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178 PART 2 Important Financial Concepts
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4–25 Future value of a mixed stream For each of the mixed streams of cash flows
shown in the following table, determine the future value at the end of the final
year if deposits are made at the beginning of each year into an account paying
annual interest of 12%, assuming that no withdrawals are made during the
period.
Year A
Cash flow stream
B C
1 $ 900 $30,000 $1,200
2 1,000 25,000 1,200
3 1,200 20,000 1,000
4 10,000 1,900
5 5,000
4–26 Future value of a single amount versus a mixed stream Gina Vitale has just
contracted to sell a small parcel of land that she inherited a few years ago. The
buyer is willing to pay $24,000 at the closing of the transaction or will pay the
amounts shown in the following table at the beginning of each of the next
5 years. Because Gina doesn’t really need the money today, she plans to let it
accumulate in an account that earns 7% annual interest. Given her desire to buy
a house at the end of 5 years after closing on the sale of the lot, she decides to
choose the payment alternative—$24,000 single amount or the mixed stream of
payments in the following table—that provides the higher future value at the end
of 5 years.
Mixed stream
Beginning of year Cash flow
1 $ 2,000
2 4,000
3 6,000
4 8,000
5 10,000
a. What is the future value of the single amount at the end of year 5?
b. What is the future value of the mixed stream at the end of year 5?
c. On the basis of your findings in parts a and b, which alternative should Gina
take?
d. If Gina could earn 10% rather than 7 percent on the funds, would your recommendation
in part c change? Explain.
4–27 Present value—Mixed streams Find the present value of the streams of cash
flows shown in the following table. Assume that the firm’s opportunity cost
is 12%.