Principles of Managerial Finance, Brief, 7e (Gitman)
Chapter 5 Time Value of Money
5.1 Discuss the role of time value in finance, the use of computational tools, and the basic
patterns of cash flow.
1) Since individuals are always confronted with opportunities to earn positive rates of return on
their funds, the timing of cash flows does not have any significant economic consequences.
2) Time value of money is based on the belief that a dollar that will be received at some future
date is worth more than a dollar today.
5.2 Understand the concepts of future value and present value, their calculation for single
amounts, and the relationship between them.
1) For a given positive interest rate, the future value of $100 increases with the passage of time.
Thus, the longer the period of time, the greater the future value.
2) Future value is the value of a future amount at the present time, found by applying compound
interest over a specified period of time.
3) The greater the interest rate and the longer the period of time, the higher the present value.
4) Everything else being equal, the higher the interest rate, the higher the future value.
5) Future value increases with increases in the interest rate or the period of time funds are left on
deposit.
6) Everything else being equal, the higher the discount rate, the higher the present value.
7) Everything else being equal, the longer the period of time, the lower the present value.
8) ________ is the amount earned on a deposit that has become the part of the principal at the
end of a specified time period.
A) Discount interest
B) Compound interest
C) Primary interest
D) Future value
9) The future value of $100 received today and deposited at 6 percent for four years is ________.
A) $126
B) $ 79
C) $124
D) $116
10) The future value of $200 received today and deposited at 8 percent for three years is
________.
A) $248
B) $252
C) $158
D) $200
11) The present value of $100 to be received 10 years from today, assuming an opportunity cost
of 9 percent, is ________.
A) $236
B) $699
C) $ 42
D) $ 75
12) The amount of money that would have to be invested today at a given interest rate over a
specified period in order to equal a future amount is called ________.
A) future value
B) present value
C) future value of an annuity
D) compounded value
13) The present value of $200 to be received 10 years from today, assuming an opportunity cost
of 10 percent, is ________.
A) $ 50
B) $200
C) $518
D) $ 77
14) The future value of a dollar ________ as the interest rate increases and ________ the further
in the future an initial deposit is to be received.
A) decreases; decreases
B) decreases; increases
C) increases; increases
D) increases; decreases
15) The annual rate of return is referred to as the ________.
A) discount rate
B) marginal rate
C) risk-free rate
D) marginal cost
16) If you expect to retire in 30 years, live on $50,000 per year and expect the inflation to
average 3% over the next 30 years, what amount of annual income will you need to live at the
same comfort level in 30 years?
A) $121,363
B) $$95,000
C) $20,599
D) $51,500
17) Calculate the future value of $4,600 received today if it is deposited at 9 percent for three
years.
18) Calculate the present value of $89,000 to be received in 15 years, assuming an opportunity
cost of 14 percent.
19) Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually.
She plans to leave the funds in this account for seven years earning interest. If the goal of this
deposit is to cover a future obligation of $65,000, what recommendation would you make to
Aunt Tillie?
20) China Manufacturing Agents, Inc. is preparing a five-year plan. Today, sales are $1,000,000.
If the growth rate in sales is projected to be 10 percent over the next five years, what will the
dollar amount of sales be in year five?
21) Colin has inherited $6,000 from the death of Grandma Anna. He would like to use this
money to buy his mom Hayley a new scooter costing $7,000, two years from now. Will Colin
have enough money to buy the gift if he deposits his money in an account paying 8 percent
compounded semiannually?
22) Dan and Jia are newlyweds and have just purchased a condominium for $70,000. Since the
condo is very small, they hope to move into a single-family house in 5 years. How much will
their condo worth in 5 years if inflation is expected to be 8 percent?
23) Congratulations! You have just won the lottery! However, the lottery bureau has just
informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000.
Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent,
based on present values, which would you choose? Using the same discount rate of 5 percent,
based on future values, which would you choose? What do your results suggest as a general rule
for approaching such problems? (Make your choices based purely on the time value of money.)
5.3 Find the future value and the present value of both an ordinary annuity and an annuity due,
and find the present value of a perpetuity.
1) An annuity due is an amount that occur at the beginning of each period.
2) An ordinary annuity is an annuity in which cash flows occur at the beginning of each period.
3) The future value of an annuity due is always greater than the future value of an otherwise
identical ordinary annuity for interest rates greater than zero.
4) Which of the following is true of annuities?
A) An ordinary annuity is an equal payment paid or received at the beginning of each period.
B) An annuity due is a payment paid or received at the beginning of each period that increases by
an equal amount each period.
C) An annuity due is an equal stream of cash flows is paid or received at the beginning of each
period.
D) An ordinary annuity is an equal payment paid or received at the end of each period that
increases by an equal amount each period.
5) The present value of a $25,000 perpetuity at a 14 percent discount rate is ________.
A) $178,571
B) $285,000
C) $350,000
D) $219,298
6) An annuity with an infinite life is called a(n) ________.
A) perpetuity
B) primia
C) option
D) deep discount
7) The present value of a $20,000 perpetuity at a 7 percent discount rate is ________.
A) $186,915
B) $285,714
C) $140,000
D) $325,000
8) A(n) ________ is an annuity with an infinite life making continual annual payments.
A) amortized loan
B) principal
C) perpetuity
D) APR
9) Bill plans to fund his individual retirement account (IRA) with the maximum contribution of
$2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his
contributions, how much will he have at the end of the twentieth year?
A) $19,292
B) $14,938
C) $40,000
D) $144,104
10) Dan plans to fund his individual retirement account (IRA) with the maximum contribution of
$2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his
contributions, how much will he have at the end of the tenth year?
A) $12,290
B) $20,000
C) $31,874
D) $51,880
11) In comparing an ordinary annuity and an annuity due, which of the following is true?
A) The future value of an annuity due is always greater than the future value of an otherwise
identical ordinary annuity.
B) The future value of an ordinary annuity is always greater than the future value of an otherwise
identical annuity due.
C) The future value of an annuity due is always less than the future value of an otherwise
identical ordinary annuity, since one less payment is received with an annuity due.
D) All things being equal, one would prefer to receive an ordinary annuity compared to an
annuity due.
12) The future value of a $2,000 annuity due deposited at 8 percent compounded annually for
each of the next 10 years is ________.
A) $28,974
B) $31,291
C) $14,494
D) $13,420
13) The future value of a $10,000 annuity due deposited at 12 percent compounded annually for
each of the next 5 years is ________.
A) $36,050
B) $63,530
C) $40,376
D) $71,152
14) The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3
percent, is ________.
A) $11,808
B) $11,464
C) $ 8,530
D) $10,000
15) The future value of an ordinary annuity of $2,000 each year for 10 years, deposited at 12
percent, is ________.
A) $35,098
B) $20,000
C) $39,310
D) $11,300
16) A college received a contribution to its endowment fund of $2 million. It can never touch the
principal, but can use the earnings. At an assumed interest rate of 9.5 percent, how much can the
college earn to help its operations each year?
A) $95,000
B) $19,000
C) $190,000
D) $18,000
17) If the present value of a perpetual income stream is increasing, the discount rate must be
________.
A) increasing
B) decreasing
C) changing unpredictably
D) increasing proportionally
18) The present value of an ordinary annuity of $350 each year for five years, assuming an
opportunity cost of 4 percent, is ________.
A) $288
B) $1,896
C) $1,750
D) $1,558
19) The present value of an ordinary annuity of $2,350 each year for eight years, assuming an
opportunity cost of 11 percent, is ________.
A) $ 1,020
B) $27,869
C) $18,800
D) $12,093
20) A generous benefactor to a local ballet plans to make a one-time endowment that would
provide the ballet with $150,000 per year into perpetuity. The rate of interest is expected to be 5
percent for all future time periods. How large must the endowment be?
A) $ 300,000
B) $3,000,000
C) $ 750,000
D) $1,428,571
21) A generous philanthropist plans to make a one-time endowment to a renowned heart research
center which would provide the facility with $250,000 per year into perpetuity. The rate of
interest is expected to be 8 percent for all future time periods. How large must the endowment
be?
A) $2,314,814
B) $2,000,000
C) $3,125,000
D) $3,000,000
22) Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance
book. What is the present value of her royalty income if the opportunity cost is 12 percent?
A) $120,000
B) $ 67,800
C) $ 38,640
D) $ 72,560
23) To pay for her college education, Gina is saving $2,000 at the beginning of each year for the
next eight years in a bank account paying 12 percent interest. How much will Gina have in that
account at the end of 8th year?
A) $16,000
B) $17,920
C) $24,600
D) $27,552
24) James plans to fund his individual retirement account, beginning today, with 20 annual
deposits of $2,000, which he will continue for the next 20 years. If he can earn an annual
compound rate of 8 percent on his deposits, the amount in the account upon retirement will be
________.
A) $19,636
B) $91,524
C) $98,846
D) $21,207
25) You have been offered a project paying $300 at the beginning of each year for the next 20
years. What is the maximum amount of money you would invest in this project if you expect 9
percent rate of return to your investment?
A) $ 2,738
B) $ 2,985
C) $15,347
D) $ 6,000
26) Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.
27) Calculate the future value of an annuity of $5,000 each year for eight years, deposited at 6
percent.
28) Calculate the present value of an annuity of $3,900 each year for four years, assuming an
opportunity cost of 10 percent.
29) Dottie has decided to set up an account that will pay her granddaughter (Lexi) $5,000 a year
indefinitely. How much should Dottie deposit in an account paying 8 percent annual interest?
30) A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income
for his grandchild into perpetuity. He stipulates in the trust agreement that the principal may not
be distributed. The grandchild may only receive the interest earned. If the interest rate earned on
the trust is expected to be at least 7 percent in all future periods, how much income will the
grandchild receive each year?
31) Nico establishes a seven-year, 8 percent loan with a bank requiring annual end-of-year
payments of $960.43. Calculate the original principal amount.
32) A lottery administrator has just completed the state’s most recent $50 million lottery.
Receipts from lottery sales were $50 million and the payout will be $5 million at the end of each
year for 10 years. The expenses of running the lottery were $800,000. The state can earn an
annual compound rate of 8 percent on any funds invested.
(a) Calculate the gross profit to the state from this lottery.
(b) Calculate the net profit to the state from this lottery (no taxes).
33) Jia has just won a $20 million lottery, which will pay her $1 million at the end of each year
for 20 years. An investor has offered her $10 million for this annuity. She estimates that she can
earn 10 percent interest, compounded annually, on any amounts she invests. She asks your
advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)
34) Mr. Jackson has been awarded a bonus for his outstanding work. His employer offers him a
choice of a lump-sum of $5,000 today, or an annuity of $1,250 a year for the next five years.
Which option should Mr. Jackson choose if his opportunity cost is 9 percent?
35) In their meeting with their advisor, Mr. and Mrs. O’Rourke concluded that they would need
$40,000 per year during their retirement years in order to live comfortably. They will retire 10
years from now and expect a 20-year retirement period. How much should Mr. and Mrs.
O’Rourke deposit now in a bank account paying 9 percent to reach financial happiness during
retirement?
36) Nico is 30 years old and will retire at age 65. He will receive retirement benefits, but the
benefits are not going to be enough to make a comfortable retirement life for him. Nico has
estimated that an additional $25,000 a year over his retirement benefits will allow him to have a
satisfactory life. How much should Nico deposit today in an account paying 6 percent interest to
meet his goal? Assume Nico will have 15 years of retirement.
37) You have been given a choice between two retirement policies as described below.
Policy A: You will receive equal annual payments of $10,000 beginning 35 years from now for
10 years.
Policy B: You will receive one lump-sum of $100,000 in 40 years from now.
Which policy would you choose? Assume rate of interest is 6 percent.