Chapter 11 Test Bank Answers Time Value Of Money

Chapter 11

Time Value of Money

MATCHING

1. Match the following terms with the descriptions below.

A. Business risk

B. Expected rate of return

C. Inflation risk

D. Liquidity risk

E. Rate of return

F. Return of investment

G. Return on investment

H. Risk

I. Risk-free rate of return

J. Risk premium

_____ 1. Return of the amount initially invested

_____ 2. The chance that an investment cannot be quickly converted to cash

_____ 3. A rate of return generated by an investment when there is virtually no chance

that the return will not be generated

_____ 4. The risk that a business will not continue to operate

_____ 5. A measure of an investment’s performance on a common size basis

_____ 6. Money received in excess of an initial investment

_____ 7. An increase in the rate of return expected by an investor for assuming greater

investment risk

_____ 8. The chance of a decline in the purchasing power of the monetary unit during

the time money is invested

_____ 9. Exposure to the chance that an unfavorable outcome will occur at some future

point in time

_____10. A summary measure of an investment’s performance, stated as a percentage,

based on the possible rates of return and on the likelihood of those rates of

return occurring

2. Match the following terms with the description below.

A. Annuity

B. Compound interest

C. Compounding

D. Future value of an annuity

E. Future value of the amount of $1

F. Present value of an annuity

G. Present value of the amount of $1

H. Simple interest

_____ 1. The amount of money that, if invested at some rate of interest today, will

generate a set number of equal periodic payments that are made over equal

time interval

_____ 2. Interest borrowed only on the amount borrowed

_____ 3. A series of equal payments made over equal time periods

_____ 4. The amount that $1 becomes at a future date, if invested at a specified annual

interest rate and compounded a certain number of times per year over the

investment period

_____ 5. Interest that is based on a principal amount that includes interest from

previous time periods

_____ 6. The amount of money that accumulates at some future date as a result of

making equal payments over equal intervals of time and earning a specified

rate of interest over that time period

_____ 7. The process of adding interest to principal for purposes of interest calculation.

_____ 8. The amount that, if invested today at some compound interest rate for a

specified period of time, will equal $1 at the end of that time period.

4. When an investment loses money, the amount of money lost is called a(n):

A) return on investment.

B) return of investment.

C) investment risk.

D) investment casualty.

5. A measure of the performance of investments on a common-size basis, which eliminates the distortion caused by the size of the initial investment, is referred to as the:

A) rate of return.

B) risk premium ratio.

C) return of capital.

D) rate of inflation.

6. The rate of return is calculated as:

A) (dollar amount of average investment) × (dollar amount of return).

B) (present value of $1)/(dollar amount of average investment).

C) (dollar amount of return)/(dollar amount of initial investment).

D) (future value of $1) × (dollar amount of initial investment).

7. Adam Gross invested $2,500 on July 1, 2009, and in return he received a total of $2,850, which he collected on July 1, 2010. The rate of return on Adam’s investment was:

A) 13.1 percent.

B) 12.3 percent.

C) 7.1 percent.

D) 14.0 percent.

8. Vladimir Boscak invested $35,000 on March 1, 2009, and in return he received a total of $39,600, which he collected on March 1, 2010. The rate of return on Vladimir’s investment was:

A) 11.6 percent.

B) 13.1 percent.

C) 12.3 percent.

D) 7.6 percent.

10. Dan Short invested $7,000 on October 1, 2009, and in return he received a total of $6,200, which he collected on October 1, 2010. The rate of return on Dan’s investment was:

A) (12.9 percent).

B) 12.9 percent.

C) 11.4 percent.

D) (11.4 percent).

11. Ivan Valentine made $4,000 on an investment that yielded an 8 percent return after 1 year.

How much did Ivan invest?

A) $40,000

B) $50,000

C) $60,000

D) $70,000

12. Yar Ebadi lost $5,000 on an investment that represented a 10 percent negative rate of

return after one year. How much did Yar invest?

A) $55,000

B) $45,000

C) $50,000

D) Cannot be determined given the information available

13. Ople Brown made an investment on November 1, 2009 that yielded $15,000 and a

10 percent return on November 1, 2010. How much did Ople invest?

A) $150,000

B) $140,000

C) $160,000

D) $155,000

14. A summary measure of an investment’s projected performance based on the possible rates of return and the likelihood of those rates of return occurring is called the:

A) inflation rate of return.

B) relative risk rate of return.

C) expected rate of return.

D) risk-free rate of return.

15. Sphinx Enterprises is contemplating investing in a copper mine. An investment of $750,000 would be made for one year with the following potential outcomes:

The expected rate of return for this investment is:

A) 22.0 percent.

B) 15.5 percent.

C) 62.0 percent.

D) 8.3 percent.

16. Bobby Bell has $500,000 and is considering investing in a project that would yield the following returns one year from today:

The expected return for this investment is:

A) $57,000.

B) $45,000.

C) $17,000.

D) $32,000.

17. Bobby Bell has $500,000 and is considering investing in a project that would yield the following returns one year from today:

The expected rate of return for this investment is:

A) 11.4 percent.

B) 9 percent.

C) 3.4 percent.

D) 6.4 percent.

18. All of the following are primary risk factors that generate risk premiums except:

A) inflation risk.

B) business risk.

C) relative risk.

D) liquidity risk.

19. Interest calculated only on the amount borrowed is referred to as:

A) compound interest.

B) risk-free interest.

C) inflation interest.

D) simple interest.

20. In compound interest calculations, as the frequency of compounding increases, the

A) total amount of interest decreases .

B) annual interest rate increases.

C) total amount of interest increases.

D) the interest rate decreases.

21. Which of the following is NOT true about compound interest?

A) As the number of compoundings increases, the annual effective interest rate increases.

B) As the number of compoundings increases, the incremental amount of interest

increases.

C) As the number of compoundings increases, the total amount of interest increases.

D) As the number of compoundings increases the interest rate remains the same.

22. Art Burtscher has a choice of investing $10,000 at either 5 percent simple interest or 5 percent compound interest that is compounded annually. What will be the difference between the total amount of interest earned after two years?

A) No difference

B) $25

C) $50

D) $100

23. The future value of a $7,000 investment at the end of 4 years with an interest rate of 6 percent compounded annually is:

A) $8,680.00.

B) $8,837.50.

C) $5,544.70.

D) $8,867.60.

24. In compound interest calculations, as the frequency of compounding decreases, the:

A) total amount of interest decreases.

B) interest rate increases.

C) total amount of interest increases.

D) the interest rate decreases.

25. Mary Fagan invested $6,500 in a bank account that pays interest at the rate of 8 percent compounded annually. If Fagan makes no withdrawals, the account balance after 5 years will be:

A) $9,550.45.

B) $9,100.00.

C) $4,423.90.

D) $9,603.75.

26. The future value of a $4,800 investment at the end of 4 years with an interest rate of 10 percent compounded semiannually is:

A) $7,092.00.

B) $6,720.00.

C) $7,027.68.

D) $3,248.64.

27. The future value of an $11,600 investment at the end of 5 years with an interest rate of 12 percent compounded quarterly is:

A) $20,442.68.

B) $18,560.00.

C) $20,950.89.

D) $ 6,581.84.

28. Kelly Smith deposited $8,500 in an account that pays interest at the rate of 8 percent compounded quarterly. At the end of 3 years, Smith will have:

A) $10,540.00.

B) $10,780.05.

C) $ 6,747.30.

D) $10,707.45.

29. Bruce Derr invested $25,000 in an account that pays interest at a rate of 7 percent that is

compounded monthly. At the end of 4 years how much will Bruce have?

A) $26,796.47.

B) $33,051.35.

C) $26,015.10.

D) $32,998.23.

30. The future value of a $20,000 investment at the end of 7 years, assuming 9 percent simple interest, is:

A) $ 36,560.00.

B) $ 32,600.00.

C) $ 10,940.00.

D) $184,008.00.

31. What is the difference in the future value of $10,000 in 5 years if it is invested at 7 percent simple interest or invested at 7 percent compounded semiannually?

A) $605.88

B) $525.52

C) $6,171.51

D) No difference

32. The present value of $13,000 received 7 years from today, assuming an interest rate of 5 percent compounded annually is:

A) $ 9,269.00.

B) $18,292.30.

C) $17,550.00.

D) $ 9,238.85.

33. What is the present value of $2,000 received nine years from today, assuming an interest rate of 8 percent compounded semiannually?

A) $987.26

B) $12,493.80

C) $ 3,998.00

D) $ 1,000.40

34. How will the present value of a future amount be affected if the interest rate is lowered?

A) The present value will increase.

B) The present value will decrease.

C) The present value will not change.

D) Must know the amount of the future value before this can be answered.

35. How will the present value of a future amount be affected if the number of compounding increases?

A) The present value will increase.

B) The present value will decrease.

C) The present value will not change.

D) Must know the amount of the future value before this can be answered.

36. Steve MacIntosh would like to have $20,000 in 5 years’ time to start his own business. The amount that MacIntosh would have to invest today, assuming an interest rate of 8 percent compounded quarterly, in order to reach his goal is:

A) $13,612.00.

B) $29,386.00.

C) $79,854.00.

D) $13,459.43.

37. If $10,000 was invested 6 years ago and has now grown to $15,007, the rate of interest earned, assuming the interest rate was compounded annually, was:

A) 8.3 percent.

B) 2.5 percent.

C) 7.0 percent.

D) cannot be determined from the information given

38. Assuming an 8 percent interest rate, the dollar amount available on June 1, 2016, resulting from seven annual deposits of $3,500 each with the first deposit made on June 1, 2010, is:

A) $18,222.40.

B) $31,229.81.

C) $41,988.10.

D) $30,498.30.

39. Ishvar Patel is going to make five annual deposits of $4,500 each into a savings account beginning on July 1, 2010. Assuming an interest rate of 6 percent, on July 1, 2014, Ishvar’s bank account will have a balance of:

A) $28,521.90.

B) $30,608.55.

C) $18,955.80.

D) $25,366.92.

40. When calculating the present or future value of an annuity we assume:

A) the number of compoundings each year is independent of the payments per year.

B) the number of compoundings per year is equal to the number of payments per year.

C) the number of compoundings depends on the size of the payment.

D) the number of compoundings depends on the annual interest rate.

41. The present value on January 1, 2010 of eight annual payments of $7,500 each with the first payment to be made on January 1, 2011, assuming a 9 percent interest rate is:

A) $63,764.25.

B) $41,511.14.

C) $30,114.00.

D) $82,713.75.

42. Terry Lampron wishes to make eight annual withdrawals of $3,000 each beginning on May 1, 2011. Assuming a 4 percent interest rate, on May 1, 2010, Lampron must deposit an amount of money equal to:

A) $20,198.23.

B) $27,642.60.

C) $26,192.10.

D) $ 9,936.30.

43. Southland, Inc. has just borrowed $50,000 to purchase a delivery truck. The contract calls for four annual payments of $15,773.54, beginning one year from today. The annual interest rate Southland is paying equals

A) 8 percent.

B) 12 percent.

C) 10 percent.

D) cannot be determined from the information given.

44. Midwest, Inc. has just borrowed $100,000 to purchase a new piece of equipment. The contract calls for 10 semiannual payments of $12,637.88, beginning six months from today. The annual interest rate Southland is paying equals:

A) 9 percent.

B) 12 percent.

C) 10 percent.

D) cannot be determined from the information given.

45. Tanya Wagner plans to make annual deposits of $7,674.36 until she has accumulated $50,000. Assuming she earns 7 percent on her investment, Wagner will need to make a total of:

A) nine payments.

B) seven payments.

C) six payments.

D) cannot be determined from the information given.

46. Gina’s Fashion plans to make semiannual deposits of $1,963.64 until she has accumulated $72,000. Assuming she earns 7 percent on her investment, Wagner will need to make a total of:

A) 12 payments

B) 36 payments

C) 24 payments

D) cannot be determined from the information given

47. If you are loaning money, which of the following would you prefer?

A) Interest compounded semiannually

B) Interest compounded quarterly

C) Interest compounded monthly

D) Simple interest

48. If compounding is changed from an annual to a semiannual basis, what happens to future value and present value?

Future value Present value

A) Decreases Decreases

B) Decreases Increases

C) Increases Decreases

D) Increases Increases

49. Which of the following should be used to compute the monthly payments on a home loan?

A) Future value of an annuity of $1 per period

B) Present value of an annuity of $1 per period

C) Future value of the amount of $1 at compound interest

D) Present value of the amount of $1 at compound interest

50. You have just purchased a new BMW for $40,000 to determine your monthly payments which of the following would you use?

A) Future value of an annuity of $1 per period

B) Present value of an annuity of $1 per period

C) Future value of the amount of $1 at compound interest

D) Present value of the amount of $1 at compound interest

51. On January 1, 2008, BP Company purchased equipment on a three-year note. To determine the amount at which to record the machine, the three annual year-end payments must be calculated by using the:

A) present value of an annuity of $1 per period.

B) future value of an annuity of $1 per period.

C) present value of the amount of $1.

D) future value of the amount of $1.

52. You want to have $50,000 in a savings account 8 years from today and you are going to make payments every month to achieve this goal. To determine the amount of monthly payments you have to make starting today, you will need to use which of the following?

A) Present value of an annuity of $1 per period

B) Future value of an annuity of $1 per period

C) Present value of the amount of $1

D) Future value of the amount of $1

53. The difference between the present and future value of an amount is:

A) income.

B) interest.

C) annuity.

D) premium.

54. The present value of a future cash receipt:

A) decreases as the interest rate goes down.

B) decreases as the time till receipt goes up.

C) increases as the time till receipt goes up.

D) increases as the interest rate goes up.

55. Sinclair Corporation wants to know how much it should deposit each month in order to have $1,000,000 in five years. What type of problem is this?

A) Present value of an annuity

B) Present value of an amount

C) Future value of an amount

D) Future value of an annuity

56. Alfred Bester wants to know how much he should have in retirement saving when he retires if he wants to withdraw $40,000 per year. What type of problem is this?

A) Present value of an annuity

B) Present value of an amount

C) Future value of an amount

D) Future value of an annuity

57. Explain the difference between return of investment and return on investment. In judging the success of an investment, is the dollar amount of the return the only factor considered? If not, what additional information is necessary to properly evaluate an investment? What available measure of the performance of investments helps eliminate the distortion caused by the relative size of an initial investment?

Answers:

Return of investment is simply the return of the amount of money originally invested. Return on investment is money received in excess of the initial investment.

The dollar amount of the return is not sufficient to judge the success of an investment. The dollar amount of the original investment and the time span covered by the investment must also be known to properly evaluate the investment.

The rate of return is a common-size measure that eliminates the distortion caused by the size of the initial investment.

58. Explain the relationship between an expected rate of return on an investment and the actual return that will actually occur. Explain the role expected return plays in investment decisions.

Answers:

An expected rate of return is a weighted average of possible rates of return. It summarizes the possible returns based on the chance of the return occurring. It does not project what the return will be but takes into consideration all the possibilities. The actual return will differ from the expected return because only one of the possible returns will occur.

The expected return gets investors to consider possible return alternatives of an investment and, therefore, consider the risks inherent in the investment. With both risk and possible returns clarified the investor can make an informed decision.

59. Explain how inflation risk, business risk, and liquidity risk impact investment decisions.

Answers:

Inflation risk is the chance that inflation will negatively impact the investment’s return by decreasing the purchasing power of the dollar. Business risk reflects the chance that an investment will fail. Liquidity risk reflects the chance the investor will not be able to sell the investment and therefore realize his/her return. As each of these risks increases, so does the return the investor expects from the potential investment. If the future cash flows from the investment are known, higher risk will drive the price of the investment down.

60. Why does the future value of an amount increase when interest is compounded semiannually instead of annually?

61. You are trying to decide between leasing a car or buying it. In each case you would have the use of the car for 48 months. At the end of that time, you expect the car to be worth $6,000. Explain how to determine whether leasing or buying is the best for you.

62. Calculate the expected rate of return for an investment of $550,000. What does the expected rate of return mean?

63. Central Metals, Inc. is considering investing in a silver mine. An investment of $500,000 would be made for one year with the following potential outcomes:

The expected rate of return for this investment is:

64. Wildcat Enterprises is considering two projects that will require the investment of $100,000. Using the expected rate of return for each project, indicate which of the two you would recommend. Justify your choice.

Project A

Project B

Answers:

Rates of return

7,000/100,000 = 0.07 or 7%

5,000/100,000 = 0.05 or 5%

1,000/100,000 = 0.01 or 1%

(2,000)/100,000 = (0.02) or (2%)

Expected Rate of Return = (7)(0.05) + (5)(0.5) + (1)(0.3) + (–2)(0.15) = 2.85%

Rates of return

30,000/100,000 = 0.3 or 30%

12,000/100,000 = 0.12 or 12%

1,000/100,000 = 0.01 or 1% p

(35,000)/100,000 = (0.35) or (35%)

Expected Rate of Return = (30)(0.25) + (12)(0.15) + (1)(0.3) + (–35)(0.3) = –0.9%

65. Johnstone Supply Company has $100,000 to invest. Determine the amount of money Johnstone will have at the end of 5 years in each of the following independent situations:

(a) Johnstone invests the $100,000 to earn 7% interest compounded annually.

(b) Johnstone invests the $100,000 to earn 6% compounded semiannually.

(c) Johnstone invests the $100,000 to earn 4% compounded quarterly.

Answers:

(a) PV = $100,000; r = 7%; c = 1; n = 5; FV = ? = $140,255.17

(b) PV = $100,000; r = 6% ; c = 2; n = 10 FV = ? = $134,391.63

(c) PV = $100,000; r = 4%: c = 4; n = 20 FV = ? = $122,019.00

66. Frank Gatta invested $15,0000 in a bank account. If Gatta makes no withdrawals, how

much will Gatta have in the bank account balance after 7 years under each of the

following circumstances?

1. Earns 4% compounded annually
2. Earns 4% compounded monthly
3. Earns 6% compounded monthly

Answers

A. PV = $15,000; r = 4%; c = 1; n = 7; FV = ? = $19,738.98

B. PV = $15,000; r = 4%; c = 12; n = 84; FV = ? = $19,837.71

C. PV = $15,000; r = 6%; c = 12; n = 84; FV = ? = $22,805.55

67. Casey Cohen would like to have $24,500 in 5 years’ time to buy a car. The amount that Cohen would have to invest today, assuming an interest rate of 4 percent compounded annually, in order to reach his goal is

68. Lisa Corsetti would like to have $50,000 in 10 years’ time to pay for her daughters’ college education. The amount that Corsetti would have to invest today, assuming an interest rate of 6 percent compounded semiannually, in order to reach her goal is

69. If $18,000 was invested at 10 percent interest compounded semiannually, and it grew to be $32,326.20, the number of years the money was invested totaled:

70. Given a 10 percent interest rate compounded semiannually, the dollar amount available on September 1, 2015, assuming 12 semiannual deposits of $2,000 each with the first deposit made on March 1, 2010, is

71. The present value on April 1, 2010 of 16 semiannual payments of $5,000 each, with the first payment to be made on October 1, 2010, assuming an 8 percent interest rate compounded semiannually is:

72. Joe Bittner has just passed his CPA exam and has a great job with a Big 4 CPA firm and has decided to buy a new BMW. If the price of the car is $36,000 how much will his monthly payments be if he make payments over the next 4 years if he can get a 6 percent interest rate?

73. Susan Ivanova has just accepted a position as a test pilot for Babylon Industries. Her starting salary is $80,000 and she has been promised raises of at least five percent each year. What will Ivanova’s salary be in 10 years?

74. Heather Whitestone wants to retire at the age of 65. She is 45 years old today and will start making semiannual deposits into an investment account in 6 months. Heather would like to have $1,000,000 on her 65th birthday. Assuming Whitestone can earn 8 percent interest compounded semiannually on her investments; determine the required amount of each semiannual deposit.

75. Marcus Perry wants to retire at age 60 with $1,500,000. He is 23 years old today and says

that on his 25th birthday he will start making annual payments into a fund that will

generate 7 percent interest. How much must Marcus put into the fund annually to achieve

his goal?

76. John Stamos will have $1,000,000 in his investment account on the day he retires.

Stamos would like to be able to make a series of equal quarterly withdrawals from the

account for 20 years beginning 3 months after he retires. Assuming the investment

account will earn 10 percent determine the amount of each quarterly withdrawal.

Answers:

Present value of annuity

PV = $1,000,000; r = 10%; c = 4; n = 80 ANN = ? = $29,026.05

77. Chuck Purinton wants to receive $120,000 a year when he retires at age 65 and expects to live until 85. He believes he can earn 7 percent. How much must he have saved to achieve this goal and what age must he have this money saved?

Answers: Present value of annuity

PV = ? r = 7% c = 1 n = 21 ANN = $120,000 PV = $1,300,263.28

The present value of an annuity assumes he will need this money by age 64.

78. Mary and Becky are 22-year-old recent college graduates. Both want to be able to retire at age 50. Mary makes $1,200 annual payments starting immediately. Becky waits 10 years, then begins making $2,400 annual payments. Both earn 6 percent annually on their savings. Which one will have paid more money into her retirement fund when she reaches age 50? Which will have the highest balance in her retirement fund? Why?

79. You have $3,000 and are going to put it into a savings account. How much will you have in 10 years if you can earn

(A.) 7 percent compounded semi-annually?

(B.) 10 percent compounded monthly?

Answers:

Future value of amount of $1

(A.)

PV = $3,000; r = 7%; c = 2; n = 20 FV = ? = $5,969.37

(B.)

PV = $3,000; r = 10%; c = 12; n = 120 FV = ? = $8,121.12

80. Acme Company wants to have $1,200,000 twenty years from today. How much must it put in the bank today to achieve this goal if it can earn 8 percent that is compounded monthly?

81. You are going to put $4,000 into a savings account every six months starting Sept 1, 2010 and ending on March 1, 2014. How much will be in the savings account on March 1, 2014 if you can earn a 6 percent annual rate?

82. How much must you invest today to receive ten, $6,000 payments every 3 months (quarterly) if you can earn 10 percent annual interest?

83. You have just purchased a new Corvette Convertible for $52,000. You have paid $5,000 down and have financed the rest. The financing arrangement calls for you to make monthly payments for the next 5 years at an 8 percent interest rate. What will be the amount of your payment?

84. Your client is 25 years old and wants to start receiving payments of $100,000 per year when she retires on her 60th birthday until her 89th birthday. As her financial advisor, how much must she invest every year staring today to achieve her goal if she can earn 7 percent annual interest?

85. If someone offered to give you a $500,000 noninterest-bearing note that was due 5 years from today (you will receive only one $500,000 payment three years from today) how much would you loan them if you wanted to earn an 6 percent annual interest rate that is compounded semiannually?

86. How much would you loan someone today, January 1, 2010, if they promised to pay you

$10,000 on January 1, 2012 and $20,000 on January 1, 2015 and you want a 9 percent

return on your investment that is compounded annually?

87. On July 1, 2010, a customer has agreed to make six, $2,000 quarterly cash payments

starting October 1, 2010, and $6,000 on July 1, 2013, in exchange for a piece of

equipment that cost you $12,000. If the annual interest rate is 8 percent, how much profit

did you earn on the sale of the equipment?

88. You are trying to decide whether to buy a machine today. The machine will generate

$12,000 cash at the end of each of the next 5 years. If you must have a 10 percent rate of

return on your investments, what is the most you would pay for this machine?

89. Badger Corp is trying to decide whether to buy a new machine with a price of $40,000. Their analysis indicates the machine will generate annual cash flows of $11,000 for each of the next 6 years. The rate of return expected of any investment Badger makes is 9 percent. Should Badger purchase the machine?

90. Champion Contractors Corp is trying to decide which of two machines to buy. The price of the machines and their respective cash flows are described below. The decision to buy is based on which of the two machines produces the largest rate of return. Given the information below which of the machines should Champion buy?

Machine A: Cost $130,000 and will produce $36,063.27 each year for 5 years

Machine B: Cost $125,000 and will produce $16,188.07 every 6 months for 5 years (10 pmts).