1. A 4-year annuity of $200 monthly payments begins 10 years from now. The required return is 10%, compounded monthly.
a. What is the value of the annuity today?
b. What is the value of the annuity in 3 years?
c. What is the value of the annuity in 7 years?
d. What is the value of the annuity in 10 years?
e. What is the value of the annuity in 12 years?
f. What is the value of the annuity in 15 years?
2. A perpetuity of $1500 quarterly payments begins six years from now. The required return is 10%, compounded quarterly.
a. What is the value of the perpetuity today?
b. What is the value of the perpetuity in 4 years?
c. What is the value of the perpetuity in 6 years?
d. What is the value of the perpetuity in 20 years?
3. You wish to purchase a car in one year. You currently have $2000 to put towards the car’s down payment and access to an account that earns 7%, compounded quarterly. You plan to have $4,000 for the down payment when you purchase the car and the expected price of the car is $20,000.
a. How much do you need to deposit into your account each quarter over the course of this year to have enough for the down payment?
b. If you borrow to purchase the car at a rate of 5% and make equal monthly payments for 4 years to pay back the car, what will your car payment be?
c. How much will you still owe on the car after making the payments from part b) for 2.5 years?
4. You are purchasing a car today that costs $25,000. You have been given the following financing options for the car. Option 1 is conventional 4-year financing at an interest rate of 4%, compounded monthly. This option requires monthly payments. Option 2 is a balloon loan which requires monthly payments of $375 for 2 years and then a final balloon payment for the remaining balance. The interest rate on this loan is 2.5%.
a. What is the payment for the conventional loan (option 1)?
b. How will you plan amortization schedule for option 1.
c. What will the balloon payment be for the balloon loan (option 2)?
d. What is the amortization schedule for option 2.
e. Which option do you prefer and why? What additional considerations are there with respect to the balloon loan?
5. Explain the various inputs to the present value of an annuity (i.e. C, r, t, and PVA). How is the value of the annuity impacted by each input?
6. Explain what happens to the value of a perpetuity over time, assuming the perpetuity has begun.
7. Explain what happens to the value of a growing perpetuity over time, assuming the growing perpetuity has begun.
8. Explain why the value today of a perpetuity that doesn’t start until sometime in the future is not simply C/r.