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.
True False
True False
2. Discounting
refers to the growth process that turns $1 today into a greater value several
periods in the future.
True False
True False
3. Compounding
refers to the growth process that turns $1 today into a greater value several
periods in the future.
True False
True False
4. The
interest factor for the future value of a single sum is equal to (1 + n)i.
True False
True False
5. The
time value of money is not a useful concept in determining the value of a bond
or in capital investment decisions.
True False
True False
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.
True False
True False
7. The
time value of money concept is fundamental to the analysis of cash inflow and
outflow decisions covering periods of over one year.
True False
True False
8. The
future value is the same concept as the way money grows in a bank
account.
True False
True False
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.
True False
True False
10. The
present value of a positive future inflow can become negative as discount rates
become higher and higher.
True False
True False
11. The
interest factor for a future value (FVIF) is equal to (1 + i)n.
True False
True False
12. The
formula PV = FV(1 + n)i will determine the present value of
$1.
True False
True False
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.
True False
True False
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.
True False
True False
15. As
the interest rate increases, the interest factor (IF) for the present value of
$1 increases.
True False
True False
16. The
interest factor for the present value of a single amount is the inverse of the
future value interest factor.
True False
True False
17. The
interest factor for the present value of a single sum is equal to (1 +
i)/i.
True False
True False
18. Higher
interest rates (discount rates) reduce the present value of amounts to be
received in the future.
True False
True False
19. In
determining the future value of an annuity, the final payment is not compounded
at all.
True False
True False
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.
True False
True False
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:
True False
True False
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:
True False
True False
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.
True False
True False
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.
True False
True False
25. In
evaluating capital investment projects, current outlays must be judged against
the current value of future benefits.
True False
True False
26. The
farther into the future any given amount is received, the larger its present
value.
True False
True False
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.
True False
True False
28. An
annuity is a series of consecutive payments of equal amount.
True False
True False
29. Using
semi-annual compounding rather than annual compounding will increase the future
value of an annuity.
True False
True False
30. When
the inflation rate is zero, the present value of $1 is identical to the future
value of $1.
True False
True False
31. Pension
fund retirement accounts use the present value of an annuity to calculate the
ending value upon retirement.
True False
True False
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.
True False
True False
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.
True False
True False
34. The
time value of money concept becomes less critical as the prime rate
increases.
True False
True False
35. Discounted
at 6%, $1000 received three years from now is worth less than $800 received
today.
True False
True False
36. Discounted
at 10%, $1000 received at the end of each year for three years is worth less
than $2,700 received today.
True False
True False
37. When
adjusting for semi-annual compounding of an annuity, the adjustments include
multiplying the periods and annuity by 2.
True False
True False
38. Calculation
of the yield of an investment provides the total return over multiple
years.
True False
True False
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.
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
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
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.
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
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
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
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.
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
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.
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.
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.
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
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.
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
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
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
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
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
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.
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.
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
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
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
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
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
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
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.
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.
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.
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
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.
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%
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
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.
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
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
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
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
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%
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%
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
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
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
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
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
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
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
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%
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
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%
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
91. You
have an opportunity to buy a $1,000 bond which matures in 10 years. The bond
pays $30 every six months. The current market interest rate is 8%. What is the
most you would be willing to pay for this bond?
92. In
January, 2000, Harold Black bought 100 shares of Country Homes for $37.50 per
share. He sold them in January, 2010 for a total of $9,715.02. Calculate
Harold's annual rate of return.
93. Samuel
Johnson invested in gold U.S.
coins ten years ago, paying $216.53 for one-ounce gold "double eagle"
coins. He could sell these coins for $734 today. What was his annual rate of
return for this investment?
94. Gary
Kiraly wants to buy a new Italian sports car in three years. The vehicle is
expected to cost $80,000 at that time. If Gary
should be so lucky as to find an investment yielding 12% over that three-year
period, how much would he have to invest now in order to accumulate $80,000 at
the end of the three years?
95. Mr.
Sullivan is borrowing $2 million to expand his business. The loan will be for
ten years at 12% and will be repaid in equal quarterly installments. What will
the quarterly payments be?
96. Marcia
Stubern is planning for her golden years. She will retire in 20 years, at which
time she plans to begin withdrawing $60,000 annually. She is expected to live
for 20 years following her retirement. Her financial advisor thinks she can
earn 9% annually. How much does she need to invest each year to prepare for her
financial needs after her retirement?
97. Sara
Shouppe has invested $100,000 in an account at her local bank. The bank will
pay her a constant amount each year for 6 years, starting one year from today,
and the account's balance will be 0 at the end of the sixth year. If the bank
has promised Ms. Shouppe a 10% return, how much will they have to pay him each
year?
98. The
Swell Computer Company has developed a new line of desktop computers. It is
estimated that the cash returns generated by the new product line will be
$800,000 per year for the next five years, and then $500,000 per year for 3 years
after that (the cash returns occur at the end of each year). At a 9% interest
rate, what is the present value of these cash returns?
99. Kimberly
Ford invested $10,000 10 years ago at 16 percent, compounded quarterly. How
much has she accumulated?
100. Sponge
Bob will receive a payment of $5,000 per year for 7 years beginning three years
from today. At a discount rate of 9 percent, what is the present value of this
deferred annuity?
Chapter 09 The
Time Value of Money Answer Key
True / False Questions
1. An
amount of money to be received in the future is worth less today than the
stated amount.
TRUE
TRUE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
2. Discounting
refers to the growth process that turns $1 today into a greater value several
periods in the future.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
3. Compounding
refers to the growth process that turns $1 today into a greater value several
periods in the future.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
4. The
interest factor for the future value of a single sum is equal to (1 + n)i.
FALSE
FALSE
Bloom's: Remember
Difficulty: Basic
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
5. The
time value of money is not a useful concept in determining the value of a bond
or in capital investment decisions.
FALSE
FALSE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
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.
TRUE
TRUE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
7. The
time value of money concept is fundamental to the analysis of cash inflow and
outflow decisions covering periods of over one year.
TRUE
TRUE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
8. The
future value is the same concept as the way money grows in a bank
account.
TRUE
TRUE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
10. The
present value of a positive future inflow can become negative as discount rates
become higher and higher.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
11. The
interest factor for a future value (FVIF) is equal to (1 + i)n.
TRUE
TRUE
Bloom's: Remember
Difficulty: Basic
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
12. The
formula PV = FV(1 + n)i will determine the present value of
$1.
FALSE
FALSE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
TRUE
TRUE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
FALSE
FALSE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
15. As
the interest rate increases, the interest factor (IF) for the present value of
$1 increases.
FALSE
FALSE
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
16. The
interest factor for the present value of a single amount is the inverse of the
future value interest factor.
TRUE
TRUE
Bloom's: Remember
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
17. The
interest factor for the present value of a single sum is equal to (1 +
i)/i.
FALSE
FALSE
Bloom's: Remember
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
18. Higher
interest rates (discount rates) reduce the present value of amounts to be
received in the future.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
19. In
determining the future value of an annuity, the final payment is not compounded
at all.
TRUE
TRUE
Bloom's: Remember
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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:
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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:
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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.
TRUE
TRUE
(App. B:
6%, 1 period)= $110 x .0.943 = $104
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
25. In
evaluating capital investment projects, current outlays must be judged against
the current value of future benefits.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
26. The
farther into the future any given amount is received, the larger its present
value.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
28. An
annuity is a series of consecutive payments of equal amount.
TRUE
TRUE
Bloom's: Remember
Difficulty: Basic
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
29. Using
semi-annual compounding rather than annual compounding will increase the future
value of an annuity.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-05 Compounding or discounting may take place on a less than annual basis such as semiannually or monthly.
30. When
the inflation rate is zero, the present value of $1 is identical to the future
value of $1.
FALSE
FALSE
Bloom's: Understand
Difficulty: Challenge
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
31. Pension
fund retirement accounts use the present value of an annuity to calculate the
ending value upon retirement.
FALSE
FALSE
AACSB: Analytic
Bloom's: Evaluate
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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.
TRUE
TRUE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
34. The
time value of money concept becomes less critical as the prime rate
increases.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
35. Discounted
at 6%, $1000 received three years from now is worth less than $800 received
today.
FALSE
FALSE
(App. B:
3 periods, 6%)= $1,000 x .840 = $840
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
36. Discounted
at 10%, $1000 received at the end of each year for three years is worth less
than $2,700 received today.
TRUE
TRUE
PVA = A ´PVIFA (App.
D: 3 periods, 10%)
= $1,000 ´ .2.487 = $2,487
= $1,000 ´ .2.487 = $2,487
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
37. When
adjusting for semi-annual compounding of an annuity, the adjustments include
multiplying the periods and annuity by 2.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-05 Compounding or discounting may take place on a less than annual basis such as semiannually or monthly.
38. Calculation
of the yield of an investment provides the total return over multiple
years.
FALSE
FALSE
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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.
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.
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
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
A. 0
B. the present value of the inflows
C. infinity
D. need more information
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
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
A. $13,860
B. $25,940
C. $3,860
D. $80,712
FV =
PV x FVIF (App. A: 10%, 10 years)
= $10,000 x 2.594 = $25,940
= $10,000 x 2.594 = $25,940
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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.
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.
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded 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
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
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
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
A. 0
B. minus infinity
C. plus infinity
D. need more information
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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
A. $3,070
B. $3,704
C. $3,105
D. none of these
(App. B:
8%, 10 periods)= $8,000 x 0.463 = $3,704
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
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.
Bloom's: Remember
Difficulty: Basic
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. Present value of an annuity of $1
B. Future value of an annuity
C. Present value of $1
D. Future value of $1
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
A. increases.
B. decreases.
C. remains the same.
D. Not enough information to tell.
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
A. decreases.
B. remains the same.
C. increases.
D. Not enough information to tell.
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
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.
Bloom's: Understand
Difficulty: Challenge
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
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
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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.
A. $7,690.
B. $34,931.
C. $63,440.
D. $62,440.
FVA = A ´FVIFA (App.
C: 12%, 18 + 1 = 19 periods)
= $1,000 ´ (63.440 - 1) = $62,440
= $1,000 ´ (63.440 - 1) = $62,440
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
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
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $2,500
B. $2,000
C. $1,724
D. none of these
(App. C:
10%, 4 periods)A = $8,000
4.641
A = $1,724
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. $11,250
B. $12,263
C. $24,003
D. $23,276
FVA = A ´FVIFA (App.
C: 6%, 15 periods)
= $1,000 ´ 23.276 = $23,276
= $1,000 ´ 23.276 = $23,276
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $2,915
B. $3,570
C. $6,254
D. $8,570
FV =
PV x FVIF (App. A: 8%, 7 periods)
= $5,000 x 1.714 = $8,570
$8,570 - initial investment of $5,000 = $3,570
= $5,000 x 1.714 = $8,570
$8,570 - initial investment of $5,000 = $3,570
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $1,558
B. $658
C. $742
D. $885
(App. D:
9%, 10 periods)A = $10,000
6.418
A = $1,558 annual payment less interest in year 1 ($10,000 x 9%) = $658
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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.
A. the $1 million dollars in 50 years.
B. $2,000 today.
C. she should be indifferent.
D. need more information.
(App. B:
14%, 50 periods)= $1,000,000 x 0.001 = $1,000
AACSB: Analytic
Bloom's: Apply
Difficulty: Basic
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
A. $58,471.
B. $62,440.
C. $67,435.
D. $72,435.
FVA = A ´FVIFA (App.
C: 8%, 9 + 1=10 periods)
= $5,000 ´ (14.487-1) = $67,435
= $5,000 ´ (14.487-1) = $67,435
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $19,034
B. $27,870
C. $32,389
D. none of these
PVA = A ´PVIFA (App.
D: 11%, 10 periods)
= $2,000 x 5.889 = $11,778
PVA = A ´ PVIFA (App. D: 11%, 10 periods)
= $2,000 x 5.889 = $17,688 x PVIF (App. B: 11%, 10 periods)
PVIF = $17,688 ´ (.352) = $7,255
$11,778 + $7,255 = $19,034
= $2,000 x 5.889 = $11,778
PVA = A ´ PVIFA (App. D: 11%, 10 periods)
= $2,000 x 5.889 = $17,688 x PVIF (App. B: 11%, 10 periods)
PVIF = $17,688 ´ (.352) = $7,255
$11,778 + $7,255 = $19,034
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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
A. $879
B. $627
C. $924
D. $1,243
(App. C:
8%, 3 periods)A = $3,000
3.246
A = $924
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. Between 17% and 18%
B. Between 15% and 16%
C. 12%
D. None of these
FVIFA
= FVA (App. C: 8 periods)
A
FVIFA = $150,000 = 15.0 Rate of return = approx. 17.5%
$10,000
A
FVIFA = $150,000 = 15.0 Rate of return = approx. 17.5%
$10,000
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. Present value of an annuity
B. Present value of a single amount
C. Future value of an annuity
D. None of these
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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
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
Bloom's: Understand
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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
A. $61, 450
B. $42,185
C. $55,379
D. $60,909
PVA
= A ´PVIFA (App. D: 10%,
10 periods)
= $12,000 x 6.145 = $73,740
(App. B: 10%, 2 periods)
= $73,740 x .826 = $60,909
= $12,000 x 6.145 = $73,740
(App. B: 10%, 2 periods)= $73,740 x .826 = $60,909
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
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.
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
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.
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.
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
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.
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.
Bloom's: Understand
Difficulty: Basic
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. 2%
B. Between 3% and 5%
C. 10%
D. None of these
PVIF
= PV (App. B: 10 periods)
FV
= $164,000 = 0.82 Return = 2%
$200,000
FV
= $164,000 = 0.82 Return = 2%
$200,000
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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.
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.
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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%
A. 12%
B. Between 12% and 13%
C. About 7%
D. Greater than 15%
PVIFA
= PVA (App. D: 10 periods)
A
= $210,000 = 7.0 Return = 7%
$30,000
A
= $210,000 = 7.0 Return = 7%
$30,000
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. $2,340
B. $4,332
C. $797
D. $1,085
FV = PV x FVIF (App. A: 5%, 12 periods)
= $2,000 x 1.796 = $3,592
A = PVA (App. D: 8%, 4 periods)
PVIFA
= $3,592 = $1,085
3.312
= $2,000 x 1.796 = $3,592
A = PVA (App. D: 8%, 4 periods)
PVIFA
= $3,592 = $1,085
3.312
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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.
A. $7,326.
B. $10,242.
C. $16,372.
D. $4,112.
PV =
FV x PVIF (App. B: 13%, 2 periods)
= $6,000 x .783 = $4,698
PV = FV x PVIF (App. B: 13%, 3 periods)
= $8,000 x .693 = $5,544
PV = FV x PVIF (App. B: 13%, 4 periods)
= $10,000 x .613 = $6,130
Net Value of Payments = ($4,698) + ($5,544) + $6,130 = $4,112
= $6,000 x .783 = $4,698
PV = FV x PVIF (App. B: 13%, 3 periods)
= $8,000 x .693 = $5,544
PV = FV x PVIF (App. B: 13%, 4 periods)
= $10,000 x .613 = $6,130
Net Value of Payments = ($4,698) + ($5,544) + $6,130 = $4,112
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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
A. $3,633
B. $9,250
C. $13,113
D. $15,445
PVA = A ´PVIFA (App. D:
6%, 15 periods)
= $150,000 ´ 9.712 = $15,445
= $150,000 ´ 9.712 = $15,445
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. $143,555
B. $134,560
C. $141,200
D. None of these
PVA
= A ´PVIFA (App. D: 6%,
15 periods)
= $150,000 ´ 9.712 = $15,445
Annual Payment - Interest = Amount to be applied to principal
$15,445 - (.06)($150,000) = $6,445
Outstanding principal at end of year 1 = Loan - Payment to principal
= $150,000 - $6,445
= $143,555
= $150,000 ´ 9.712 = $15,445
Annual Payment - Interest = Amount to be applied to principal
$15,445 - (.06)($150,000) = $6,445
Outstanding principal at end of year 1 = Loan - Payment to principal
= $150,000 - $6,445
= $143,555
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
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
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
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
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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%
A. 19%
B. 2.5%
C. 8.5%
D. 6%
PVIF
= PV (App. B: 10 periods)
FV
= $500 = 0.555 Yield = approx 6%
$900
FV
= $500 = 0.555 Yield = approx 6%
$900
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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%
A. between 9% and 10%
B. between 16% and 17%
C. between 10% and 11%
D. between 15% and 16%
PVIF
= PV (App. B: 15 periods)
FV
= $10,000 = 0.10 Return: between 16% and 17%
$100,000
FV
= $10,000 = 0.10 Return: between 16% and 17%
$100,000
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. $805
B. $814
C. $750
D. $923
FV = PV x FVIF (App. A: 5%, 10 periods)
= $500 x 1.629 = $814
= $500 x 1.629 = $814
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $20,518
B. $40,850
C. $18,900
D. $58,000
E. $25,304
(App. C:
8%, 25 periods)= $1,500,000 = $20,518
73.106
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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
A. $596,250
B. $2,953,000
C. $1,345,100
D. $469,020
FV =
PV x FVIF (App. A: 8%, 40 periods)
= $10,000 x 46.902 = $469,020
= $10,000 x 46.902 = $469,020
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $566,400
B. $681,550
C. $150,000
D. $162,000
FVA = A ´FVIFA (App.
C: 8%, 30 periods)
= $5,000 ´ 113.28 = $566,400
= $5,000 ´ 113.28 = $566,400
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $12,065
B. $37,500
C. $5,790
D. $10,018
(App. C:
7%, 40 periods)= $2,000,000 = $10,018
199.64
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
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
A. $724,055
B. $1,600,000
C. $688,200
D. $209,320
PVA = A ´PVIFA (App.
D: 6%, 20 periods)
= $60,000 ´ 11.470 = $688,200
= $60,000 ´ 11.470 = $688,200
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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
A. $295,334
B. $20,953
C. $70,952
D. $78,229
A = PVA
(App. D: 6%, 25 periods)
PVIFA
PVIFA
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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%
A. About 12%
B. About 13%
C. About 9%
D. About 10%
PVIF
= PV (App. B: 10 periods)
FV
= $50,000 = 0.82 Return = 12%
$150,000
FV
= $50,000 = 0.82 Return = 12%
$150,000
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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
A. $40,305
B. $30,000
C. $108,078
D. $161,220
FVA = A ´FVIFA (App.
C: 3%, 20 periods)
= $1,500 ´ 26.870 = $40,305
= $1,500 ´ 26.870 = $40,305
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-05 Compounding or discounting may take place on a less than annual basis such as semiannually or monthly.
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%
A. Between 8% and 9%
B. Between 10% and 11%
C. Between 9% and 10%
D. Between 7% and 8%
PVIF
= PV (App. B: 10 periods)
FV
= $12,000 = 0.48 Return: between 7% and 8%
$25,000
FV
= $12,000 = 0.48 Return: between 7% and 8%
$25,000
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
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.
|
4
|
2. future
value
|
The interest or return is
accumulated every six months.
|
3
|
3. semi-annual
compounding
|
The discounted value of a
future sum or annuity as of today's value.
|
8
|
4. future
value of an annuity
|
A series of consecutive
payments or receipts of an equal amount.
|
5
|
5. Annuity
|
The percentage rate at
which future sums or annuities are brought back to their present value.
|
6
|
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.
|
2
|
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.
|
7
|
8. present
value
|
The interest rate that
equates a future value of an annuity to a given present value.
|
1
|
Bloom's: Understand
Difficulty: Intermediate
Learning Objective: 09-01 Money has a time value associated with it and therefore a dollar received today is worth more than a dollar received in the future.
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
Learning Objective: 09-05 Compounding or discounting may take place on a less than annual basis such as semiannually or monthly.
Essay
Questions
91. You
have an opportunity to buy a $1,000 bond which matures in 10 years. The bond
pays $30 every six months. The current market interest rate is 8%. What is the
most you would be willing to pay for this bond?
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
92. In
January, 2000, Harold Black bought 100 shares of Country Homes for $37.50 per
share. He sold them in January, 2010 for a total of $9,715.02. Calculate Harold's
annual rate of return.
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
93. Samuel
Johnson invested in gold U.S.
coins ten years ago, paying $216.53 for one-ounce gold "double eagle"
coins. He could sell these coins for $734 today. What was his annual rate of
return for this investment?
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
94. Gary
Kiraly wants to buy a new Italian sports car in three years. The vehicle is
expected to cost $80,000 at that time. If Gary
should be so lucky as to find an investment yielding 12% over that three-year
period, how much would he have to invest now in order to accumulate $80,000 at
the end of the three years?
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
95. Mr.
Sullivan is borrowing $2 million to expand his business. The loan will be for
ten years at 12% and will be repaid in equal quarterly installments. What will
the quarterly payments be?
A =
PVA/PVIFA(3%, 40 years), Appendix D.
A = $2 million/23.115 = $86,524
A = $2 million/23.115 = $86,524
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
96. Marcia
Stubern is planning for her golden years. She will retire in 20 years, at which
time she plans to begin withdrawing $60,000 annually. She is expected to live
for 20 years following her retirement. Her financial advisor thinks she can
earn 9% annually. How much does she need to invest each year to prepare for her
financial needs after her retirement?
Amount
to be needed in 20 years:
Amount to be deposited annually in order to attain that goal:
Amount to be deposited annually in order to attain that goal:
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
97. Sara
Shouppe has invested $100,000 in an account at her local bank. The bank will
pay her a constant amount each year for 6 years, starting one year from today,
and the account's balance will be 0 at the end of the sixth year. If the bank
has promised Ms. Shouppe a 10% return, how much will they have to pay him each
year?
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
Learning Objective: 09-04 Not only can future value and present value be computed; but other factors such as yield (rate of return) can be determined as well.
98. The
Swell Computer Company has developed a new line of desktop computers. It is
estimated that the cash returns generated by the new product line will be
$800,000 per year for the next five years, and then $500,000 per year for 3
years after that (the cash returns occur at the end of each year). At a 9%
interest rate, what is the present value of these cash returns?
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
99. Kimberly
Ford invested $10,000 10 years ago at 16 percent, compounded quarterly. How
much has she accumulated?
AACSB: Analytic
Bloom's: Apply
Difficulty: Intermediate
Learning Objective: 09-02 The future value is based on the number of periods over which the funds are to be compounded at a given interest rate.
100. Sponge
Bob will receive a payment of $5,000 per year for 7 years beginning three years
from today. At a discount rate of 9 percent, what is the present value of this
deferred annuity?
Using
Appendix D, a seven period annuity discounted at 9percent is:
This value at the beginning of year three (end of year three) must now be discounted back for two years to get the present value of the deferred annuity. Use Appendix B.
This value at the beginning of year three (end of year three) must now be discounted back for two years to get the present value of the deferred annuity. Use Appendix B.
AACSB: Analytic
Bloom's: Apply
Difficulty: Challenge
Learning Objective: 09-03 The present value is based on the current value of funds to be received.
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