Principles of Managerial Finance, 15e (Zutter)
Chapter 5 Time Value of Money
5.1 The role of time value in finance
1) The main idea behind the time value of money is that a dollar today is worth more than a dollar in the
future because ________.
A) inflation erodes the value of money over time
B) investors can earn a return on money they have today and thereby have more money in the future
C) the future is more uncertain than the present
D) investors are impatient
2) You invest a certain amount of money today. The process of determining how much money that
investment will produce in the future is called ________.
A) discounting
B) compounding
C) present value
D) annuitizing the cash flow
3) The process of taking cash flow that is received or paid in the future and stating that cash flow in
present value terms is called discounting.
4) A certain investment that costs $10,000 today promises to pay you $10,500 in five years. This
investment ________.
A) is unambiguously a good investment
B) is unambiguously a bad investment
C) may be a good investment if the rate of return you can earn an alternative investments is very low
D) may be a good investment if the rate of return you can earn on alternative investments is very high
5) Since individuals generally have opportunities to earn positive rates of return on their funds, the
timing of cash flows does not have any significant economic consequences.
6) The 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 Single amounts
1) For any 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 closest to ________.
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 approximately
________.
A) $248
B) $252
C) $159
D) $253
11) The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9
percent, is approximately ________.
A) $237
B) $190
C) $42
D) $10
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 approximately ________.
A) $50
B) $400
C) $519
D) $77
14) The future value of a dollar ________ as the interest rate increases and ________ the longer the money
remains invested.
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) Your current income is $50,000 per year, and you would like to maintain your current standard of
living (i.e., your purchasing power) when you retire. If you expect to retire in 30 years and expect
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 his grandmother. He would like to invest this money for two years
and then use the proceeds from that investment to buy a new high-end gaming computer for $7,000. Will
Colin have enough money to buy the computer if he deposits his money in an account paying 8 percent
compounded semiannually?
22) Dan and Jia are 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 be 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. You can elect to receive a payment of $1,000,000
now or a payment of $1,750,000 in five years. Assume you can earn 5% on funds that you invest today.
How much money would you have in five years if you take the immediate $1,000,000 payment and invest
it? What does this tell you about the wisdom of selecting the immediate payment versus the future
payment? Using the same 5% interest rate, what is the present value of the $1,750,000 that you could
receive in five years? What does this calculation tell you about which lottery payout option you should
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 Annuities
1) An annuity due is a stream of equal cash flows with each cash flow arriving 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 that 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) by contributing $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) $19,293
B) $14,939
C) $40,000
D) $144,105
10) Dan plans to fund his individual retirement account (IRA) by contributing $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) $12,289
B) $20,000
C) $31,875
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 present 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) $28,973
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) $63,528
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) $8,786
15) The future value of an ordinary annuity of $2,000 each year for 10 years, deposited at 12 percent, is
________.
A) $35,097
B) $12,656
C) $39,309
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) The present value of a perpetual income stream increases when the discount rate ________.
A) increases
B) decreases
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) $1,620
B) $1,896
C) $1,971
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) $30,935
B) $27,870
C) $13,424
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? Assume that
payments come at the end of each year.
A) $235,855
B) $67,803
C) $210,585
D) $75,939
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) $11,128
B) $9,935
C) $24,599
D) $27,551
24) James plans to fund his individual retirement account, beginning today, with 20 annual deposits of
$2,000. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account 20
years from today 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) $2,739
B) $2,985
C) $15,348
D) $16,729
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 $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) Rachel takes out 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? Assume that once they retire,
the O’Rourkes will withdraw $40,000 from their retirement account at the end of each year.
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. Assume that he withdraws $25,000 at the end of each year during 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.
38) A charitable foundation has $500,000 invested in an account that earns 7%. The foundation has
promised to begin making annual payments to beneficiaries in one year, and the first payment will be
$25,000. The foundation has promised that future payments will grow at a constant rate forever. At what
rate can the foundation afford to increase payments assuming that it makes no additional deposits into
the account?
A) 0%; it can’t afford to increase payments forever without adding more money to the account.
B) 1%
C) 2%
D) 3%
39) A university has $16,000,000 invested in its endowment. The university wants to withdraw $800,000
from this endowment starting next year and continuing at annual intervals forever, with each subsequent
payment growing at 4% per year. What rate of return does the endowment have to earn to sustain the
desired withdrawals?
40) A wealthy benefactor wants to make a donation to a charity that will provide the charity with annual
income of $250,000 forever, with the first payment to the charity made exactly 10 years from today.
Assume that money donated to the charity will be invested in an account that earns 6%. How large must
the donation be to generate the desired income stream?