 25 +9 8.1 0.1 388.69 SD = 388.69 = 19.72 i.e.£19,720 approx 39.0 SD = 39.0 = 6.24 i.e. £6,240 approx Although Project A has a higher ENPV, it also has a bigger deviation of NPV, and so has greater business risk associated with it. Project selection clearly depends on the attitude of the company's management to business risk: (a) If management is prepared to take the risk of a lower NPV and go for the possibility of a higher NPV, they will opt for Project A; (b) If the management is "risk-averse" and prefer to play it safe, they will opt for the much less risky Project B. 12. Average debtors Reduction in Working Capital (a) Interest Savings (15%) Current Policy 800,000 - Option 1 600,000 200,000 30,000 Option 2 400,000 400,000 60,000 144,000 - 96,000 48,000 48,000 96,000 - 78,000 156,000 (6,000) 72,000 (160,000) (£4,000) Bad Debt Losses (b) Reduction in losses Benefits of each Option (a) and (b) Extra Costs of Debt Collection Net Benefit/(loss) from option Conclusion: Option 1 is preferable to the current policy, but Option 2 is more costly. Note: When reducing working capital average debtors should always be based on sales and not the variable cost on sales as the former is the opportunity cost of the reduction. When increasing working capital however it is always the cost of sales that should be used. 13. The change in credit policy would be justifiable, in the context of this question, if the rate of return on the additional investment in working capital exceeds 20%. Extra profit: Contribution/sales ratio Increase in sales revenue Increase in contribution and profit (a) 15% £600,000 £90,000 Extra investment, if only the new debtors take 2 months credit: Increase in debtors (2/12 of £600,000 x 0.85) Increase in stocks Increase in creditors Net increase in working capital investment Return on extra investment £90,000/£165,000 = 54.5% £ 85,000 100,000 185,000 (20,000) 165,000 14. Shannon 250,000 Moderate Weak 100,000 0.7 0.2 Strong 550,000 0.3 Moderate 35,000 Moderate C 0.7 Strong 350,00 0 0.3 250,000 Moderate Good B 250,00 200,000 0.5 Invest A D E 0.7 300,000 0.3 Strong 350,000 F 0.3 Don't A B C D E F E(NPV)=£35.680 PROB NPVxPROB NPV2xPROB -86.4 -6.7 2.8 82.6 92.1 171.9 0.14 0.06 0.35 0.15 0.21 0.09 -12.100 -0.402 0.980 12.390 19.341 15.471 35.680 1047.515 2.693 2.744 1023.414 1781.306 2659.465 6517.137 SDNPV = P(NPV) < 0 P(z) 0 − 35.68 = 72.401 < NPV 6517.137 − (35.68) 2 = £72.401 -0.4928 From tables = 31.21% If "Weak" in YR1 PV1 = 250 Abandon If "Moderate" in YR1 PV1 = 250 Abandon If "Strong" in YR1 PV1 = 250 Abandon Increase in E(NPV) 262,000-250,000 = £10,000 Q15 SUIR Additional Costs Raw Materials Direct Labour Overheads 700000 x 0.20 = 700,000 x 0.35 = 700,000 x 0.15 = 140,000 245,000 105,000 W/C Requirement Stock of RM: WIP Mat Lab O/H 140000 x 2/52 140000 x 4/52 245000 x 4/52 x 1/2 105000 x 4/52 x 1/2 490000 x 3/52 700000 x 8/52 140000 x 4/52 FG Debtors Creditors 5385 10769 9423 4038 24230 28269 107692 (10769) 154507 (ii) Evaluating Option Proposed Debtors Current Debtors Increase in Debtors Financing Cost @ 12% 1725000 x 60/365 1500000 x 30/365 Increase in contribution 15% x 1500000 x 0.4 = Bad debts New Old 725000 x 0.04 1500000x 0.01 283562 123288 160274 x0.12 (19233) 90000 69000 15000 Admin Costs (iii) Changing the Credit Terms (1+2/98) 360/30 - 1 = 27.43% Supplies will change as 27.43% if we don't pay after 10 days (54000) (5000) 11767 16. Ballyvaden E(Rx) = 0.3(0.30) + 0.4(0.25) + 0.3(0.20) = 0.25 E(Rx) = 0.2(0.50) + 0.6(0.30) + 0.2(0.10) = 0.30 VARx = 0.3(0.30-0.25)2 + 0.4 (0.25-0.25)2 + 0.3(0.20-0.25)2 = 0.0015 VARy = 0.2(0.50-0.30)2 + 0.6 (0.30-0.30)2 + 0.2(0.10-0.30)2 = 0.0240 SDx = 0.0015 = 0.039 SDy = 0.0240 = 0.155 COV (Rx Ry) = 0.006 E(Rp) = 0.6(0.25) + 0.4(0.30) = 0.27 VAR(p) = 0.62 (0.0015) + 0.42 (0.024) + 2(0.6)(0.4)(0.006) = SDp 0.00726 0.00726 = = 0.0852 or 8.52% 17. Hilliard (i) E(IRRp) = WA E(IRRA) + WB E(IRRB) + WC E(IRRc) = 0.5 (0.1) + 0.3(0.2) + 0.2(0.4) = 0.19 or 19% = WA2VARA + WB2VARB + WC2VARC + + 2WA WB COVAB + 2 WAWCCOVAC + 2WBWCCOVBC VAR(IRRP) = (0.5)2(0.05)2+(0.3)2 (0.15)2 + (0.2)2(0.2)2 + 2(0.5)(0.3)(-0.0075) + 2(0.5)(0.2)(0.0100) + 2(0.3) (0.2)(0.0180) = 0.00616 0.00616 = 0.0785 or 7.85% SDIRR = (ii) It depends upon the risk- return trade off Return of portfolio is higher that A but lower than C and B Risk of portfolio is higher than A but lower than C and B (iii) Alternative strategy might just focus on A and B Since the correlation between these two is -1.0 Q 18 (i) (ii) After-tax cost of debt = PV(Leasing) = PV (Purchase) = Therefore Lease. (iii) NPV @15% = -£112915 Therefore reject the project 0.167 x (1-0.4) =0.10 -£221891 -£348665 19. Conroy fav Expand -200 1040+900 0.2 Unfav Favourable 800 320+900 0.2 0.5 Fav Not 800+800 0.8 Unfav -1500 200+800 0.2 1040+900 Fav Expand -200 Small Plant 0.4 320 + 900 unfav Unfavourable 200 0.6 0.5 fav Not 800 + 800 0.4 unfav 200+800 0.6 fav Contract 150 Large Plant 1040+900 0.8 unfav Favourable 1300 320 + 900 0.2 1300+1000 Fav 0.5 Not 0.8 unfav 100 + 1000 0.2 -2000 Fav Contract 150 0.4 Unfav Unfavourable 1040+900 320+900 0.6 100 0.5 Fav Not 1300+1000 0.4 Unfav 0.6 100+1000 7AU Fav +Expand 1940 1 1220 2 0.8 600 0.5 Unfav -1500 1600 Fav 0.4 Unfav + No Expand 200 Small Unfav 4 1000 Fav Large Fav+No.Contraction 3 2300 A 1100 B 0.8 1300 0.5 Unfav 0.2 -2000 Fav Unfav + Contraction C 1940 0.4 250 0.5 Unfav D 1220 0.6 SMALL PLANT NPV 1 648.76 0.4 NPVxProb 259.50 NPV2xProb 168356 Prob 2 53.75 0.1 5.37 289 3 4.13 0.2 0.83 3 4 -491.74 0.3 -147.52 72541 118.18 241189 E(NPV) = 118.18 Sdenpv = = 476.68 241189 − (118.18) 2 LARGE PLANT NPV Prob NPV2 x Prob NPVxProb A 1082.65 0.4 433.06 468848 B 90.91 0.1 9.09 826 C -169.42 0.2 -33.88 5741 D -764.46 0.3 -229.34 175321 178.93 650736 E(NPV) = 178.93 SDpv = 650736 − (178.93) 2 = 786.59 Other factors 1. high standard of deviation of outcomes for LARGE plant 2. high prob. Of obtaining negative NPV of LARGE plant. Q20 Glenroe (i) (ii) Draw the Decision tree Work out the ENPV NPV A -300 + B -300 + C -300 + D -300 + E -300 + F -300 + G -300 + H -300 + I -300 + i. E(NPV) = £44.524 ii. SDnpv = 100 1.1 100 1.1 100 1.1 200 1.1 200 1.1 200 1.1 300 1.1 300 1.1 300 1.1 + + + + + + + + + 0 (1.1)² 100 (1.1)² 100 (1.1)² 100 (1.1)² 200 (1.1)² 300 (1.1)² 200 (1.1)² 300 (1.1)² 350 (1.1)² 192.3E8 − (44.524) = £131347.7 2 Prob NPVxProb NPV²xProb = 209.090 0.0625 -13.068 2.7E = -126.446 0.1250 -15.806 2.0E = -43.802 0.0625 -2.738 1.2E8 = 35.537 0.0625 -4.442 1.6E8 = 47.107 0.1250 11.777 5.5E8 = 129.752 0.0625 16.219 2.1E9 = 138.017 0.0625 8.626 1.2E9 = 280.661 0.1250 27.583 6.1E9 261.938 0.0625 1.00 16.374 44.525 4.3E9 192.3E8 = iii. Prob NPV < 0 From tables p= 36.7% iv. Abandon project if PV1 of year 2 cash flows < 150,000 If cashflow in yr 1 = 100,000 PV2 = 1/4(o) + 1/2(100,000) + 1/4(200,000) = 90,909 1.1 1.1 If cashflow in yr 1 = 200,000 PV2 = 1/4(100,000) + 1/2(200,000) + 1/4(300,000) = 181818 1.1 1.1 1.1 If cashflow in yr 1 = 300,000 PV2 = 1/4(200,000) + 1/2(300,000) + 1/4(300,000) = 261363 1.1 1.1 1.1 Abandon the site if cashflow in yr1 = £100,000 21 E(Rx) = 0.25 E(Rx) = 0.32 VARx = 0.0015 VARy = 0.0246 SDx = 0.039 SDy = 0.157 COV (Rx Ry) = -0.006 E(Rp) = 0.278 VAR(p) = 0.0016 SDp 22. (b) (c) = 0.04 or 4% Lower limit Spread Upper limit Return Point = = = = EOQ Average Cash Balance Number of transactions Total Cost £40,000 £230,952 £270,952 £116,984 = = = = £35,000 £17,500 7 £175+£175 = £350 23 2FM/SGF/DMP/17 SCHOOL OF SOCIAL SCIENCES 2FM - INTERMEDIATE FINANCIAL MANAGEMENT Revision Questions 1. Taxco Ltd Taxco Ltd is deciding whether to proceed with a project that will attract capital allowances of 25% reducing balance. The project requires an initial investment of £1 million, will last for five years and have a resale value of £200,000 in five years time. The following profit estimates have been produced by the company: £000 Sales Cost of Sales Depreciation Consultant Fees (tax allowable) Year 1 Year 2 Year 3 Year 4 Year 5 100 25 160 150 400 100 160 700 150 160 750 150 160 800 200 160 (235) 140 390 440 440 The company pays tax at 50% with a one year lag. If the company's cost of capital is 10% advise the company on whether to accept the project. 2. Rubber Duck Ltd Rubber Duck Ltd produces novelties for the bathroom and is considering whether to produce a new product, the singing mermaid. For purposes of investment appraisal, the company use their equity and debt holders weighted average cost of capital. The company has in issue two million ordinary shares of 25p each with a current market price of 50p. The dividend declared is 5½p per share. Also in issue are 312,500 4.8% debentures with a current price of 80 pence. The singing mermaid project is estimated to have the following cash flows: Year 0 Year 1 Year 2 (500,000) 275,000 350,000 You are required to: a) b) c) d) Calculate the cost of capital to be used in investment appraisal. Calculate the payback period to the nearest day. Calculate the IRR of the project using similar triangles and quadratic equations. Advise the company whether to accept the project 2 3. Inflatable Tyres Inflatable Tyres Ltd is deciding on whether or not to go ahead with a new inflator system. The new system would require an investment of £250,000 now and £50,000 in one year's time. It will last for five years and be worth £10,000 in scrap at that time. 1. Sales Sales are forecast to be £200,000 in the first year and will rise in line with the retail price index which is expected to increase at a rate of 12% pa. 2. Labour Labour required will be 20,000 man hours per year. The current wage rate which has just been agreed for the current year is £3 per hour. It is anticipated that wage increases will be 10% pa for the foreseeable future. The men are currently on short time working, working only half time at the moment. This is expected to last for this year only. 3. Material A There is currently 20,000 kilos in stock and if the project is not undertaken it will cost £10,000 to dispose of it now. The new system will require 10,000 kilos per annum. The current price just introduced is £2 per kilo. 4. Material B Annual usage will be 15,000 kilos. The current price is £5 per kilo. In years 2 and 3 there will be a shortage of material B and if used elsewhere could earn a contribution of £2 per kilo. Material prices for both A and B will increase by 5% pa. 5. Depreciation Depreciation is charged at 20% reducing balance. 6. Overheads The overheads will be £50,000 pa which are the same as with the current system. The company uses a cost of capital of 10% for investment appraisal purposes. Cashflows occur at the end of the year unless otherwise stated. Ignore tax. You are required to advise the company whether to proceed with the project. 4. On 1 January 1996 Mr Smith sought your advice on determining the prices of the shares of the following companies in his portfolio: i) Company W is expected to pay a dividend in December 1996, of £10 per share, after which the share price is expected to be £210. ii) Company X is expected to pay an annual dividend each December of £4 per share indefinitely. iii) Company Y's dividend per share is expected to grow by 5% a year for the foreseeable future. The dividend is expected to be £8 per share in December 1996. iv) Company Z is expected to pay a dividend of £4 per share in December of this year. Short term prospects for the company are excellent and a 20% annual growth rate is expected for the next three years (1995-97). At the end of three years the growth rate is expected to decline to a more normal 6%. The current rate of return required, which is expected to remain unchanged, is 10% per annum. 3 5. Advise Mr Smith. Hyper Ltd Hyper Ltd has an authorised ordinary share capital of 2 million shares of £1 each and an issued ordinary share capital of 1 million shares of £1 each. It also has 800,000 £1 8% debentures. The market price of the shares is £1.60 per share and the debentures are valued at par. Dividends and interest are paid annually. An ordinary dividend has just been paid of £176,000 and the debenture interest has also just been paid. Hyper Ltd has been asked to consider a contract of £600,000 to manufacture six Itzabargain machines. Manufacturing would take place over three years commencing immediately on 1 June 1996. The contract price would be payable in two instalments, one-third on 1 June 1996 and the final two-thirds on 31 May 1999. Two machines would be manufactured each year. The following details are relevant: 1) Raw Materials There is one raw material, the Cheepie, which will be used on the contract. One year's supply of Cheepie currently costs £40,000. Materials are purchased and paid for annually in advance. Material values and prices are expected to increase at an annual compound rate of 20%. 2) Labour Labour in the first year will cost £65,000. Wage rates are expected to increase at a compound rate of 15%. 3) Equipment Equipment for the contract will be purchased and paid for now at a cost of £200,000 and will be sold at the end of the contract for £50,000. Assume that all payments arise on the last day of the year to which they relate unless otherwise stated. Input prices change annually at midnight on 31 May. Required i) Calculate the weighted average cost of capital. ii) Calculate the payback period to the nearest month. iii) Calculate the internal rate of return of the contract (in the range of 14% to 18%). iv) Using a cost of capital of 10%, advise Hyper Ltd whether to accept the contract. 6. Sleigh Manufacturing Ltd a) Sleigh Manufacturing has 100,000 50p ordinary shares in issue with a current value of £2.50 per share. They are also 200,000 7% £1 debentures in issue which have a current market value of 75p per debenture. The current dividend per share is 50p. You are required to show that Sleigh Manufacturing Ltd's weighted average cost of capital is 16%. b) You have been asked to advise on the current year's investment proposals for Sleigh Manufacturing Ltd. The proposed projects shown below are not mutually exclusive. They are: A) To replace the existing data processing equipment. Initial cost £250,000. Expected life of new equipment 6 years. Expected annual after tax cash inflow £72,500. B) To develop a new type of sleigh costing £70,000 where all the cost is to be incurred immediately. The expected life of the product is 5 years. Expected annual after tax cash inflow for each year £30,000. The inflows will commence in year 2. 4 C) To install safety equipment at an initial cost of £110,000. Expected life three years. Expected annual after tax cash inflow £45,000. D) To construct a new factory building. Initial cost of £210,000. Expected life 8 years. Expected annual after tax cash inflow £57,000. E) To extend the existing loading equipment. Initial cost of £170,000. Expected life 4 years. Expected annual after tax cash inflow £70,000. F) To purchase patent rights to a new process. Initial cost £135,000. Expected life 15 years. Expected annual after tax cash inflows £30,000 for the first five years and £20,000 for the next ten years. With the exception of project B, all cash inflows commence in the current year, and are always received on the last day of the year. Tax is paid when the inflow is received. The company's cost of capital is 16%. The company is, however, in a capital rationing situation and estimates it will only have £600,000 to invest in the current year. The company normally adopts a payback period of 3 years for its investment appraisal. Required a) Recommend to the company, using the NPV method of investment appraisal, which projects to undertake, bearing in mind its £600,000 spending limit. Give reasons for your choice. 7. b) Calculate to the nearest month which projects the company would accept using its payback period of within 3 years. c) Explain why your choice is different from the company's choice under its normal investment appraisal method. A firm is considering an investment that requires an initial outlay of £1m and will yield the resultant cashflows for the next two years. During the first year there are three possible outcomes. Cash Flows Possibility Outcome 1 Outcome 2 Outcome 3 £600,000 0.5 £700,000 0.3 £800,000 0.2 In year two the following possible cash inflows may arise: If Outcome 1 Cash flow = 600,000 If Outcome 2 Cash flow = 700,000 If Outcome 3 Cash flow = 800,000 Then Cash Flow £300,000 £600,000 Then Cash Flow £300,000 £500,000 £700,000 Then Cash Flow £400,000 £600,000 £800,000 Prob 0.2 0.8 Prob 0.2 0.3 0.5 Prob 0.2 0.7 0.1 Find the Expected NPV and Standard Deviation of NPV for the project if the cost of capital is 10%. 5 8. The following are the variances and the covariance for the returns of two different shares A and B. VAR A VAR B COV (A,B) = = = 0.08 0.02 0.001 If an investor holds 50% of his wealth in A and 50% of his wealth in B find the Expected Return and Risk of this portfolio if: E (RA) E (RB) = = 0.12 0.10 9. Ms M Audrey is considering investing in two shares. The first - WP - is expected to earn a return of 15% over the next year and the standard deviation of the expected returns is 20%. The second - LO -is expected to earn a return of 6% and the standard deviation of the expected returns is estimated at 10%. If the correlation between the expected returns is - 0.5 estimate the expected return and standard deviation of returns for a portfolio with 60% of wealth invested in WP and 40% of wealth invested in LO. 10. X Ltd has monthly sales of £90,000. About half of its customers pay their accounts within the month of invoicing, one third in the following month, and the remainder during the second month after invoicing. It has been decided to offer 1¼% discount for payment within the month of invoicing. During the first six months of the new policy, collections are improved so that on average three-quarters of the customers pay in the first month, this improvement coming entirely from those customers who had previously paid in the month after invoicing. The current cost of capital is 15% a year. Ignoring any additional clerical costs is the change in policy financially justified? 11. Frame plc is considering which of two mutually exclusive projects, A or B, to undertake. There is some uncertainty about the running costs with each project, and a probability distribution of the NPV for each has been estimated, as follows: NPV £000 -20 +10 +25 +40 Project A Probability NPV £000 +5 +15 +20 +25 0.15 0.20 0.35 0.30 Project B Probability 0.2 0.3 0.4 0.1 Which project should the company choose, if any? 12. Couttes Purse Ltd requires advice on its debt collection policy. Should the current policy be discarded in favour of Option 1 or Option 2? Current Policy Option 1 Option 2 £240,000 £300,000 £400,000 Bad debt losses (% of sales) 3% 2% 1% Average collection period 2 months 1½ months 1 month Expenditure on debt collection procedures, per annum Current sales are £4.8 million per annum, and the variable cost of sales is 90% of sales value. The company requires a 15% return on its investments. 6 13. Russian Beard Ltd is considering a change in its credit policy which will result in a slowing down in the average collection period from one to two months. The relaxation in credit standards is expected to produce an increase in sales in each year amounting to 25% of the current sales volume. Sales price per unit Variable cost per unit Current sales per annum £10 £8.50 £2.4 million The required rate of return on investment is 20%. Assume that the 25% increase in sales would result in additional stocks of £100,000 and additional creditors of £20,000. Advise the company on whether or not to extend the credit period offered to customers if existing customers do not change they payment habits, and only the new customers take a full 2 months' credit. 14. (a) Outline the main advantages and disadvantages of the decision tree approach to evaluating the riskiness of a capital investment proposal. (b) Shannon plc is considering a two-year investment with an initial outlay of £375,000. The estimated net cash flows and probabilities in year 1 are as follows: Economic Conditions Weak Moderate Good Net Cash Flows in Year 1 Probability 0.2 0.5 0.3 Cash Flow (£) 100,000 200,000 300,000 At the end of year 1, economic conditions in year 2 are forecast to be either moderate or good and the cash flows (and probabilities) associated with these conditions are predicted to be as follows: Economic Conditions Moderate Good Net Cash Flows in Year 2 Probability 0.7 0.3 Cash Flow (£) 250,000 350,000 Required (i) Represent the problem as a decision tree. (ii) Calculate the Expected Net Present Value and Standard Deviation of the Net Present Value of the investment. (iii) Estimate the probability of obtaining a negative Net Present Value. (iv) If the company has the option to abandon the project at the end of the first year and sell the plant and equipment for £262,000, calculate the increase in net present value associated with this option. 7 15. (a) Mrs B Suir, a recently appointed finance director of a large divisionalised water company, seeks your advice in dealing with capital issues raised by financial controllers at three of the company’s divisions: (i) The Corrib division which makes hose pipes has budgeted sales of £700,000 per annum. Its costs as a percentage of sales are as follows: Raw Materials 20%: Direct Labour 35%; Overheads 15%. The division carries raw materials in stock for two weeks, while finished goods are held in stock for three weeks before sale. Production takes four weeks. The division takes four weeks’ credit from suppliers and gives eight weeks’ credit to its customers. Both overheads and production costs are incurred evenly throughout the year and work in progress is normally 100% complete with respect to material costs but only 50% complete with regards to labour and overheads. Required Calculate the total working capital requirement for the Corrib division. (ii) The Erin division which makes sprinkler systems, has current sales of £1.5m per year. Cost of sales is 75% of sales and bad debts are 1% of sales. The manager of the division reports that 80% of these costs are variable while 20% are fixed. The division currently allows customers 30 days credit but is considering increasing this to 60days, in order to increase sales. It has been estimated that this change in policy will increase sales by 15% while bad debts will rise from 1% to 4%. It is expected that this change in policy will result in an increase of £5,000 in administration costs while creditors and stock will remain unchanged. Required If the division’s cost of capital is 12% should they proceed with the change in credit policy? (iii) The Derg division is considering taking a discount of 2% from their suppliers if they pay within 10 days. If the discount is not taken, payment will occur after 40 days. Required If the division’s cost of capital is 12% and assuming 360 days in the year, advise Mrs Suir on whether the discount should be taken. 16. (a) Ballyvaden plc is considering two different investment projects with the following return possibilities: Project X State 1 2 3 Return (%) 30 25 20 Project Y Probability 0.3 0.4 0.3 Return (%) 50 30 10 Probability 0.3 0.4 0.3 The financial director of the firm is unsure about which opportunity or which combination of opportunities, to choose and seeks your advice. Required (i) Calculate the expected return and standard deviation of return for each project. (ii) Calculate the covariance between the returns offered by this pair of projects. (iii) Consider whether a portfolio comprising 60% of project X and 40% of project Y might offer the firm a more attractive combination of risk and return if fractions of the projects can be undertaken. 8 17. (a) Comment on whether standard deviation is an appropriate measure of risk in investment appraisal in the light of the views expressed in March and Shapira (1986). (b) Hilliard plc is considering investing in three projects with the following characteristics: Project A B C E(IRR) 0.10 0.20 0.40 SD (IRR) 0.05 0.15 0.20 where E (IRR) is the expected IRR of the project and SD (IRR) is the standard deviation of the IRR. In addition, the financial director of the company has ascertained that the covariance between the IRRs of projects A and B is –0.0075 while the correlation between the IRRs of projects B and C is 1.0 and between the IRRs of projects A and C is 0.2. Required (i) Estimate the E (IRR) and SD (IRR) of a portfolio of these projects if the £1m available for investment is spent as follows: A = £500,000 B = £300,000 C = £200,000 (ii) Comment on whether Hilliard plc would wish to proceed with this portfolio of projects and identify what further information might help the directors in making their decision. (iii) Suggest an alternative investment strategy which would reduce the risk faced by the company when deciding to invest in some or all of these projects. 18. Leasco plc is deciding on how to finance the purchase of a new machine costing £500,000 which will have a useful life of 4 years. It can either be purchased with a loan where the pre-tax interest rate is 16.67% or it can be leased. If it is leased, four annual lease payments of £100,000 would have to be paid in advance to the leasing firm. The machine is needed to produce the following product which can be sold at the following costs over the next four years: Year 1 2 3 4 Quantity 50,000 60,000 40,000 30,000 Price £5 £6 £4 £4 Variable Cost £3 £4 £3 £3 In addition, fixed annual costs of £20,000 would be incurred in the production process. Required (i) (ii) (iii) If the tax rate is 40% and if a 25% writing down allowance is available on the purchase of the machine, advise the firm on whether the machine should be purchased or leased? Work out the after-tax cash flows associated with the production output from the machine. Calculate the NPV from the investment decision associated with the machine if the after-tax WACC is 15%. 9 19 (a) “Real Options commonly occurred and were generally significant in determining how decision makers regard an investment.” (Busby and Pitts, 1997) Outline the various real options which management believed to be useful when making investment decisions. (b) Conroy plc has to decide what size of new plant to build. A large plant will provide economies of scale but is also likely to lead to a reduced selling price. The capital costs and annual fixed and variable costs for two different size plants are as follows: Capacity (millions of units) 0.4 0.8 Investment (£000) 1500 2000 Annual Fixed Costs (£000) 200 300 Unit Cost (£) 2.00 1.80 Conroy plc believes that market conditions will either be favourable or unfavourable and that both of these conditions are equally likely to occur. Depending upon these conditions, the following unit prices are expected to be obtained for the product. Quality Sold (millions of units) Price Per Unit (£) ...