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b. Rework part a under the assumption that the $1,000,000 payment will be
received in 15 rather than 10 years.
c. On the basis of your findings in parts a and b, discuss the effect of both the
size of the rate of return and the time until receipt of payment on the present
value of a future sum.
4–15 Present value comparisons of single amounts In exchange for a $20,000 payment
today, a well-known company will allow you to choose one of the alternatives
shown in the following table. Your opportunity cost is 11%.
Alternative Single amount
A $28,500 at end of 3 years
B $54,000 at end of 9 years
C $160,000 at end of 20 years
a. Find the value today of each alternative.
b. Are all the alternatives acceptable, i.e., worth $20,000 today?
c. Which alternative, if any, will you take?
4–16 Cash flow investment decision Tom Alexander has an opportunity to purchase
any of the investments shown in the following table. The purchase price, the
amount of the single cash inflow, and its year of receipt are given for each investment.
Which purchase recommendations would you make, assuming that Tom
can earn 10% on his investments?
Investment Price Single cash inflow Year of receipt
A $18,000 $30,000 5
B 600 3,000 20
C 3,500 10,000 10
D 1,000 15,000 40
4–17 Future value of an annuity For each of the cases shown in the following
table, calculate the future value of the annuity at the end of the deposit
period, assuming that the annuity cash flows occur at the end of each
year.
Amount of Interest Deposit period
Case annuity rate (years)
A $ 2,500 8% 10
B 500 12 6
C 30,000 20 5
D 11,500 9 8
E 6,000 14 30
CHAPTER 4 Time Value of Money 175