Fundamentals of Corporate Finance, 3e (Berk/DeMarzo/Harford)
Chapter 4 Time Value of Money: Valuing Cash Flow Streams
4.1 Valuing a Stream of Cash Flows
1) The present value (PV) of a stream of cash lows is just the sum of the present values of
each individual cash low.
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
2) You are given two choices of investments, Investment A and Investment B. Both
investments have the same future cash lows. Investment A has a discount rate of 4%, and
Investment B has a discount rate of 5%. Which of the following is true?
A) The present value of cash lows in Investment A is higher than the present value of cash
lows in Investment B.
B) The present value of cash lows in Investment A is lower than the present value of cash
lows in Investment B.
C) The present value of cash lows in Investment A is equal to the present value of cash
lows in Investment B.
D) No comparison can be made—we need to know the cash lows to calculate the present
value.
AACSB Objective: Analytic Skills
Author: JP
Question Status: New
1
3) Which of the following investments has a higher present value, assuming the same
(strictly positive) interest rate applies to both investments?
Year Investment X Investment Y
1 $5,000 $11,000
2 $7,000 $9,000
3 $9,000 $7,000
4 $11,000 $5,000
A) Investment X has a higher present value.
B) Investment Y has a higher present value.
C) Investment X and Investment Y have the same present value, since the total of the cash
lows is the same for both.
D) No comparison can be made—we need to know the interest rate to calculate the present
value.
AACSB Objective: Relective Thinking Skills
Author: JP
Question Status: New
4) An investment pays you $30,000 at the end of this year, and $10,000 at the end of each
of the four following years. What is the present value (PV) of this investment, given that the
interest rate is 5% per year?
A) $39,614
B) $63,382
C) $79,228
D) $95,074
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
2
5) A lottery winner will receive $6 million at the end of each of the next twelve years. What
is the future value (FV) of her winnings at the time of her inal payment, given that the
interest rate is 8.6% per year?
A) $94.40 million
B) $118.00 million
C) $165.20 million
D) $188.80 million
AACSB Objective: Analytic Skills
Author: DS
Question Status: Revised
6) Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of
11%. The amount of money will you have in ten years is closest to which of the following?
The amount you will have in 50 years is closest to which of the following?
A) $1420; $110,739
B) $2271; $166,109
C) $2839; $184,565
D) $3123; $221,478
AACSB Objective: Analytic Skills
Author: JN
Question Status: Previous Edition
3
7) Consider the following timeline detailing a stream of cash lows:
If the current market rate of interest is 10%, then the present value (PV) of this stream of
cash lows is closest to ________.
A) $10,114
B) $20,227
C) $24,272
D) $32,363
AACSB Objective: Analytic Skills
Author: JN
Question Status: Previous Edition
8) Consider the following timeline detailing a stream of cash lows:
If the current market rate of interest is 8%, then the future value (FV) of this stream of
cash lows is closest to ________.
A) $11,699
B) $5850
C) $14,039
D) $18,718
AACSB Objective: Analytic Skills
Author: JN
Question Status: Previous Edition
4
9) Consider the following timeline detailing a stream of cash lows:
If the current market rate of interest is 8%, then the present value (PV) of this stream of
cash lows is closest to ________.
A) $242
B) $581
C) $484
D) $774
AACSB Objective: Analytic Skills
Author: JN
Question Status: Previous Edition
10) Consider the following timeline detailing a stream of cash lows:
If the current market rate of interest is 6%, then the future value (FV) of this stream of
cash lows is closest to ________.
A) $1723
B) $1,500
C) $2068
D) $2757
AACSB Objective: Analytic Skills
Author: JN
Question Status: Previous Edition
11) If $8000 is invested in a certain business at the start of the year, the investor will
receive $2400 at the end of each of the next four years. What is the present value of this
business opportunity if the interest rate is 6% per year?
A) $158.13
5
B) $316.25
C) $379.50
D) $506.00
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
12) A business promises to pay the investor of $6000 today for a payment of $1500 in one
year’s time, $3000 in two years’ time, and $3000 in three years’ time. What is the present
value of this business opportunity if the interest rate is 6% per year?
A) $603.94
B) $301.97
C) $724.73
D) $966.30
AACSB Objective: Analytic Skills
Author: DS
Question Status: Revised
13) Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of
each of the next 5 years. He must invest $10,000 at the start of the irst year and an
additional $10,000 at the end of the irst year. What is the present value of this investment
if the interest rate is 3%?
A) -$3189.80
B) -$5907.57
C) 5907.57
D) $3189.80
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
14) Joe just inherited the family business, and having no desire to run the family business,
he has decided to sell it to an entrepreneur. In exchange for the family business, Joe has
been ofered an immediate payment of $100,000. Joe will also receive payments of $50,000
in one year, $50,000 in two years, and $75,000 in three years. The current market rate of
interest for Joe is 6%.
In terms of present value (PV), how much will Joe receive for selling the family business?
AACSB Objective: Analytic Skills
Author: JN
Question Status: Previous Edition
15) If a few intermediate cash lows in valuing a stream of cash lows are zero can we
delete those points on the timeline and squeeze the timeline to show only nonzero cash
lows?
AACSB Objective: Analytic Skills
Author: SS
Question Status: Previous Edition
4.2 Perpetuities
1) A homeowner in a sunny climate has the opportunity to install a solar water heater in his
home for a cost of $2900. After installation the solar water heater will produce a small
amount of hot water every day, forever, and will require no maintenance. How much must
the homeowner save on water heating costs every year if this is to be a sound investment?
(The interest rate is 5% per year.)
A) $145
B) $160
C) $175
D) $190
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
7
2) What is the present value (PV) of an investment that will pay $500 in one year’s time,
and $500 every year after that, when the interest rate is 10%?
A) $2500
B) $4000
C) $3000
D) $5000
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
3) A perpetuity has a PV of $20,000. If the interest rate is 6%, how much will the perpetuity
pay every year?
A) $600
B) $960
C) $1200
D) $720
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
4) Ally wishes to leave a provision in her will that $7000 will be paid annually in perpetuity
to a local charity. How much must she provide in her will for this perpetuity if the interest
rate is 6%?
A) $58,334
B) $93,334
C) $116,667
D) $70,000
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
8
5) A perpetuity will pay $900 per year, starting ive years after the perpetuity is purchased.
What is the present value (PV) of this perpetuity on the date that it is purchased, given that
the interest rate is 11%?
A) $2695
B) $4312
C) $5390
D) $3234
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
6) A perpetuity will pay $1000per year, starting ive years after the perpetuity is purchased.
What is the future value (FV) of this perpetuity, given that the interest rate is 3%?
A) $1456
B) $19,867
C) $21,320
D) There is no solution to this problem.
AACSB Objective: Analytic Skills
Author: JP
Question Status: Revised
7) Which of the following statements regarding perpetuities is FALSE?
A) To ind the value of a perpetuity by discounting one cash low at a time would take
forever.
B) A perpetuity is a stream of equal cash lows that occurs at regular intervals and lasts
forever.
C) PV of a perpetuity =
D) One example of a perpetuity is the British government bond called a consol.
AACSB Objective: Analytic Skills
Author: JN
Question Status: Revised
9
8) Which of the following is true about perpetuities?
A) Since a perpetuity generates cash lows every period ininitely, the cash low generated
equals the PV times the interest rate.
B) Since a perpetuity generates cash lows every period ininitely, initial cash outlow must
be discounted to calculate the present value.
C) Since a perpetuity generates cash lows every period ininitely, there is no way to solve
for the cash low using the present value and the interest rate.
D) Since a perpetuity generates cash lows every period ininitely, its FV is the same as its
PV.
AACSB Objective: Analytic Skills
Author: JP
Question Status: Revised
9) Which of the following is true about perpetuities?
A) All else equal, the present value of a perpetuity is higher when the periodic cash low is
higher.
B) All else equal, the present value of a perpetuity is higher when the interest rate is lower.
C) If two perpetuities have the same present value and the same interest rate, they must
have the same cash lows.
D) All of the above are true statements.
AACSB Objective: Analytic Skills
Author: JP
Question Status: Revised
4.3 Annuities
1) Cash lows from an annuity occur every year in the future.
AACSB Objective: Analytic Skills
Author: DS
Question Status: Previous Edition
10