Chapter 09 the Time Value of Money

Chapter 09 - The Time Value of Money

Chapter 09

The Time Value of Money

True / False Questions

1.An amount of money to be received in the future is worth less today than the stated amount.
TrueFalse

2.Discounting refers to the growth process that turns $1 today into a greater value several periods in the future.
TrueFalse

3.Compounding refers to the growth process that turns $1 today into a greater value several periods in the future.
TrueFalse

4.The interest factor for the future value of a single sum is equal to (1 + n)i.
TrueFalse

5.The time value of money is not a useful concept in determining the value of a bond or in capital investment decisions.
TrueFalse

6.If a single amount were put on deposit at a given interest rate and allowed to grow, its future value could be determined by reference to the future value of $1 table.
TrueFalse

7.The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year.
TrueFalse

8.The future value is the same concept as the way money grows in a bank account.
TrueFalse

9.Cash flow decisions that ignore the time value of money will probably not be as accurate as those decisions that do rely on the time value of money.
TrueFalse

10.The present value of a positive future inflow can become negative as discount rates become higher and higher.
TrueFalse

11.The interest factor for a future value (FVIF) is equal to (1 + i)n.
TrueFalse

12.The formula PV = FV(1 + n)i will determine the present value of $1.
TrueFalse

13.In determining the interest factor (IF) for the present value of $1, one could use the reciprocal of the IF for the future value of $1 at the same rate and time period.
TrueFalse

14.To determine the current worth of 4 annual payments of $1,000 at 4%, one would refer to a table for the present value of $1.
TrueFalse

15.As the interest rate increases, the interest factor (IF) for the present value of $1 increases.
TrueFalse

16.The interest factor for the present value of a single amount is the inverse of the future value interest factor.
TrueFalse

17.The interest factor for the present value of a single sum is equal to (1 + i)/i.
TrueFalse

18.Higher interest rates (discount rates) reduce the present value of amounts to be received in the future.
TrueFalse

19.In determining the future value of an annuity, the final payment is not compounded at all.
TrueFalse

20.The future value of an annuity assumes that the payments are received at the end of the year and that the last payment does not compound.
TrueFalse

21.The future value of an annuity table provides a short-cut for calculating the future value of a steady stream of payments, denoted as A. The same value can be calculated directly from the following equation:

TrueFalse

22.The present value of an annuity table provides a short-cut for calculating the future value of a steady stream of payments, denoted as A. The same value can be calculated directly from the following equation:

TrueFalse

23.The amount of annual payments necessary to accumulate a desired total can be found by reference to the present value of an annuity table.
TrueFalse

24.If an individual's cost of capital were 6%, he/she would prefer to receive $110 at the end of one year rather than $100 right now.
TrueFalse

25.In evaluating capital investment projects, current outlays must be judged against the current value of future benefits.
TrueFalse

26.The farther into the future any given amount is received, the larger its present value.
TrueFalse

27.The interest factor for the future value of an annuity is simply the sum of the interest factors for the future value using the same number of periods.
TrueFalse

28.An annuity is a series of consecutive payments of equal amount.
TrueFalse

29.Using semi-annual compounding rather than annual compounding will increase the future value of an annuity.
TrueFalse

30.When the inflation rate is zero, the present value of $1 is identical to the future value of $1.
TrueFalse

31.Pension fund retirement accounts use the present value of an annuity to calculate the ending value upon retirement.
TrueFalse

32.The amount of annual payments necessary to repay a mortgage loan can be found by reference to the present value of an annuity table.
TrueFalse

33.In paying off a mortgage loan, the amount of the periodic payment that goes toward the reduction of principal increases over the life of the mortgage.
TrueFalse

34.The time value of money concept becomes less critical as the prime rate increases.
TrueFalse

35.Discounted at 6%, $1000 received three years from now is worth less than $800 received today.
TrueFalse

36.Discounted at 10%, $1000 received at the end of each year for three years is worth less than $2,700 received today.
TrueFalse

37.When adjusting for semi-annual compounding of an annuity, the adjustments include multiplying the periods and annuity by 2.
TrueFalse

38.Calculation of the yield of an investment provides the total return over multiple years.
TrueFalse

Multiple Choice Questions

39.Under what conditions must a distinction be made between money to be received today and money to be received in the future?
A.A period of recession.
B.When idle money can earn a positive return.
C.When there is no risk of nonpayment in the future.
D.When current interest rates are different from expected future rates.

40.As the compounding rate becomes lower and lower, the future value of inflows approaches
A.0
B.the present value of the inflows
C.infinity
D.need more information

41.If you invest $10,000 at 10% interest, how much will you have in 10 years?
A.$13,860
B.$25,940
C.$3,860
D.$80,712

42.In determining the future value of a single amount, one measures
A.the future value of periodic payments at a given interest rate.
B.the present value of an amount discounted at a given interest rate.
C.the future value of an amount allowed to grow at a given interest rate.
D.the present value of periodic payments at a given interest rate.

43.The concept of time value of money is important to financial decision making because
A.it emphasizes earning a return on invested capital.
B.it recognizes that earning a return makes $1 worth more today than $1 received in the future.
C.it can be applied to future cash flows in order to compare different streams of income.
D.all of these

44.As the discount rate becomes higher and higher, the present value of inflows approaches
A.0
B.minus infinity
C.plus infinity
D.need more information

45.How much must you invest at 8% interest in order to see your investment grow to $8,000 in 10 years?
A.$3,070
B.$3,704
C.$3,105
D.none of these

46.An annuity may be defined as
A.a payment at a fixed interest rate.
B.a series of payments of unequal amount.
C.a series of yearly payments.
D.a series of consecutive payments of equal amounts.

47.You are to receive $12,000 at the end of 5 years. The available yield on investments is 6%. Which table would you use to determine the value of that sum today?
A.Present value of an annuity of $1
B.Future value of an annuity
C.Present value of $1
D.Future value of $1

48.As the interest rate increases, the present value of an amount to be received at the end of a fixed period
A.increases.
B.decreases.
C.remains the same.
D.Not enough information to tell.

49.As the time period until receipt increases, the present value of an amount at a fixed interest rate
A.decreases.
B.remains the same.
C.increases.
D.Not enough information to tell.

50.To find the yield on investments which require the payment of a single amount initially, and which then return a single amount some time in the future, the correct table to use is
A.the present value of $1
B.the future value of $1
C.present value of an annuity of $1
D.(a) and (b) above.

51.Ali Shah sets aside 2,000 each year for 5 years. He then withdraws the funds on an equal annual basis for the next 4 years. If Ali wishes to determine the amount of the annuity to be withdrawn each year, he should use the following two tables in this order:
A.present value of an annuity of $1; future value of an annuity of $1
B.future value of an annuity of $1; present value of an annuity of $1
C.future value of an annuity of $1; present value of a $1
D.future value of an annuity of $1; future value of a $1

52.To save for her newborn son's college education, Lea Wilson will invest $1,000 at the beginning of each year for the next 18 years. The interest rate is 12 percent. What is the future value?
A.$7,690.
B.$34,931.
C.$63,440.
D.$62,440.

53.If you were to put $1,000 in the bank at 6% interest each year for the next ten years, which table would you use to find the ending balance in your account?
A.Present value of $1
B.Future value of $1
C.Present value of an annuity of $1
D.Future value of an annuity of $1

54.The IF for the future value of an annuity is 4.641 at 10% for 4 years. If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be?
A.$2,500
B.$2,000
C.$1,724
D.none of these

55.Mr. Blochirt is creating a college investment fund for his daughter. He will put in $1,000 per year for the next 15 years and expects to earn a 6% annual rate of return. How much money will his daughter have when she starts college?
A.$11,250
B.$12,263
C.$24,003
D.$23,276

56.Mr. Nailor invests $5,000 in a money market account at his local bank. He receives annual interest of 8% for 7 years. How much return will his investment earn during this time period?
A.$2,915
B.$3,570
C.$6,254
D.$8,570

57.Lou Lewis borrows $10,000 to be repaid over 10 years at 9 percent. Repayment of principal in the first year is:
A.$1,558
B.$658
C.$742
D.$885

58.Sharon Smith will receive $1 million in 50 years. The discount rate is 14%. As an alternative, she can receive $1,000 today. Which should she choose?
A.the $1 million dollars in 50 years.
B.$2,000 today.
C.she should be indifferent.
D.need more information.

59.Pedro Gonzalez will invest $5,000 at the beginning of each year for the next 9 years. The interest rate is 8 percent. What is the future value?
A.$58,471.
B.$62,440.
C.$67,435.
D.$72,435.

60.Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20 year cash flow? Use an 11% discount rate.
A.$19,034
B.$27,870
C.$32,389
D.none of these

61.Dr. J. wants to buy a Dell computer which will cost $3,000 three years from today. He would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. He can earn 8% annual return. How much should he set aside?
A.$879
B.$627
C.$924
D.$1,243

62.Mr. Fish wants to build a house in 8 years. He estimates that the total cost will be $150,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn in order to have the amount needed?
A.Between 17% and 18%
B.Between 15% and 16%
C.12%
D.None of these

63.Babe Ruth Jr. has agreed to play for the Cleveland Indians for $3 million per year for the next 10 years. What table would you use to calculate the value of this contract in today's dollars?
A.Present value of an annuity
B.Present value of a single amount
C.Future value of an annuity
D.None of these

64.Football player Walter Johnson signs a contract calling for payments of $250,000 per year, to begin 10 years from now. To find the present value of this contract, which table or tables should you use?
A.The future value of $1
B.The future value of an annuity of $1 and the future value of $1
C.The present value of an annuity of $1 and the present value of $1
D.None of these

65.Mike Carlson will receive $12,000 a year from the end of the third year to the end of the 12thyear (10 payments). The discount rate is 10%. The present value today of this deferred annuity is:
A.$61, 450
B.$42,185
C.$55,379
D.$60,909

66.The shorter the length of time between a present value and its corresponding future value,
A.the lower the present value, relative to the future value.
B.the higher the present value, relative to the future value.
C.the higher the interest rate used in the present-valuation.
D.none of these.

67.A dollar today is worth more than a dollar to be received in the future because
A.risk of nonpayment in the future.
B.the dollar can be invested today and earn interest.
C.inflation will reduce purchasing power of a future dollar.
D.None of these.

68.The higher the rate used in determining the future value of a $1 annuity,
A.the smaller the future value at the end of the period.
B.the greater the future value at the end of a period.
C.the greater the present value at the beginning of a period.
D.none of these - the interest has no effect on the future value of an annuity.

69.Mr. Darden is selling his house for $200,000. He bought it for $164,000 ten years ago. What is the annual return on his investment?
A.2%
B.Between 3% and 5%
C.10%
D.None of these

70.Increasing the number of periods will increase all of the following except
A.the present value of an annuity.
B.the present value of $1.
C.the future value of $1.
D.the future value of an annuity.

71.Joe Nautilus has $210,000 and wants to retire. What return must his money earn so he may receive annual benefits of $30,000 for the next 10 years.
A.12%
B.Between 12% and 13%
C.About 7%
D.Greater than 15%

72.You will deposit $2,000 today. It will grow for 6 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 4 years. The annual interest rate is 8%. Your annual withdrawal will be:
A.$2,340
B.$4,332
C.$797
D.$1,085

73.Carol Thomas will pay out $6,000 at the end of the year 2, $8,000 at the end of year 3, and receive $10,000 at the end of year 4. With an interest rate of 13 percent, what is the net value of the payments vs. receipts in today's dollars?
A.$7,326.
B.$10,242.
C.$16,372.
D.$4,112.

74.John Doeber borrowed $150,000 to buy a house. His loan cost was 6% and he promised to repay the loan in 15 equal annual payments. How much are the annual payments?
A.$3,633
B.$9,250
C.$13,113
D.$15,445

75.John Doeber borrowed $150,000 to buy a house. His loan cost was 6% and he promised to repay the loan in 15 equal annual payments. What is the principal outstanding after the first loan payment?
A.$143,555
B.$134,560
C.$141,200
D.None of these

76.A home buyer signed a 20-year, 8% mortgage for $72,500. Given the following information, how much should the annual loan payments be?
Present value of $1 PVIF= .215
Future value of $1 FVIF= 4.661
Present value of annuity PVIFA= 9.818
Future value of annuity FVIFA= 45.762
A.$1,584
B.$7,384
C.$15,555
D.$15,588

77.A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years. At the time of retirement you will have $73,425 to your credit in the plan. The plan anticipates earning 9% interest. Given the following information, how much will your annual benefits be?
Present value of $1 PVIF= .178
Future value of $1 FVIF= 5.604
Present value of annuity PVIFA= 9.129
Future value of annuity FVIFA= 51.16
A.$1,435
B.$13,070
C.$8,043
D.$13,102

78.After 10 years, 100 shares of stock originally purchased for $500 was sold for $900. What was the yield on the investment? Choose the closest answer.
A.19%
B.2.5%
C.8.5%
D.6%

79.Mr. Smith has just invested $10,000 for his son (age 7). The money will be used for his son's education 15 years from now. He calculates that he will need $100,000 for his son's education by the time the boy goes to school. What rate of return will Dr. Stein need to achieve this goal?
A.between 9% and 10%
B.between 16% and 17%
C.between 10% and 11%
D.between 15% and 16%

80.The future value of a $500 investment today at 10 percent annual interest compounded semiannually for 5 years is
A.$805
B.$814
C.$750
D.$923

81.Dan would like to save $1,500,000 by the time he retires in 25 years and believes he can earn an annual return of 8%. How much does he need to invest in each of the following years to achieve his goal?
A.$20,518
B.$40,850
C.$18,900
D.$58,000
E.$25,304

82.Sydney saved $10,000 during her first year of work after college and plans to invest it for her retirement in 40 years. How much will she have available for retirement if she can make 8% on her investment?
A.$596,250
B.$2,953,000
C.$1,345,100
D.$469,020

83.Luke believes that he can invest $5,000 per year for his retirement in 30 years. How much will he have available for retirement if he can earn 8% on his investment?
A.$566,400
B.$681,550
C.$150,000
D.$162,000

84.Ian would like to save $2,000,000 by the time he retires in 40 years. If he believes that he can achieve a 7% rate of return, how much does he need to deposit each year to achieve his goal?
A.$12,065
B.$37,500
C.$5,790
D.$10,018

85.Jeff believes he will need $60,000 annual income during retirement. If he can achieve a 6% return during retirement and believes he will live 20 years after retirement, how much does he need to save by the time he retires?
A.$724,055
B.$1,600,000
C.$688,200
D.$209,320

86.If Allison has saved $1,000,000 upon retirement, how much can she live on each year if she can earn 6% per year and will end with $0 when she expects to die 25 years after retirement?
A.$295,334
B.$20,953
C.$70,952
D.$78,229

87.Kathy has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years with this investment. What return must she achieve in order to buy her home in 10 years?
A.About 12%
B.About 13%
C.About 9%
D.About 10%

88.If Gerry makes a deposit of $1,500 at the end of each quarter for 5 years, how much will he have at the end of the 5 years assuming a 12% annual return and quarterly compounding?
A.$40,305
B.$30,000
C.$108,078
D.$161,220

89.Sara would like to evaluate the performance of her portfolio over the past 10 years. What compound annual rate of return has she achieved is she invested $12,000 10 years ago and now has $25,000?
A.Between 8% and 9%
B.Between 10% and 11%
C.Between 9% and 10%
D.Between 7% and 8%

Matching Questions

90.Match the following with the items below:?

1.Yield / The payment of an equal stream of cash into a fund which increases in size (depending on the interest rate received) up to a future point in time. / ____
2.future value / The interest or return is accumulated every six months. / ____
3.semi-annual compounding / The discounted value of a future sum or annuity as of today's value. / ____
4.future value of an annuity / A series of consecutive payments or receipts of an equal amount. / ____
5.Annuity / The percentage rate at which future sums or annuities are brought back to their present value. / ____
6.discount rate / The future value of a single amount or annuity when compounded at a given interest rate for a specified period of time. / ____
7.interest factor (IF) / It is based on the number of periods (n) and the interest rate (i) and whether or not there is more than one cash flow. / ____
8.present value / The interest rate that equates a future value of an annuity to a given present value. / ____

Essay Questions