182 PA RT 3 Valuation of Future Cash Flows
QUESTIONS AND PROBLEMS
BASIC 1. Present Value and Multiple Cash Flows [LO1] Wainright Co. has identified an
(Questions 1–28) investment project with the following cash flows. If the discount rate is 10 percent,
what is the present value of these cash flows? What is the present value at 18 percent?
At 24 percent?
Year Cash Flow
1 $ 720
2 930
3 1,190
4 1,275
2. Present Value and Multiple Cash Flows [LO1] Investment X offers to pay you
$5,200 per year for eight years, whereas Investment Y offers to pay you $7,300 per
year for five years. Which of these cash flow streams has the higher present value if
the discount rate is 5 percent? If the discount rate is 15 percent?
3. Future Value and Multiple Cash Flows [LO1] Toadies, Inc., has identified an
investment project with the following cash flows. If the discount rate is 8 percent,
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what is the future value of these cash flows in Year 4? What is the future value at a
discount rate of 11 percent? At 24 percent?
Year Cash Flow
1 $1,375
2 1,495
3 1,580
4 1,630
4. Calculating Annuity Present Value [LO1] An investment offers $6,100 per year
for 15 years, with the first payment occurring one year from now. If the required
return is 6 percent, what is the value of the investment? What would the value be if
the payments occurred for 40 years? For 75 years? Forever?
5. Calculating Annuity Cash Flows [LO1] If you put up $45,000 today in exchange
for a 6.25 percent, 15-year annuity, what will the annual cash flow be?
6. Calculating Annuity Values [LO1] Your company will generate $68,000 in an-
nual revenue each year for the next seven years from a new information database. If
the appropriate interest rate is 8.5 percent, what is the present value of the savings?
7. Calculating Annuity Values [LO1] If you deposit $5,000 at the end of each of the
next 20 years into an account paying 10.8 percent interest, how much money will
you have in the account in 20 years? How much will you have if you make deposits
for 40 years?
8. Calculating Annuity Values [LO1] You want to have $75,000 in your savings
account 12 years from now, and you’re prepared to make equal annual deposits into
the account at the end of each year. If the account pays 6.8 percent interest, what
amount must you deposit each year?
9. Calculating Annuity Values [LO2] Dinero Bank offers you a $60,000, five-year
term loan at 7.5 percent annual interest. What will your annual loan payment be?
10. Calculating Perpetuity Values [LO1] The Maybe Pay Life Insurance Co. is trying
to sell you an investment policy that will pay you and your heirs $30,000 per year
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Chapter 6 Discounted Cash Flow Valuation 183
forever. If the required return on this investment is 5.8 percent, how much will you
pay for the policy?
11. Calculating Perpetuity Values [LO1] In the previous problem, suppose a sales
associate told you the policy costs $475,000. At what interest rate would this be a
fair deal?
12. Calculating EAR [LO4] Find the EAR in each of the following cases:
Stated Rate (APR) Number of Times Compounded Effective Rate (EAR)
9% Quarterly
18 Monthly
14 Daily
11 Infinite
13. Calculating APR [LO4] Find the APR, or stated rate, in each of the following
cases:
Stated Rate (APR) Number of Times Compounded Effective Rate (EAR)
Semiannually 11.5%
Monthly 12.4
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Weekly 10.1
Infinite 13.8
14. Calculating EAR [LO4] First National Bank charges 13.2 percent compounded
monthly on its business loans. First United Bank charges 13.5 percent compounded
semiannually. As a potential borrower, which bank would you go to for a new loan?
15. Calculating APR [LO4] Barcain Credit Corp. wants to earn an effective annual
return on its consumer loans of 15 percent per year. The bank uses daily compound-
ing on its loans. What interest rate is the bank required by law to report to potential
borrowers? Explain why this rate is misleading to an uninformed borrower.
16. Calculating Future Values [LO1] What is the future value of $2,600 in 19 years
assuming an interest rate of 7.9 percent compounded semiannually?
17. Calculating Future Values [LO1] Gold Door Credit Bank is offering 6.7 percent
compounded daily on its savings accounts. If you deposit $5,100 today, how much
will you have in the account in 5 years? In 10 years? In 20 years?
18. Calculating Present Values [LO1] An investment will pay you $43,000 in
10 years. If the appropriate discount rate is 7 percent compounded daily, what is
the present value?
19. EAR versus APR [LO4] Big Dom’s Pawn Shop charges an interest rate of
27 percent per month on loans to its customers. Like all lenders, Big Dom must
report an APR to consumers. What rate should the shop report? What is the
effective annual rate?
20. Calculating Loan Payments [LO2, 4] You want to buy a new sports coupe for
$83,500, and the finance office at the dealership has quoted you a 6.5 percent APR
loan for 60 months to buy the car. What will your monthly payments be? What is
the effective annual rate on this loan?
21. Calculating Number of Periods [LO3] One of your customers is delinquent on his
accounts payable balance. You’ve mutually agreed to a repayment schedule of $500
per month. You will charge 1.7 percent per month interest on the overdue balance. If
the current balance is $16,000, how long will it take for the account to be paid off?
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