财务管理试题5

CHAPTER 5

Discounted Cash Flow Valuation I. DEFINITIONS

Topic: ANNUITY

1. An annuity stream of cash flow payments is:

A) A set of level cash flows occurring each time period for a fixed length of time.

B) A set of level cash flows occurring each time period forever.

C) A set of increasing cash flows occurring each time period for a fixed length of time.

D) A set of increasing cash flows occurring each time period forever.

E) A set of arbitrary cash flows occurring each time period for no more than 10 years.

Answer: A

Topic: PRESENT VALUE FACTOR FOR ANNUITIES

2. The present value factor for annuities is calculated as:

A) (1 + present value factor)/r

B) (1 – present value factor)/r

C) Present value factor + (1/r)

D) (Present value factor*r) + (1/r)

Answer: B

Topic: FUTURE VALUE FACTOR FOR ANNUITIES

3. The future value factor for annuities is calculated as:

A) Future value factor + r

B) (1/r) + (future value factor*r)

C) (1/r) + future value factor

D) (Future value factor – 1)/r

E) (Future value factor + 1)/r

Answer: D

Topic: ANNUITIES DUE

4. Annuities where the payments occur at the end of each time period are called ___________,

whereas __________ refer to annuity streams with payments occuring at the beginning of each time period.

A) ordinary annuities; early annuities

B) late annuities; straight annuities

C) straight annuities; late annuities

D) annuities due; ordinary annuities

E) ordinary annuities; annuities due

Answer: E

Topic: PERPETUITY

5. An annuity stream where the payments occur forever is called a(n) ____________.

A) annuity due

B) indemnity

C) perpetuity

D) amortized cash flow stream

E) amortization table

Answer: C

Topic: STATED INTEREST RATES

6. The interest rate expressed in terms of the interest payment made each period is called the:

A) Stated interest rate.

B) Compound interest rate.

C) Effective annual rate.

D) Periodic interest rate.

E) Daily interest rate.

Answer: A

Topic: EFFECTIVE ANNUAL RATE

7. The interest rate expressed as if it were compounded once per year is called the:

A) Stated interest rate.

B) Compound interest rate.

C) Effective annual rate.

D) Periodic interest rate.

E) Daily interest rate.

Answer: C

Topic: ANNUAL PERCENTAGE RATE

8. The interest rate charged per period multiplied by the number of periods per year is called the:

A) Effective annual rate (EAR).

B) Annual percentage rate (APR).

C) Periodic interest rate.

D) Compound interest rate.

E) Daily interest rate.

Answer: B

Topic: PURE DISCOUNT LOAN

9. A loan where the borrower receives money today and repays a single lump sum at some time in the

future is called a(n) _____________ loan.

A) amortized

B) continuous

C) balloon

D) pure discount

E) interest-only

Answer: D

Topic: INTEREST-ONLY LOAN

10. A loan where the borrower pays interest each period and repays the entire principal of the loan at

some point in the future is called a(n) _________ loan.

A) amortized

B) continuous

C) balloon

D) pure discount

E) interest-only

Answer: E

Topic: AMORTIZED LOAN

11. A loan where the borrower pays interest each period, and repays some or all of the principal of the

loan over time is called a(n) _________ loan.

A) amortized

B) continuous

C) balloon

D) pure discount

E) interest-only

Answer: A

Topic: BALLOON LOAN

12. A loan where the borrower pays interest each period, repays part of the principal of the loan over

time, and repays the remainder of the principal at the end of the loan, is called a(n)

_______________ loan.

A) amortized

B) continuous

C) balloon

D) pure discount

E) interest-only

Answer: C

II CONCEPTS

Topic: EFFECTIVE ANNUAL RATE

13. You are trying to compare the desirability of two alternative investments with rates of return quoted

using different compounding periods. To make the proper decision, you should:

A) Convert each quoted return to an effective annual rate.

B) Convert each quoted return to an annual nominal rate.

C) Convert each quoted return to a monthly nominal rate.

D) Compare the investments by using the quoted returns.

E) Convert each quoted return to an APR.

Answer: A

Topic: ANNUAL PERCENTAGE RATE

14. Which of the following statements is FALSE?

A) When comparing investments it is best not to rely solely on quoted rates.

B) Compounding typically leads to differences between quoted and effective rates.

C) The APR on a loan with monthly payments is less than the annual interest you actually pay.

D) The APR is the interest rate per period multiplied by the number of periods per year.

E) With monthly compounding, the APR will be larger than the effective annual rate.

Answer: E

Topic: PERPETUITY

15. Which of the following CANNOT be calculated?

A) The present value of a perpetuity.

B) The interest rate on a perpetuity given the present value and payment amount.

C) The present value of an annuity due.

D) The future value of an annuity due.

E) The future value of a perpetuity.

Answer: E

Topic: PRESENT VALUE PERPETUITY

16. You are considering two perpetuities which are identical in every way, except that perpetuity A will

begin making annual payments of $P to you two years from today while the first $P payment for perpetuity B will occur one year from today. It must be true that the present value of perpetuity:

A) A is greater than that of B by $P.

B) B is greater than that of A by $P.

C) B is equal to that of perpetuity A.

D) A exceeds that of B by the PV of $P for one year.

E) B exceeds that of A by the PV of $P for one year.

Answer: E

Topic: COMPARING SAVINGS ACCOUNTS

17. You have $800 that you would like to invest. You have 2 choices: Savings account A which earns

8% compounded annually, or savings account B which earns 7.90% compounded semiannually.

Which would you choose and why?

A) A because it has a higher effective annual rate.

B) A because it has the higher quoted rate.

C) B because it has a higher effective annual rate.

D) B because the future value in one year is lower.

E) B because it has the higher quoted rate.

Answer: C

Topic: COMPARING SAVINGS ACCOUNTS

18. You have $800 that you would like to invest. You have 2 choices: Savings account A which earns

8% compounded annually, or savings account B which earns 7.70% compounded monthly. Which would you choose and why?

A) A because it has a higher effective annual rate.

B) A because the future value in one year is lower.

C) B because it has a higher effective annual rate.

D) B because the future value in one year is lower.

E) A because it has the higher quoted rate.

Answer: A

Topic: COMPARING SAVINGS ACCOUNTS

19. You are planning to save your Christmas bonuses from work and are comparing savings accounts:

Account A compounds semiannually while account B compounds monthly. If both accounts have the same quoted annual rate of interest and you place only the bonuses in the account, you should choose _______________.

A) account A because it has a higher APR

B) account B because it has a higher APR

C) account B because it is compounded more often

D) account A because you will pay less in taxes

E) either account, since both quote the same rate of interest

Answer: C

Topic: INTERPRETING INTEREST RATES

20. Which of the following statements is true?

A) Present values and discount rates move in the same direction with one another.

B) On loans with monthly compounding, the APR will exceed the EAR.

C) Compounding essentially means earning interest on interest.

D) Future values decrease with increases in interest rates.

E) All else the same, the longer the term of a loan the lower will be the total interest you pay on it.

Answer: C

Topic: COMPARING LOANS

21. You want to borrow money to buy a new car, and you are trying to decide whether to borrow

short-term (24 months) or long-term (60 months). Which of the following would be

IRRELEVANT to your borrowing decision?

A) The EARs on the two alternative loans.

B) The APRs on the two alternative loans.

C) The interest you could earn by investing the difference between the two loan payments.

D) The fact that you must make 48 more payments on the longer term loan.

E) The amount of money to be borrowed.

Answer: E

Topic: PRESENT VALUE ANNUITY

22. You are going to invest $500 at the end of each year for ten years. Given an interest rate, you can

find the present value of this investment by:

I. Adding the cash flows together and finding the present value of the sum using the appropriate

present value factor.

II. Applying the proper present value factor to each cash flow, then adding up these present values.

III. Finding the future value of each cash flow, adding all of the future values together, then finding the discounted present value of this future value sum.

IV. Finding the future value of the entire payment stream.

A) II only

B) III only

C) II and III only

D) I, II, and IV only

E) II, III, and IV only

Answer: C

Topic: ANNUITIES DUE

23. You are evaluating two annuities. They are identical in every way, except that one is an ordinary

annuity and one is an annuity due. Which of the following is FALSE?

A) The ordinary annuity must have a lower present value than the annuity due.

B) The ordinary annuity must have a lower future value than the annuity due.

C) The annuity due must have the same present value as the ordinary annuity.

D) The two annuities will differ in present value by the amount (1+r).

E) The annuity due and the ordinary annuity will make the same number of total payments over

time.

Answer: C

III. PROBLEMS

Topic: PRESENT VALUE UNEVEN CASH FLOWS

24. What is the total present value of $80 received in one year, $300 received in two years, and $700

received in six years if the discount rate is 7%?

A) $582.72

B) $681.68

C) $757.25

D) $803.24

E) $852.83

Answer: D

Response: PV = $80 / 1.07 + 300 / 1.072 + 700 / 1.076 = $803.24

25. What is the total future value six years from now of $80 received in one year, $300 received in two

years, and $700 received in six years if the discount rate is 7%?

A) $1,080.00

B) $1,047.15

C) $1,205.44

D) $1,254.44

E) $1,299.15

Answer: C

Response: FV = $80 (1.07)5 + 300 (1.07)4 + 700 = $1,205.44

Topic: PRESENT VALUE UNEVEN CASH FLOWS

26. Given the following cash flows, what is the present value if the discount rate is 8%?

Year1234

Cash Flow$400$250$900$1925

A) $1,415.07

B) $2,714.09

C) $2,865.70

D) $3,058.96

E) $3,222.62

Answer: B

Response: PV = $400 / 1.08 + 250 / 1.082 + 900 / 1.083 + 1,925 / 1.084 = $2,714.09

Topic: PRESENT VALUE UNEVEN CASH FLOWS

27. What is the present value of the following set of cash flows at an 10% discount rate?

Year1234

Cash Flow$800?800$800?800

A) $ 0.00

B) $ 120.76

C) $ 173.31

D) $ 379.41

E) $3,312.13

Answer: B

Response: PV = $800 / 1.1 - 800 / 1.12 + 800 / 1.13 - 800 / 1.14 = $120.76

28. What is the future value at the end of year 4 of the following set of cash flows? Assume an interest

rate of 10%.

Year1234

Cash Flow$800?800$800?800

A) $ 0.00

B) $ 127.38

C) $ 176.80

D) $ 379.41

E) $3,312.13

Answer: C

Response: FV = $800 (1.1)3 - 800 (1.1)2 + 800 (1.1) - 800 = $176.80

Topic: FUTURE VALUE UNEVEN CASH FLOWS

29. What is the future value of the following set of cash flows 4 years from now? Assume an interest

rate of 6.5%.

Year01234

Cash Flow?700$300$600$400$500

A) $ 555.18

B) $ 785.72

C) $ 942.12

D) $1,068.39

E) $1,100.00

Answer: D

Response: FV = -$700(1.065)4 + 300 (1.065)3 + 600 (1.065)2 + 400 (1.065) + 500 = $1,068.39 Topic: INTEREST RATE

30. Given the following cash flows, what is the implicit discount rate if the present value is $2,450?

Year 1 2 3

Cash Flow $700 $950 $1400

A) 5.45%

B) 8.72%

C) 10.48%

D) 12.89%

E) 15.91%

Answer: C

Response: $2,450 = $700 / (1 + r) + 950 / (1 + r)2 + 1,400 / (1 + r)3; r = 10.48%

Topic: INTEREST RATE

31. Given the following cash flows, what is the interest rate if the future value at the end of year 3 is

equal to $3,218?

Year123

Cash Flow$700$950$1400

A) 4%

B) 5%

C) 6%

D) 7%

E) 8%

Answer: D

Response: $3,218 = $700 (1 + r)2 + 950 (1 + r) + 1,400; r = 7.0%

Topic: ANNUITY PAYMENT

32. You need to borrow $23,000 to buy a truck. The current loan rate is 7.9% compounded monthly and

you want to pay the loan off in equal monthly payments over 5 years. What is the size of your monthly payment?

A) $323.39

B) $374.04

C) $465.26

D) $494.69

E) $555.66

Answer: C

Response: $23,000 = C [1 -(1 / 1.0065860)] / .00658; C = $465.26

Topic: PRESENT VALUE ANNUITY

33. The monthly mortgage payment on your house is $821.69. It is a 30 year mortgage at 6.5%

compounded monthly. How much did you borrow?

A) $ 85,000

B) $100,000

C) $115,000

D) $130,000

E) $140,000

Answer: D

Response: PVA = $821.69 [1 -(1 / 1.0054360] / .0054 = $130,000

Topic: PRESENT VALUE PERPETUITY

34. You just won the lottery. You and your heirs will receive $40,000 per year forever, beginning one

year from now. What is the present value of your winnings at an 10% discount rate?

A) $ 44,000

B) $300,000

C) $387,500

D) $400,000

E) $437,500

Answer: D

Response: PVP = $40,000 / .10 = $400,000

Topic: PERPETUITY INTEREST RATE

35. You just won the lottery. You and your heirs will receive $40,000 per year forever, beginning one

year from now. If the present value of the lottery is $500,000, what is the discount rate used to value this perpetuity?

A) 6%

B) 7%

C) 8%

D) 9%

E) 10%

Answer: C

Response: $500,000 = $40,000 / r; r = 8%

Topic: PRESENT VALUE PERPETUITY DUE

36. You just won the lottery. You and your heirs will receive $40,000 per year forever, with the first

payment received immediately. What is the present value at a 9% discount rate?

A) $182,500

B) $375,222

C) $400,000

D) $444,444

E) $484,444

Answer: E

Response: PV = $40,000 + $40,000 / .09 = $484,444

Topic: EFFECTIVE ANNUAL RATE

37. What is the effective annual rate of 6% compounded quarterly?

A) 5.37%

B) 6.00%

C) 6.14%

D) 7.50%

E) 24.00%

Answer: C

Response: EAR = [1 + (.06/4)]4 -1 = 6.14%

Topic: EFFECTIVE ANNUAL RATE

38. What is the effective annual rate of 11% compounded semiannually?

A) 11.00%

B) 11.15%

C) 11.30%

D) 11.84%

E) 12.16%

Answer: C

Response: EAR = [1 + (.11/2)]2 -1 = 11.30%

Topic: EFFECTIVE ANNUAL RATE

39. What is the effective annual rate of 10% compounded monthly?

A) 9.27%

B) 10.00%

C) 10.25%

D) 10.38%

E) 10.47%

Answer: E

Response: EAR = [1 + (.10/12)]12 -1 = 10.47%

Topic: EFFECTIVE ANNUAL RATE COMPOUNDING

40. A given rate is quoted as 12% APR, but has an EAR of 12.55%. What is the rate of compounding

during the year?

A) Annually

B) Semiannually

C) Quarterly

D) Monthly

E) Daily

Answer: C

Response: .1255 = [1 + (1 + .12/m)]m -1; m = 4 or quarterly

Topic: FUTURE VALUE ANNUITY DUE

41. What is the future value in 12 years of $800 payments received at the beginning of each year for the

next 12 years? Assume an interest rate of 8.25%.

A) $14,259.63

B) $15,408.65

C) $16,679.86

D) $18,495.48

E) $20,782.15

Answer: C

Response: FVA due = $800 [(1.082512 -1) / .0825] (1.0825) = $16,679.86

Topic: PRESENT VALUE ANNUITY DUE

42. What is the present value of $1,500 payments received at the beginning of each year for the next 10

years? Assume an interest rate of 6.525%.

A) $ 978.75

B) $ 7,093.62

C) $10,770.64

D) $11,473.43

E) $15,000.00

Answer: D

Response: PVA due = $1,500 {[1- (1 / 1.0652510)] / .06525} ( 1.06525) = $11,473.43

Topic: LOAN PAYMENTS

43. Fast Eddie's Used Cars will sell you a 1989 Mazda Miata for $5,000 with no money down. You

agree to make weekly payments for 2 years, beginning one week after you buy the car. The stated rate on the loan is 13%. How much is each payment?

A) $42.96

B) $54.66

C) $68.19

D) $75.90

E) $99.65

Answer: B

Response: $5,000 = C {[1 - (1 / 1.0025104)] / .0025}; C = $54.66

Topic: PRESENT VALUE ANNUITY

44. You win the lottery and are given the option of receiving $250,000 now or an annuity of $25,000 at

the end of each year for 30 years. Which of the following is correct? (Ignore taxes)

A) You cannot choose between the two without first calculating future values.

B) You will always choose the lump regardless of interest rates.

C) You will choose the annuity payment if the interest rate is 7%.

D) You will always choose the annuity.

E) Comparing the future value of the two alternatives will lead to a different decision than you

will reach from a comparison of the present values.

Answer: C

Response: PVA = $25,000 {[1 - (1 / 1.0730)] / .07} = $310,226; choose annuity

Topic: PRESENT VALUE ANNUITY

45. You are going to withdraw $5,000 at the end of each year for the next four years from an account

that pays interest at a rate of 9% compounded annually. How much must there be in the account today in order for the account to reduce to a balance of zero after the last withdrawal?

A) $14,793.83

B) $16,198.60

C) $18,602.29

D) $19,713.75

E) $20,000.00

Answer: B

Response: PVA = $5,000 {[1 - (1 / 1.094)] / .09} = $16,198.60

Topic: PRESENT VALUE ANNUITY

46. You are going to withdraw $5,000 at the end of each year for the next four years from an account

that pays interest at a rate of 9% compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much money will be in the account immediately after the third withdrawal is made?

A) $ 4,587.16

B) $ 4,977.10

C) $ 5,000.00

D) $ 6,982.29

E) $10,000.00

Answer: A

Response: PV = $5,000 / 1.09 = $4,587.16

Topic: ANNUITY INTEREST

47. You are going to withdraw $5,000 at the end of each year for the next four years from an account

that pays interest at a rate of 9% compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much interest will you earn on the account over the four year life?

A) $ 0.00

B) $2,409.60

C) $3,801.40

D) $4,000.00

E) $5,711.20

Answer: C

Response:

PVA = $5,000 {[1 - (1 / 1.094)] / .09} = $16,198.60;

interest = $20,000 - 16,198.60 = $3,801.40

Topic: PRESENT VALUE ANNUITY

48. At the end of each year for the next 8 years you will receive cash flows of $500. If the appropriate

discount rate is 7.5%, how much would you pay for this annuity?

A) $4,000.00

B) $5,841.22

C) $1,259.47

D) $2,928.65

E) $3,148.30

Answer: D

Response: PVA = $500 {[1 - (1 / 1.0758)] / .075} = $2,928.65

Topic: RETURN ON ANNUITY

49. At the end of each year for the next 8 years you will receive cash flows of $500. The initial

investment is $2,500. What rate of return are you expecting from this investment?

A) 11.81%

B) 10.27%

C) 9.01%

D) 8.28%

E) 7.21%

Answer: A

Response: $2,500 = $500 {[1 - 1 / (1 + r)8] / r}; r = 11.81%

Topic: ANNUITY PAYMENT

50. You are considering investing $400 in a 12-year annuity. The rate of return you require is 9%. What

annual cash flow from the annuity will provide the required return?

A) $ 10.77

B) $ 42.96

C) $ 55.86

D) $ 78.31

E) $129.27

Answer: C

Response: $400 = C {[1 - (1 / 1.0912)] / .09}; C = $55.86

Topic: EFFECTIVE ANNUAL RATE

51. You are considering an investment with a quoted return of 10% per year. If interest is compounded

daily, what is the effective return on this investment?

A) 1.11%

B) 10.00%

C) 10.25%

D) 10.47%

E) 10.52%

Answer: E

Response: EAR = [1 + (.10 / 365)]365 -1 = 10.52%

Topic: NUMBER OF PERIODS

52. You borrowed $1,200 at 8% compounded annually. Your payments are $96 at the end of each year.

How many years will you make payments on the loan?

A) 9 years

B) 10 years

C) 11 years

D) 12 years

E) forever

Answer: E

Response:

annual interest = $1,200 x .08 = $96; you are only making interest payments and will never repay the principal

Topic: APR/EAR

53. You agree to loan your parents $32,000 to buy a new van. They agree to pay you $650 a month for

5 years. The ________________.

A) interest rate on the loan is 0.75% per month

B) APR on the loan is 7.87%

C) EAR on the loan is 8.08%

D) APR on the loan is 8.22%

E) EAR on the loan is 8.38%

Answer: E

Response: $32,000 = $650 {[1 - 1 / (1 + r)60] / r}; r = .6730%; EAR = (1 + .006730)12 - 1 = 8.38% Topic: PRESENT VALUE ANNUITY

54. Your brother-in-law borrowed $3,000 from you 5 years ago and then disappeared. Yesterday he

returned and expressed a desire to pay back the loan, including the interest accrued. Assuming that you had agreed to charge him 12%, and assuming that he wishes to make 5 equal annual payments beginning in one year, how much would your brother-in-law have to pay you annually in order to pay off the debt? (Assume that the loan continues to accrue interest at 12% per year.)

A) $ 941.89

B) $1,200.00

C) $1,322.33

D) $1,466.67

E) $3,002.56

Answer: D

Response:

FV = $3,000 (1.12)5 = $5,287.03 is the amount you are currently owed

PVA = $5,287.03 = C {[1 - (1 / 1.125)] / .12}; C = $1,466.67

Topic: PRESENT VALUE ANNUITY

55. A "Name That Tune" contest has a grand prize of $500,000. However, the contest stipulates that the

winner will receive just $200,000 immediately, and $30,000 at the end of each of the next 10 years.

Assuming that one can earn 8% on their money, how much has the contest winner actually won?

A) $250,000.00

B) $309,225.11

C) $365,826.02

D) $401,302.44

E) $500,000.00

Answer: D

Response: PV = $200,000 + 30,000 {[1 - (1 / 1.0810)] / .08} = $401,302.44

Topic: ANNUITY PAYMENT

56. Denzel wishes to save money to provide for his retirement. Beginning one month from now, he will

begin depositing a fixed amount into a retirement savings account that will earn 10% compounded monthly. He will make 420 such deposits. Then, one year after making his final deposit, he will withdraw $75,000 annually for 20 years. The fund will continue to earn 10% compounded monthly.

How much should the monthly deposits be for his retirement plan?

A) $119.11

B) $149.58

C) $162.92

D) $184.89

E) $209.38

Answer: C

Response:

EAR = [1 + (.10 / 12)]12 -1 = 10.47%

PVA = $75,000 {[1 - (1 / 1.104720)] / .1047} = $618,557.45

FVA = $618,557.45 = C [(1.0083420 1) / .0083]; C = $162.92

Topic: COMPARING RATES

57. You have $100,000 to invest. Your bank offers one-year certificates of deposit with a stated rate of

3.50% compounded quarterly. What rate compounded semiannually would provide you with the

same amount of money at the end of one year?

A) 3.485%

B) 3.500%

C) 3.505%

D) 3.510%

E) 3.515%

Answer: E

Response:

EAR = [1 + (.035 / 4)]4 -1 = 3.5462%; EAR = .035462 = [1 + (r / 2)]2 -1; r = 3.5153%

Topic: ANNUAL PERCENTAGE RATE

58. Vito Corleone will loan you money on a "four-for-five" arrangement; i.e., for every $4 he gives you

today, you give him $5 one week from now. What is the APR of this loan?

A) 250%

B) 869%

C) 1,000%

D) 1,300%

E) 1,800%

Answer: D

Response: $5 = $4 (1 + r); r = 25% per week; APR = 25% x 52 = 1,300%

Topic: EFFECTIVE ANNUAL RATE

59. Vito Corleone will loan you money on a "four-for-five" arrangement; i.e., for every $4 he gives you

today, you give him $5 one week from now. What is the EAR of this loan?

A) 250%

B) 869%

C) 1,095%

D) 109,475%

E) 10,947,544%

Answer: E

Response:

$5 = $4 (1 + r); r = 25% per week; APR = 25% x 52 = 1,300%

EAR = [1 + (13 / 52)]52 -1 = 10,947,544%

Topic: PRESENT VALUE PERPETUITY

60. You own a bond issued by the Canadian Pacific railroad that promises to pay the holder $50

annually forever. You plan to sell the bond 10 years from now. If similar investments yield 7% at that time, how much will the bond be worth?

A) $350.00

B) $592.17

C) $714.29

D) $825.00

E) $938.44

Answer: C

Response: PVP = $50 / .07 = $714.29

Topic: COMPARING PRESENT VALUES

61. Moe purchases a $50, 30-year annuity. Larry purchases a $50 perpetuity. In both cases, payments

begin in one year, and the appropriate interest rate is 12.5%. What is the present value of Larry's payments that will occur from year 31 onwards?

A) $ 11.68

B) $ 68.11

C) $ 91.27

D) $124.40

E) More than $150

Answer: A

Response:

PVP = $50 / .125 = $400; PVA = $50 {[1 - (1 / 1.12530)] / .125} = $388.32; difference = $11.68

Topic: COMPARING PRESENT VALUES

62. Moe purchases a $50 annual perpetuity for which payments begin in one year. Larry purchases a

$50 annual perpetuity for which payments begin immediately. If a 12.5% interest rate is

appropriate for both cash flow streams, which of the following statements is true?

A) Moe's perpetuity is worth $50 more than Larry's.

B) Larry's perpetuity is worth $50 more than Moe's.

C) The perpetuities are of equal value today.

D) Larry's perpetuity is worth $44.44 more than Moe's.

E) Moe's perpetuity is worth $44.44 more than Larry's.

Answer: B

Response: Moe: PVP = $50 / .125 = $400; Larry: PV = $50 + 50 / .125 = $450

Topic: PRESENT VALUE ANNUITY DUE

63. In order to help you through college, your parents just deposited $20,000 into a bank account

paying 6% interest. Starting tomorrow, you plan to withdraw equal amounts from the account at the beginning of each of the next four years. What is the MOST you can withdraw annually?

A) $5,136.91

B) $5,445.12

C) $5,771.83

D) $6,101.88

E) $6,395.88

Answer: B

Response: PVA due = $20,000 = C {[1 - (1 / 1.064)] / .06} (1.06); C = $5,445.12

Topic: PRESENT VALUE ANNUITY

64. In order to help you through college, your parents just deposited $20,000 into a bank account

paying 6% interest. Starting next year, you plan to withdraw equal amounts from the account at the end of each of the next four years. What is the MOST you can withdraw annually?

A) $5,136.91

B) $5,445.12

C) $5,771.83

D) $6,101.88

E) $6,395.88

Answer: C

Response: PVA = $20,000 = C {[1 - (1 / 1.064)] / .06}; C = $5,771.83

Topic: PRESENT VALUE OF UNEVEN CASH FLOWS

65. Analysts expect Placer Corp. to pay shareholders $2.25 per share annually for the next five years.

After that, the dividend will be $3.50 annually forever. Given a discount rate of 12%, what is the value of the stock today?

A) $16.55

B) $19.87

C) $22.37

D) $24.66

E) $27.88

Answer: D

Response:

PVP = $3.50 / .12 = $29.17; PV = $29.17 / 1.125 = $16.55

PVA = $2.25 {[1 - (1 / 1.125)] / .12} = $8.11; Price = $16.55 + 8.11 = $24.66

Topic: PERPETUITY RETURN

66. The preferred stock of Placer Corp. currently sells for $44.44 per share. The annual dividend of $4

is fixed. Assuming a constant dividend forever, what is the rate of return on this stock?

A) 7.0%

B) 8.0%

C) 9.0%

D) 10.0%

E) 11.0%

Answer: C

Response: $44.44 = $4 / r; r = 9.0%

Topic: EAR LOAN RATE

67. Fast Eddie's Used Cars will sell you a 1989 Mazda Miata for $5,000 with no money down. You

agree to make weekly payments of $60.00 for 2 years, beginning one week after you buy the car.

What is the EAR of this loan?

A) 20.04%

B) 22.85%

C) 25.61%

D) 32.34%

E) 43.01%

Answer: C

Response:

$5,000 = $60 {[1 - 1 / (1 + r)104] / r}; r = .4394%; APR = .4394 x 52 = 22.85%

EAR = (1 + .004394)52 - 1 = 25.61%

Topic: PRESENT VALUE ANNUITY DUE WITH EAR

68. What is the present value of $600 payments received at the beginning of each year for the next 10

years? Assume an interest rate of 8% compounded monthly.

A) $3,069.13

B) $3,972.13

C) $4,026.05

D) $4,301.82

E) $4,955.26

Answer: D

Response:

EAR = [1 + (.08/12)]12 -1 = 8.30%

PVA due = $600 {[1 - (1 / 1.08310)] / .083} (1.083) = $4,301.82

Topic: PRESENT VALUE PERPETUITY

69. Five years from now you will begin to receive cash flows of $125 per year. These cash flows will

continue forever. If the discount rate is 10%, what is the present value of these cash flows?

A) $ 776.15

B) $ 853.77

C) $ 934.07

D) $1,136.36

E) $1,250.00

Answer: B

Response: PVP = $125 / .1 = $1,250; PV = $1,250 / (1.1)4 = $853.77

Topic: MULTIPLE RATES

70. Four years from now you will receive the first of seven annual $6,000 payments. The current

interest rate is 8%, but by the beginning of year 4, the rate will rise to 10%. What is the present value of this cash flow stream?

A) $18,770.49

B) $21,946.29

C) $23,617.66

D) $26,131.56

E) $32,131.56

Answer: C

Response:

PV = $6,000 + 6,000 {[1 - (1 / 1.16)] / .01} = $32,131.56 at t = 4

PV = $32,131.56 / 1.084 = $23,617.66