Ch2 Test Questions & Answers How To Calculate Present Values

Principles of Corporate Finance, 13e (Brealey)

Chapter 2 How to Calculate Present Values

1) The present value of $100 expected two years from today at a discount rate of 6 percent is

A) $112.36.

B) $106.00.

C) $100.00.

D) $89.00.

2) Present value is defined as:

A) future cash flows discounted to the present by an appropriate discount rate.

B) inverse of future cash flows.

C) present cash flows compounded into the future.

D) future cash flows multiplied by the factor (1 + r)t.

3) If the annual interest rate is 12 percent, what is the two-year discount factor?

A) 0.7972

B) 0.8929

C) 1.2544

D) 0.8065

4) If the present value of cash flow X is $240, and the present value of cash flow Y is $160, then the present value of the combined cash flows is:

A) $240.

B) $160.

C) $80.

D) $400.

5) The rate of return is also called the:

A) discount rate.

B) discount rate and hurdle rate only.

C) discount rate, hurdle rate, and opportunity cost of capital.

D) discount rate and opportunity cost of capital only.

6) The present value of $121,000 expected one year from today at an interest rate (discount rate) of 10 percent per year is:

A) $121,000.

B) $100,000.

C) $110,000.

D) $108,900.

7) The one-year discount factor, at a discount rate of 25 percent per year, is:

A) 1.25.

B) 1.0.

C) 0.8.

D) 0.75.

8) The one-year discount factor, at an interest rate of 100 percent per year, is:

A) 1.50.

B) 0.50.

C) 0.25.

D) 1.00.

9) The present value of $100,000 expected at the end of one year, at a discount rate of 25 percent per year, is:

A) $80,000.

B) $125,000.

C) $100,000.

D) $75,000.

10) If the one-year discount factor is 0.8333, what is the discount rate (interest rate) per year?

A) 10 percent

B) 20 percent

C) 30 percent

D) 40 percent

11) If the present value of $480 to be paid at the end of one year is $400, what is the one-year discount factor?

A) 0.8333

B) 1.20

C) 0.20

D) 1.00

12) If the present value of $250 expected one year from today is $200, what is the one-year discount rate?

A) 10 percent

B) 20 percent

C) 25 percent

D) 30 percent

13) If the one-year discount factor is 0.90, what is the present value of $120 expected one year from today?

A) $100

B) $96

C) $108

D) $133

14) If the present value of $600, expected one year from today, is $400, what is the one-year discount rate?

A) 15 percent

B) 20 percent

C) 25 percent

D) 50 percent

15) The present value formula for a cash flow expected one period from now is:

A) PV = C1 × (1 + r).

B) PV = C1/(1 + r).

C) PV = C1/r.

D) PV = (1 + r)/C1.

16) The net present value formula for one period is:

A) NPV = C0 + [C1/(1 + r)].

B) NPV = PV required investment.

C) NPV = C0/C1.

D) NPV = C1/C0.

17) An initial investment of $400,000 is expected to produce an end-of-year cash flow of $480,000. What is the NPV of the project at a discount rate of 20 percent?

A) $176,000

B) $80,000

C) $0 (zero)

D) $64,000

18) If the present value of a cash flow generated by an initial investment of $200,000 is $250,000, what is the NPV of the project?

A) $250,000

B) $50,000

C) $200,000

D) -$50,000

19) What is the present value of the following cash flows at a discount rate of 9 percent?

A) $372,431.81

B) $450,000.00

C) $405,950.68

D) $412,844.04

20) At an interest rate of 10 percent, which of the following sequences of cash flows should you prefer?

A) Option A

B) Option B

C) Option C

D) Option D

21) What is the net present value of the following cash flow sequence at a discount rate of 11 percent?

A) $69,108.03

B) $231,432.51

C) $80,000.00

D) $88,000.00

22) What is the net present value of the following sequence of annual cash flows at a discount rate of 16 percent APR?

A) $136,741.97

B) $122,948.87

C) $158,620.69

D) $139,418.23

23) What is the net present value (NPV) of the following sequence of cash flows at a discount rate of 9 percent?

A) $122,431.81

B) $200,000.00

C) $155,950.68

D) $177,483.77

24) Which of the following statements regarding the NPV rule and the rate of return rule is false?

A) Accept a project if its NPV > 0.

B) Reject a project if the NPV < 0.

C) Accept a project if its rate of return > 0.

D) Accept a project if its rate of return > opportunity cost of capital.

25) An initial investment of $500 produces a cash flow of $550 one year from today. Calculate the rate of return on the project.

A) 10 percent

B) 15 percent

C) 20 percent

D) 25 percent

26) According to the net present value rule, an investment in a project should be made if the:

A) net present value is greater than the cost of investment.

B) net present value is greater than the present value of cash flows.

C) net present value is positive.

D) net present value is negative.

27) Which of the following statements regarding the net present value rule and the rate of return rule is false?

A) Accept a project if NPV > cost of investment.

B) Accept a project if NPV is positive.

C) Accept a project if return on investment exceeds the rate of return on an equivalent-risk investment in the financial market.

D) Reject a project if NPV is negative.

28) The opportunity cost of capital for a risky project is:

A) the expected rate of return on a government security having the same maturity as the project.

B) the expected rate of return on a well-diversified portfolio of common stocks.

C) the expected rate of return on a security of similar risk as the project.

D) the expected rate of return on a typical bond portfolio.

29) A perpetuity is defined as a sequence of:

A) equal cash flows occurring at equal intervals of time for a specific number of periods.

B) equal cash flows occurring at equal intervals of time forever.

C) unequal cash flows occurring at equal intervals of time forever.

D) unequal cash flows occurring at equal intervals of time for a specific number of periods.

30) Which of the following is generally considered an example of a perpetuity?

A) Interest payments on a 10-year bond

B) Interest payments on a 30-year bond

C) Interest payments on a consol

D) Interest payments on government bonds

31) You would like to have enough money saved after your retirement such that you and your heirs can receive $100,000 per year in perpetuity. How much would you need to have saved at the time of your retirement in order to achieve this goal? (Assume that the perpetuity payments start one year after the date of your retirement. The annual interest rate is 12.5 percent.)

A) $1,000,000

B) $10,000,000

C) $800,000

D) $1,125,000

32) What is the present value of $10,000 per year in perpetuity at an annual interest rate of 10 percent? Assume the perpetuity starts in one year.

A) $10,000

B) $100,000

C) $200,000

D) $1,000

33) You would like to have enough money saved to receive $80,000 per year in perpetuity after retirement for you and your heirs. How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start one year from the date of your retirement. The annual interest rate is 8 percent.)

A) $7,500,000

B) $750,000

C) $1,000,000

D) $800,000

34) You would like to have enough money saved to receive a $50,000 per year perpetuity after retirement. How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start on the day of your retirement. The annual interest rate is 8 percent.)

A) $1,000,000

B) $675,000

C) $625,000

D) $500,000

35) You would like to have enough money saved to receive an $80,000 per year perpetuity after retirement. How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start on the day of your retirement. The annual interest rate is 10 percent.)

A) $1,500,000

B) $880,000

C) $800,000

D) $80,000

36) An annuity is defined as a set of:

A) equal cash flows occurring at equal intervals of time for a specified period.

B) equal cash flows occurring at equal intervals of time forever.

C) unequal cash flows occurring at equal intervals of time forever.

D) unequal cash flows occurring at equal intervals of time for a specified period.

37) If you are paid $1,000 at the end of each year for the next five years, what type of cash flow did you receive?

A) Uneven cash flow stream

B) An annuity

C) An annuity due

D) A perpetuity

38) If the three-year present value annuity factor is 2.673 and the two-year present value annuity factor is 1.833, what is the present value of $1 received at the end of the three years?

A) $1.19

B) $0.84

C) $0.89

D) $0.92

39) If the five-year present value annuity factor is 3.60478 and the four-year present value annuity factor is 3.03735, what is the present value of the $1 received at the end of five years?

A) $0.63552

B) $1.76233

C) $0.56743

D) $1.2132

40) What is the eight-year present value annuity factor at a discount rate of 11 percent?

A) 5.7122

B) 11.8594

C) 5.1461

D) 6.9158

41) What is the six-year present value annuity factor at an interest rate of 9 percent?

A) 7.5233

B) 4.4859

C) 1.6771

D) 3.1432

42) What is the present value of a $1,000 per year annuity for five years at an interest rate of 12 percent?

A) $6,352.85

B) $3,604.78

C) $567.43

D) $2,743.28

43) What is the present value of a six-year, $5,000 per year annuity at a discount rate of 10 percent?

A) $21,776.30

B) $3,371.91

C) $16,760.78

D) $18,327.82

44) After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income, if the annual interest rate is 9 percent per year? (Assume that the payments start on the day of your retirement.)

A) $736,693.47

B) $802,995.88

C) $2,043,750.21

D) $1,427,831.93

45) After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income if the annual interest rate is 9 percent per year? (Assume that the payments start one year after your retirement.)

A) $736,693.47

B) $83,431.17

C) $1,875,000

D) $1,213,487.12

46) For $10,000, you can purchase a five-year annuity that will pay $2,504.57 per year for five years. The payments occur at the end of each year. Calculate the effective annual interest rate implied by this arrangement.

A) 8 percent

B) 9 percent

C) 10 percent

D) 11 percent

47) If the present value annuity factor for 10 years at 10 percent interest rate is 6.1446, what is the present value annuity factor for an equivalent annuity due?

A) 6.1446

B) 7.3800

C) 6.7590

D) 5.7321

48) If the present value annuity factor is 3.8896, what is the present value annuity factor for an equivalent annuity due if the interest rate is 9 percent?

A) 3.5684

B) 4.2397

C) 3.8896

D) 5.3127

49) For $10,000, you can purchase a five-year annuity that will pay $2,358.65 per year for five years. The payments occur at the beginning of each year. Calculate the effective annual interest rate implied by this arrangement.

A) 8 percent

B) 9 percent

C) 10 percent

D) 11 percent

50) John House has taken a $250,000 mortgage on his house at an interest rate of 6 percent per year. If the mortgage calls for 20 equal, annual payments, what is the amount of each payment?

A) $21,796.14

B) $10,500.00

C) $16,882.43

D) $24,327.18

51) John House has taken a 20-year, $250,000 mortgage on his house at an interest rate of 6 percent per year. What is the remaining balance (or value) of the mortgage after the payment of the fifth annual installment?

A) $128,958.41

B) $211,689.53

C) $141,019.50

D) $248,719.21

52) If the present value of $1 received n years from today at an interest rate of r is 0.3855, then what is the future value of $1 invested today at an interest rate of r percent for n years?

A) $1.3855

B) $2.594

C) $1.701

D) Not enough information is given to solve the problem.

53) If the present value of $1 received n years from today at an interest rate of r is 0.621, then what is the future value of $1 invested today at an interest rate of r% for n years?

A) $1.000

B) $1.610

C) $1.621

D) Not enough information is given to solve the problem.

54) If the future value of $1 invested today at an interest rate of r percent for n years is 9.6463, what is the present value of $1 to be received in n years at r percent interest rate?

A) $9.6463

B) $1.0000

C) $0.1037

D) $0.4132

55) If the future value annuity factor at 10 percent and five years is 6.1051, calculate the equivalent present value annuity factor:

A) 6.1051

B) 3.7908

C) 6.7156

D) 4.8127

56) If the present value annuity factor at 10 percent for 10 years is 6.1446, what is the equivalent future value annuity factor?

A) 3.1080

B) 15.9375

C) 2.5937

D) 8.4132

57) If the present value annuity factor at 12 percent for five years is 3.6048, what is the equivalent future value annuity factor?

A) 2.0455

B) 6.3529

C) 1.7623

D) 5.1237

58) If the present value annuity factor at 8 percent for 10 years is 6.71, what is the equivalent future value annuity factor?

A) 3.108

B) 14.486

C) 2.159

D) 5.384

59) You are considering investing in a retirement fund that requires you to deposit $5,000 per year, and you want to know how much the fund will be worth when you retire. What financial technique should you use to calculate this value?

A) Future value of a single payment

B) Future value of an annuity

C) Present value of an annuity

D) Present value of a perpetuity

60) Mr. Hopper expects to retire in 25 years, and he wishes to accumulate $750,000 in his retirement fund by that time. If the interest rate is 10 percent per year, how much should Mr. Hopper put into his retirement fund each year in order to achieve this goal? (Assume that he makes payments at the end of each year.)

A) $4,559.44

B) $2,500

C) $7,626.05

D) $8,418.29

61) Mr. Hopper expects to retire in 30 years, and he wishes to accumulate $1,000,000 in his retirement fund by that time. If the interest rate is 12 percent per year, how much should Mr. Hopper put into his retirement fund at the end of each year in order to achieve this goal?

A) $4,143.66

B) $8,287.32

C) $4,000.00

D) $12,483.17

62) You would like to have enough money saved to receive a growing annuity for 20 years, growing at a rate of 5 percent per year, with the first payment of $50,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? The interest rate is 10 percent.

A) $1,000,000.00

B) $425,678.19

C) $605,604.20

D) $827,431.28

63) You would like to have enough money saved to receive a growing annuity for 25 years, growing at a rate of 4 percent per year, with the first payment of $60,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? The interest rate is 12 percent.

A) $1,500,000.00

B) $632,390

C) $452,165

D) $1,043,287

64) The managers of a firm can maximize stockholder wealth by:

A) taking all projects with positive NPVs.

B) taking all projects with NPVs greater than the cost of investment.

C) taking all projects with NPVs greater than the present value of cash flows.

D) taking only the highest NPV project each year.

65) If you invest $100 at 12 percent for three years, how much would you have at the end of three years using compound interest?

A) $136

B) $140.49

C) $240.18

D) $173.18

66) Which of the following statements is true?

A) The process of discounting is the inverse of the process of compounding.

B) Ending balances using simple interest are always greater than ending balances using compound interest at positive interest rates.

C) The present value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates.

D) The future value of an annuity due is always less than the present value of an equivalent ordinary annuity at positive interest rates.

67) The concept of compound interest is best described as:

A) interest earned on an investment.

B) the total amount of interest earned over the life of an investment.

C) interest earned on interest.

D) the inverse of simple interest.

68) Ms. Colonial has just taken out a $150,000 mortgage at an interest rate of 6 percent per year. If the mortgage calls for equal monthly payments for 20 years, what is the amount of each payment? (Assume monthly compounding or discounting.)

A) $1,254.70

B) $1,625.00

C) $1,263.06

D) $1,074.65

69) An investment having a 10.47 percent effective annual rate (EAR) has what APR? (Assume monthly compounding.)

A) 10.99 percent

B) 9.57 percent

C) 10.00 percent

D) 8.87 percent

70) An investment at 12 percent APR compounded monthly is equal to an effective annual rate of:

A) 12.68 percent.

B) 12.36 percent.

C) 12.00 percent.

D) 11.87 percent.

71) Mr. Williams expects to retire in 30 years and would like to accumulate $1 million in his pension fund. If the annual interest rate is 12 percent, how much should Mr. Williams put into his pension fund each month in order to achieve his goal? (Assume that Mr. Williams will deposit the same amount each month into his pension fund, using monthly compounding.)

A) $286.13

B) $771.60

C) $345.30

D) $437.13

72) An investment at 10 percent compounded continuously has an equivalent annual rate of:

A) 10.250 percent.

B) 10.517 percent.

C) 10.381 percent.

D) none of the options.

73) The present value of a $100 per year perpetuity at 10 percent per year interest rate is $1,000. What would be the present value of this perpetuity if the payments were compounded continuously?

A) $1,000.00

B) $1,049.21

C) $1,024.40

D) $986.14

74) You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly four more years. Assuming an 8 percent annual interest rate, what is the value of this trust?

A) $918,787

B) $992,290

C) $1,000,000

D) $1,250,000

75) You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly four more years. Assuming a 10 percent annual interest rate, what is the value of this trust?

A) $683,013

B) $751,315

C) $1,000,000

D) $1,100,000

76) You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly five more years. Assuming an 8 percent annual interest rate, what is the value of this trust?

A) $850,729

B) $918,787

C) $1,000,000

D) $1,250,000

77) You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly five more years. Assuming a 10 percent annual interest rate, what is the value of this trust?

A) $620,921

B) $683,013

C) $1,000,000

D) $1,100,000

78) The rate of return, discount rate, hurdle rate, and opportunity cost of capital all have the same meaning.

79) A dollar today is worth more than a dollar tomorrow if the interest rate is positive.

80) One can find the present value of a future cash flow by dividing it by an appropriate discount factor.

81) One can find a project's net present value by subtracting the present value of its required investment from the present value of its future cash flows.

82) The opportunity cost of capital is higher for safe investments than for risky ones.

83) A safe dollar is always worth less than a risky dollar because the rate of return on a safe investment is generally low and the rate of return on a risky investment is generally high.

84) "Accept investments that have positive net present values" is called the net present value rule.

85) Generally, one should accept investments that offer rates of return in excess of their opportunity costs of capital.

86) The rate of return on any perpetuity is equal to its cash flow multiplied by its price.

87) An annuity is an asset that pays a fixed amount each period for a specified number of periods.

88) The value of a five-year annuity is equal to the sum of two perpetuities. One makes its first payment in year 1, and the other makes its first payment in year 6.

89) An equal-payment home mortgage is an example of an annuity.

90) In the amortization of a mortgage loan with equal payments, the fraction of each payment devoted to interest steadily increases over time and the fraction devoted to reducing the loan balance decreases steadily.

91) The present value of a growing perpetuity, with cash flow C1 occurring one year from now, is given by: [C1/(r - g)], where r > g.

92) Briefly explain the term discount rate.

93) Intuitively explain the concept of present value.

94) State the net present value rule.

95) Briefly explain the concept of risk.

96) State the rate of return rule.

97) Define the term perpetuity.

98) Describe how you would go about finding the present value of any annuity given the formula for the present value of a perpetuity.

99) What is the difference between simple interest and compound interest?

100) Briefly explain continuous compounding.