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Unformatted text preview: CHAPTER 9
Capital Budgeting Techniques and Practice
Multiple Choice: Conceptual
Ranking methods
1. Answer: b Assume a project has normal cash flows (i.e., the initial cash flow is
negative, and all other cash flows are positive).
Which of the
following statements is most correct?
a. All else equal, a
declines.
b. All else equal, a
declines.
c. All else equal, a
cost of capital.
d. Answers a and b are
e. Answers b and c are project's IRR increases as the cost of capital
project's NPV increases as the cost of capital
project's MIRR is unaffected by changes in the
correct.
correct. Ranking conflicts
2. Diff: E Answer: a Diff: E Which of the following statements is most correct?
a. The NPV method assumes that cash flows will be reinvested at the
cost of capital while the IRR method assumes reinvestment at the
IRR.
b. The NPV method assumes that cash flows will be reinvested at the
riskfree rate while the IRR method assumes reinvestment at the IRR.
c. The NPV method assumes that cash flows will be reinvested at the
cost of capital while the IRR method assumes reinvestment at the
riskfree rate.
d. The NPV method does not consider the inflation premium.
e. The IRR method does not consider all relevant cash flows, and
particularly cash flows beyond the payback period. Payback period
3. Answer: e Diff: E A major disadvantage of the payback period method is that it
a.
b.
c.
d.
e. Is useless as a risk indicator.
Ignores cash flows beyond the payback period.
Does not directly account for the time value of money.
All of the answers above are correct.
Only answers b and c are correct. Chapter 10 Page 1 NPV and IRR
4. Answer: a Diff: E Which of the following statements is most correct?
a. If a project’s internal rate of return (IRR) exceeds the cost of
capital, then the project’s net present value (NPV) must be
positive.
b. If Project A has a higher IRR than Project B, then Project A must
also have a higher NPV.
c. The IRR calculation implicitly assumes that all cash flows are
reinvested at a rate of return equal to the cost of capital.
d. Answers a and c are correct.
e. None of the answers above is correct. NPV and IRR
5. Answer: a Diff: E Project A has an internal rate of return (IRR) of 15 percent. Project
B has an IRR of 14 percent. Both projects have a cost of capital of 12
percent. Which of the following statements is most correct?
a. Both projects have a positive net present value (NPV).
b. Project A must have a higher NPV than Project B.
c. If the cost of capital were less than 12 percent, Project B would
have a higher IRR than Project A.
d. Statements a and c are correct.
e. Statements a, b, and c are correct. Postaudit
6. Answer: e Diff: E The postaudit is used to
a. Improve cash flow forecasts.
b. Stimulate management to improve operations and bring results into
line with forecasts.
c. Eliminate potentially profitable but risky projects.
d. All of the answers above are correct.
e. Answers a and b are correct. IRR
7. Answer: b Diff: E Project A has an IRR of 15 percent.
Project B has an IRR of 18
percent. Both projects have the same risk.
Which of the following
statements is most correct?
a. If the WACC is 10 percent, both projects will have a positive NPV,
and the NPV of Project B will exceed the NPV of Project A.
b. If the WACC is 15 percent, the NPV of Project B will exceed the NPV
of Project A.
c. If the WACC is less than 18 percent, Project B will always have a
shorter payback than Project A.
d. If the WACC is greater than 18 percent, Project B will always have a
shorter payback than Project A.
e. If the WACC increases, the IRR of both projects will decline. Chapter 10 Page 2 NPV profiles
8. Answer: b Diff: M Projects L and S each have an initial cost of $10,000, followed by a
series of positive cash inflows.
Project L has total, undiscounted
cash inflows of $16,000, while S has total undiscounted inflows of
$15,000. Further, at a discount rate of 10 percent, the two projects
have identical NPVs.
Which project's NPV will be more sensitive to
changes in the discount rate?
(Hint: Projects with steeper NPV
profiles are more sensitive to discount rate changes.)
a. Project S.
b. Project L.
c. Both projects are equally sensitive to changes in the discount rate
since their NPVs are equal at all costs of capital.
d. Neither project is sensitive to changes in the discount rate, since
both have NPV profiles which are horizontal.
e. The solution cannot be determined unless the timing of the cash
flows is known. NPV profiles
9. Answer: a Diff: M Two mutually exclusive projects each have a cost of $10,000.
total, undiscounted cash flows from Project L are $15,000, while
undiscounted cash flows from Project S total $13,000.
Their
profiles cross at a discount rate of 10 percent.
Which of
following statements best describes this situation? The
the
NPV
the a. The NPV and IRR methods will select the same project if the cost of
capital is greater than 10 percent; for example, 18 percent.
b. The NPV and IRR methods will select the same project if the cost of
capital is less than 10 percent; for example, 8 percent.
c. To determine if a ranking conflict will occur between the two
projects the cost of capital is needed as well as an additional
piece of information.
d. Project L should be selected at any cost of capital, because it has
a higher IRR.
e. Project S should be selected at any cost of capital, because it has
a higher IRR. Chapter 10 Page 3 NPV and IRR
10. Answer: c Assume that you are comparing two mutually exclusive projects.
of the following statements is most correct? Diff: M
Which a. The NPV and IRR rules will always lead to the same decision unless
one or both of the projects are "nonnormal" in the sense of having
only one change of sign in the cash flow stream, i.e., one or more
initial cash outflows (the investment) followed by a series of cash
inflows.
b. If a conflict exists between the NPV and the IRR, the conflict can
always be eliminated by dropping the IRR and replacing it with the
MIRR.
c. There will be a meaningful (as opposed to irrelevant) conflict only
if the projects' NPV profiles cross, and even then, only if the cost
of capital is to the left of (or lower than) the discount rate at
which the crossover occurs.
d. Statements a, b, and c are true.
NPV and IRR
11. Answer: a Diff: M Which of the following statements is incorrect?
a. Assuming a project has normal cash flows, the NPV will be positive
if the IRR is less than the cost of capital.
b. If the multiple IRR problem does not exist, any independent project
acceptable by the NPV method will also be acceptable by the IRR
method.
c. If IRR = k (the cost of capital), then NPV = 0.
d. NPV can be negative if the IRR is positive.
e. The NPV method is not affected by the multiple IRR problem. NPV, IRR, and payback
12. Answer: e Diff: M Project X has an internal rate of return of 20 percent. Project Y has
an internal rate of return of 15 percent.
Both projects have a
positive net present value. Which of the following statements is most
correct?
a. Project X must have a higher net present value than Project Y.
b. If the two projects have the same WACC, Project X must have a higher
net present value.
c. Project X must have a shorter payback than Project Y.
d. Both answers b and c are correct.
e. None of the above answers is correct. Chapter 10 Page 4 IRR
13. Answer: e Diff: M The internal rate of return of a capital investment
a. Changes when the cost of capital changes.
b. Is equal to the annual net cash flows divided by one half of the
project's cost when the cash flows are an annuity.
c. Must exceed the cost of capital in order for the firm to accept the
investment.
d. Is similar to the yield to maturity on a bond.
e. Answers c and d are correct. Ranking methods
14. Answer: b Diff: M Which of the following statements is correct?
a. Because discounted payback takes account of the cost of capital, a
project's discounted payback is normally shorter than its regular
payback.
b. The NPV and IRR methods use the same basic equation, but in the NPV
method the discount rate is specified and the equation is solved for
NPV, while in the IRR method the NPV is set equal to zero and the
discount rate is found.
c. If the cost of capital is less than the crossover rate for two
mutually exclusive projects' NPV profiles, a NPV/IRR conflict will
not occur.
d. If you are choosing between two projects which have the same life,
and if their NPV profiles cross, then the smaller project will
probably be the one with the steeper NPV profile.
e. If the cost of capital is relatively high, this will favor larger,
longerterm projects over smaller, shorterterm alternatives because
it is good to earn high rates on larger amounts over longer periods. Ranking methods
15. Answer: e Diff: M In comparing two mutually exclusive projects of equal size and equal
life, which of the following statements is most correct?
a. The project with the higher
the higher IRR.
b. The project with the higher
the higher MIRR.
c. The project with the higher
the higher MIRR.
d. All of the answers above are
e. Answers a and c are correct. NPV may not always be the project with
NPV may not always be the project with
IRR may not always be the project with
correct. Chapter 10 Page 5 Miscellaneous concepts
16. Answer: e Diff: M Which of the following statements is most correct?
a. The IRR method is appealing to some managers because it produces a
rate of return upon which to base decisions rather than a dollar
amount like the NPV method.
b. The discounted payback method solves all the problems associated
with the payback method.
c. For independent projects, the decision to accept or reject will
always be the same using either the IRR method or the NPV method.
d. All of the statements above are correct.
e. Statements a and c are correct. Miscellaneous concepts
17. Answer: a Diff: M Which of the following statements is most correct?
a. One of the disadvantages of choosing between mutually exclusive
projects on the basis of the discounted payback method is that you
might choose the project with the faster payback period but with the
lower total return.
b. Multiple IRRs can occur in cases when project cash flows are normal,
but they are more common in cases where project cash flows are
nonnormal.
c. When choosing between mutually exclusive projects, managers should
accept all projects with IRRs greater than the weighted average cost
of capital.
d. All of the statements above are correct.
e. Two of the statements above are correct. Miscellaneous concepts
18. Answer: a Diff: M Normal projects C and D are mutually exclusive. Project C has a higher
net present value if the WACC is less than 12 percent, whereas Project
D has a higher net present value if the WACC exceeds 12 percent. Which
of the following statements is most correct?
a.
b.
c.
d.
e. Project D has a higher internal
Project D is probably larger in
Project C probably has a faster
All of the statements above are
Answers a and c are correct. Chapter 10 Page 6 rate of return.
scale than Project C.
payback.
correct. Project selection
19. Answer: a Diff: M A company estimates that its weighted average cost of capital (WACC) is
10 percent.
Which of the following independent projects should the
company accept?
a. Project A requires an upfront expenditure of $1,000,000
generates a net present value of $3,200.
b. Project B has a modified internal rate of return of 9.5 percent.
c. Project C requires an upfront expenditure of $1,000,000
generates a positive internal rate of return of 9.7 percent.
d. Project D has an internal rate of return of 9.5 percent.
e. None of the projects above should be accepted. and and Multiple Choice: Problems
Payback period
20. Answer: b Diff: E The Seattle Corporation has been presented with an investment
opportunity which will yield cash flows of $30,000 per year in Years 1
through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year
10. This investment will cost the firm $150,000 today, and the firm's
cost of capital is 10 percent.
Assume cash flows occur evenly during
the year, 1/365th each day.
What is the payback period for this
investment?
a.
b.
c.
d.
e. 5.23
4.86
4.00
6.12
4.35 years
years
years
years
years Chapter 10 Page 7 NPV
21. Answer: a Diff: E As the director of capital budgeting for Denver Corporation, you are
evaluating two mutually exclusive projects with the following net cash
flows:
Project X
Cash Flow
$100,000
50,000
40,000
30,000
10,000 Year
0
1
2
3
4 Project Z
Cash Flow
$100,000
10,000
30,000
40,000
60,000 If Denver's cost of capital is 15 percent, which project would you
choose?
a.
b.
c.
d.
e. Neither
Project
Project
Project
Project project.
X, since
Z, since
X, since
Z, since it
it
it
it has
has
has
has the
the
the
the higher
higher
higher
higher IRR.
NPV.
NPV.
IRR. NPV
22. Answer: a
Two projects being considered
following projected cash flows: Year
0
1
2
3
4
5 are Project A
Cash Flow
$50,000
15,625
15,625
15,625
15,625
15,625 mutually exclusive and Diff: E
have the Project B
Cash Flow
$50,000
0
0
0
0
99,500 If the required rate of return on these projects is 10 percent, which
would be chosen and why?
a.
b.
c.
d.
e. Project B because it has the higher NPV.
Project B because it has the higher IRR.
Project A because it has the higher NPV.
Project A because it has the higher IRR.
Neither, because both have IRRs less than the cost of capital. Chapter 10 Page 8 Payback period
23. Answer: c Michigan Mattress Company is considering the purchase of land and the
construction of a new plant.
The land, which would be bought
immediately (at t = 0), has a cost of $100,000 and the building, which
would be erected at the end of the first year (t = 1), would cost
$500,000. It is estimated that the firm's aftertax cash flow will be
increased by $100,000 starting at the end of the second year, and that
this incremental flow would increase at a 10 percent rate annually over
the next 10 years. What is the approximate payback period?
a. 2
b. 4
c. 6
d. 8
e. 10 years
years
years
years
years Payback period
24. Answer: c Diff: M Haig Aircraft is considering a project which has an upfront cost paid
today at t = 0.
The project will generate positive cash flows of
$60,000 a year at the end of each of the next five years.
The
project’s NPV is $75,000 and the company’s WACC is 10 percent. What
is the project’s simple, regular payback?
a.
b.
c.
d.
e. 3.22
1.56
2.54
2.35
4.16 years
years
years
years
years Discounted payback
25. Diff: M Answer: e Diff: M Lloyd Enterprises has a project which has the following cash flows:
Year
0
1
2
3
4
5
The cost of capital is 10 percent.
payback?
a.
b.
c.
d.
e. 1.8763
2.0000
2.3333
2.4793
2.6380 Cash Flow
$200,000
50,000
100,000
150,000
40,000
25,000
What is the project's discounted years
years
years
years
years Chapter 10 Page 9 Discounted payback
26. Answer: b Polk Products is considering an investment project with the following
cash flows:
Year
0
1
2
3
4 Cash Flow
$100,000
40,000
90,000
30,000
60,000 The company has a 10 percent cost of capital.
discounted payback ?
a.
b.
c.
d.
e. 1.67
1.86
2.11
2.49
2.67 What is the project’s years
years
years
years
years Discounted payback
27. Diff: M Answer: d Diff: M Davis
Corporation
is
faced
with
two
independent
investment
opportunities. The corporation has an investment policy which requires
acceptable projects to recover all costs within 3 years.
The
corporation uses the discounted payback method to assess potential
projects and utilizes a discount rate of 10 percent.
The cash flows
for the two projects are: Year
0
1
2
3
4 Project A
Cash Flow
$100,000
40,000
40,000
40,000
30,000 Project B
Cash Flow
$80,000
50,000
20,000
30,000
0 Which investment project(s) does the company invest in?
a.
b.
c.
d. Project
Neither
Project
Project Chapter 10 Page 10 A only.
Project A nor Project B.
A and Project B.
B only. NPV
28. Answer: d The Seattle Corporation has been presented with an investment
opportunity which will yield endofyear cash flows of $30,000 per year
in Years 1 through 4, $35,000 per year in Years 5 through 9, and
$40,000 in Year 10. This investment will cost the firm $150,000 today,
and the firm's cost of capital is 10 percent. What is the NPV for this
investment?
a.
b.
c.
d.
e. $135,984
$ 18,023
$219,045
$ 51,138
$ 92,146 NPV
29. Answer: b Diff: M You are considering the purchase of an investment that would pay you
$5,000 per year for Years 15, $3,000 per year for Years 68, and
$2,000 per year for Years 9 and 10. If you require a 14 percent rate
of return, and the cash flows occur at the end of each year, then how
much should you be willing to pay for this investment?
a.
b.
c.
d.
e. $15,819.27
$21,937.26
$32,415.85
$38,000.00
$52,815.71 NPV and payback
30. Diff: M Answer: b Diff: M Shannon Industries is considering a project which has the following
cash flows:
Year
0
1
2
3
4 Cash Flow
?
$2,000
3,000
3,000
1,500 The project has a payback of 2.5 years. The firm’s cost of capital is
12 percent. What is the project’s net present value NPV?
a.
b.
c.
d.
e. $ 577.68
$ 765.91
$1,049.80
$2,761.32
$3,765.91 Chapter 10 Page 11 Beforetax cash flows
31. $1,993
$3,321
$1,500
$4,983
$5,019 IRR Answer: c Diff: E The capital budgeting director of Sparrow Corporation is evaluating a
project which costs $200,000, is expected to last for 10 years and
produce aftertax cash flows, including depreciation, of $44,503 per
year. If the firm's cost of capital is 14 percent and its tax rate is
40 percent, what is the project's IRR?
a.
b.
c.
d.
e. 8%
14%
18%
5%
12% IRR
33. Diff: M Scott Corporation's new project calls for an investment of $10,000. It
has an estimated life of 10 years. The IRR has been calculated to be
15 percent. If cash flows are evenly distributed and the tax rate is
40 percent, what is the annual beforetax cash flow each year? (Assume
depreciation is a negligible amount.)
a.
b.
c.
d.
e. 32. Answer: b Answer: c Diff: E An insurance firm agrees to pay you $3,310 at the end of 20 years if
you pay premiums of $100 per year at the end of each year for 20 years.
Find the internal rate of return to the nearest whole percentage point.
a. 9%
b. 7%
c. 5%
d. 3%
e. 11% Chapter 10 Page 12 IRR and mutually exclusive projects
34. Answer: d Diff: E A company is analyzing two mutually exclusive projects, S and L, whose
cash flows are shown below:
Years 0 1 2 3    1,000
0 350
300 50
1,500 k = 12% 
S 1,100
L 1,100 The company's cost of capital is 12 percent, and it can get an
unlimited amount of capital at that cost. What is the regular IRR (not
MIRR) of the better project, i.e., the project which the company should
choose if it wants to maximize its stock price?
a.
b.
c.
d.
e. 12.00%
15.53%
18.62%
19.08%
20.46% NPV and IRR
35. Answer: b Diff: E Your company is choosing between the following nonrepeatable, equally
risky, mutually exclusive projects with the cash flows shown below.
Your cost of capital is 10 percent.
How much value will your firm
sacrifice if it selects the project with the higher IRR?
Project S: 3    500 500 500 k = 10% k = 10% 
2,000
a.
b.
c.
d.
e. 2 1,000
0 1  Project L: 0 1
 668.76 2

668.76 3

668.76 4

668.76 5

668.76 $243.43
$291.70
$332.50
$481.15
$535.13 Chapter 10 Page 13 NPV and IRR
36. Answer: e Diff: E Green Grocers is deciding among two mutually exclusive projects.
two projects have the following cash flows:
Project A
Cash Flow
$50,000
10,000
15,000
40,000
20,000 Year
0
1
2
3
4 The Project B
Cash Flow
$30,000
6,000
12,000
18,000
12,000 The company’s cost of capital is 10 percent (WACC = 10%). What is the
net present value (NPV) of the project with the highest internal rate
of return (IRR)?
a.
b.
c.
d.
e. $ 7,090
$ 8,360
$11,450
$12,510
$15,200 NPV, IRR, and payback
37. Answer: d Diff: E Braun Industries is considering an investment project which has the
following cash flows:
Year
0
1
2
3
4 Cash Flow
$1,000
400
300
500
400 The company’s WACC is 10 percent.
What is the project’s payback,
internal rate of return, and net present value?
a.
b.
c.
d.
e. Payback
Payback
Payback
Payback
Payback Chapter 10 Page 14 =
=
=
=
= 2.4,
2.4,
2.6,
2.6,
2.6, IRR
IRR
IRR
IRR
IRR =
=
=
=
= 10.00%,
21.22%,
21.22%,
21.22%,
24.12%, NPV
NPV
NPV
NPV
NPV =
=
=
=
= $600.
$260.
$300.
$260.
$300. Replacement chain
38. Answer: d Vanderheiden Inc. is considering two averagerisk alternative ways of
producing its patented polo shirts. Process S has a cost of $8,000 and
will produce net cash flows of $5,000 per year for 2 years. Process L
will cost $11,500 and will produce cash flows of $4,000 per year for 4
years.
The company has a contract that requires it to produce the
shirts for 4 years, but the patent will expire after 4 years, so the
shirts will not be produced after 4 years. Inflation is expected to be
zero during the next 4 years. If cash inflows occur at the end of each
year, and if Vanderheiden's cost of capital is 10 percent, by what
amount will the better project increase Vanderheiden's value?
a.
b.
c.
d.
e. $ 677.69
$1,098.89
$1,179.46
$1,237.76
$1,312.31 Mutually exclusive projects
39. Diff: E Answer: b Diff: M Two projects being considered by a firm are mutually exclusive and have
the following projected cash flows: Year
0
1
2
3 Project A
Cash Flow
($100,000)
39,500
39,500
39,500 Project B
Cash Flow
($100,000)
0
0
133,000 Based only on the information given, which of the two projects would be
preferred, and why?
a.
b.
c.
d. Project A, because it has a shorter payback period.
Project B, because it has a higher IRR.
Indifferent, because the projects have equal IRRs.
Include both in the capital budget, since the sum
inflows exceeds the initial investment in both cases.
e. Choose neither, since their NPVs are negative. of the cash Chapter 10 Page 15 IRR
40. Answer: d Diff: M Genuine Products Inc. requires a new machine.
Two companies have
submitted bids, and you have been assigned the task of choosing one of
the machines. Cash flow analysis indicates the following:
Machine A
Cash Flow
$2,000
0
0
0
3,877 Year
0
1
2
3
4 Machine B
Cash Flow
$2,000
832
832
832
832 What is the internal rate of return for each machine?
a.
b.
c.
d.
e. IRRA
IRRA
IRRA
IRRA
IRRA =
=
=
=
= 16%;
24%;
18%;
18%;
24%; IRRB
IRRB
IRRB
IRRB
IRRB =
=
=
=
= 20%
20%
16%
24%
26% IRR
41. Answer: c
Whitney
Crane
Inc.
has
the
opportunities for the coming year: Project
A
B
C
D Cost
$10,000
5,000
12,000
3,000 following Annual
Cash Inflows
$11,800
3,075
5,696
1,009 independent Life
(Years)
1
2
3
4 The IRRs for Projects A and C, respectively, are:
a.
b.
c.
d.
e. 16%
18%
18%
18%
16% and
and
and
and
and Chapter 10 Page 16 14%
10%
20%
13%
13% IRR
15
13 Diff: M investment NPV and IRR
42. Answer: a Diff: M A company is analyzing two mutually exclusive projects, S and L, whose
cash flows are shown below:
Years 0 1 2 3 4 S
L 1,100
1,100 900
0 350
300 50
500 10
850 The company's cost of capital is 12 percent, and it can get an
unlimited amount of capital at that cost. What is the regular IRR (not
MIRR) of the better project? (Hint: Note that the better project may
or may not be the one with the higher IRR.)
a.
b.
c.
d.
e. 13.09%
12.00%
17.46%
13.88%
12.53% IRR of uneven CF stream
43. Diff: M Your company is planning to open a new gold mine which will cost $3
million to build, with the expenditure occurring at the end of the year
three years from today.
The mine will bring yearend aftertax cash
inflows of $2 million at the end of the two succeeding years, and then
it will cost $0.5 million to close down the mine at the end of the
third year of operation. What is this project's IRR?
a.
b.
c.
d.
e. 14.36%
10.17%
17.42%
12.70%
21.53% IRR of uneven CF stream
44. Answer: d Answer: e Diff: M As the capital budgeting director for Chapel Hill Coffins Company, you
are evaluating construction of a new plant. The plant has a net cost
of $5 million in Year 0 (today), and it will provide net cash inflows
of $1 million at the end of Year 1, $1.5 million at the end of Year 2,
and $2 million at the end of Years 3 through 5. Within what range is
the plant's IRR?
a.
b.
c.
d.
e. 14
15
16
17
18  15%
16%
17%
18%
19% Chapter 10 Page 17 NPV profiles
45. Answer: d The following
projects: cash flows Year
0
1
2
3
4 are estimated Project A
Cash Flow
$100,000
60,000
40,000
20,000
10,000 for two mutually Diff: M exclusive Project B
Cash Flow
$110,000
20,000
40,000
40,000
50,000 When is Project B more lucrative than Project A? (That is, over what
range of costs of capital (k) does Project B have a higher NPV than
Project A?) (Choose the best answer.)
a.
b.
c.
d.
e. For all
Project
Project
For all
For all values of k
B is always
A is always
values of k
values of k Replacement chain
46. less than 7.25%.
more profitable than Project A.
more profitable than Project B.
less than 6.57%.
greater than 6.57%.
Answer: c Diff: M Doherty Industries wants to invest in a new computer system.
The
company only wants to invest in one system, and has narrowed the choice
down to System A and System B.
System A requires an upfront cost of $100,000 and then generates
positive aftertax cash flows of $60,000 at the end of each of the next
two years.
The system can be replaced every two years with the cash
inflows and outflows remaining the same.
System B also requires an upfront cost of $100,000 and then generates
positive aftertax cash flows of $48,000 at the end of each of the next
three years. System B can be replaced every three years, but each time
the system is replaced, both the cash inflows and outflows increase by
10 percent.
The company needs a computer system for the six years, after which time
the current owners plan on retiring and liquidating the firm.
The
company's cost of capital is 11 percent.
What is the NPV (on a sixyear extended basis) of the system which creates the most value to the
company?
a.
b.
c.
d.
e. $ 17,298.30
$ 22,634.77
$ 31,211.52
$ 38,523.43
$103,065.82 Chapter 10 Page 18 Replacement chain
47. Answer: e Diff: M Johnson Jets is considering two mutually exclusive machines. Machine A
has an upfront cost of $100,000
(CF 0 = 100,000), and produces
positive aftertax cash inflows of $40,000 a year at the end of each of
the next six years.
Machine B has an upfront cost of $50,000(CF 0 = 50,000) and produces
aftertax cash inflows of $30,000 a year at the end of the next three
years.
After three years, machine B can be replaced at a cost of
$55,000 (paid at t = 3). The replacement machine will produce aftertax cash inflows of $32,000 a year for three years (inflows received at
t = 4, 5, and 6).
The company’s cost of capital is 10.5 percent. What is the net present
value (on a sixyear extended basis) of the most profitable machine?
a.
b.
c.
d.
e. $23,950
$41,656
$56,238
$62,456
$71,687 Chapter 10 Page 19 CHAPTER 10
Answers and Solutions
1. Ranking methods Answer: b Diff: E A project's NPV increases as the cost of capital declines. A project's
IRR is independent of its cost of capital, while a project's MIRR is
dependent on the cost of capital since the terminal value in the MIRR
equation is compounded at the cost of capital.
2. Ranking conflicts Answer: a Diff: E 3. Payback period Answer: e Diff: E 4. NPV and IRR Answer: a Diff: E Statement a is correct; the other statements are false.
If the
projects are mutually exclusive, then project B may have a higher NPV
even though Project A has a higher IRR.
IRR is calculated assuming
cash flows are reinvested at the IRR, not the cost of capital.
5. NPV and IRR Answer: a Diff: E Statement a is true; projects with IRRs greater than the cost of
capital will have a positive NPV.
Statement b is false because you
know nothing about the relative magnitudes of the projects. Statement
c is false because the IRR is independent of the cost of capital.
Therefore, the correct choice is statement a.
6. Postaudit Answer: e Diff: E 7. IRR Answer: b Diff: E The correct statement is b; the other statements are false.
Since
Project A’s IRR is 15%, at a WACC of 15% NPV A = 0; however, Project B
would still have a positive NPV. Given the information in a, we can’t
conclude which project’s NPV is going to be greater.
Since we are
given no details about each project’s cash flows we cannot conclude
anything about payback.
Finally, IRR is independent of the discount
rate, i.e., IRR stays the same no matter what the WACC is.
8. NPV profiles Answer: b Diff: M 9. NPV profiles Answer: a Diff: M 10. NPV and IRR Answer: c Diff: M 11. NPV and IRR Answer: a Diff: M Statement a is the incorrect statement.
greater than the cost of capital. Chapter 10 Page 20 NPV is positive if IRR is 12. NPV, IRR, and payback Answer: e Diff: M Statement e is correct; the other statements are incorrect. Statement a
is incorrect; the two projects' NPV profiles could cross, consequently,
a higher IRR doesn't guarantee a higher NPV. Statement b is incorrect;
if the two projects' NPV profiles cross, Y could have a higher NPV.
Statement c is incorrect; we don't have enough information.
13. IRR Answer: e Diff: M 14. Ranking methods Answer: b Diff: M This statement reflects exactly the difference between the NPV and IRR
methods.
15. Ranking methods Answer: e Diff: M Both statements a and c are correct; therefore, statement e is the
correct choice. Due to reinvestment rate assumptions, NPV and IRR can
lead to conflicts; however, there will be no conflict between NPV and
MIRR if the projects are equal in size (which is one of the assumptions
in this question).
16. Miscellaneous concepts Answer: e Diff: M Statements a and c are correct; therefore, statement e is the correct
choice.
The discounted payback method still ignores cash flows after
the payback period.
17. Miscellaneous concepts Answer: a Diff: M Statement a is correct; the other statements are false. Multiple IRRs
can occur only for projects with nonnormal cash flows.
Mutually
exclusive projects imply that only one project should be chosen.
The
project with the highest NPV should be chosen.
18. Miscellaneous concepts Answer: a Diff: M Statement a is correct; the other statements are false.
Sketch the
profiles.
From the information given, D has the higher IRR.
The
project’s scale cannot be determined from the information given.
As
C’s NPV declines more rapidly with an increase in rates, this implies
that more of the cash flows are coming later on.
So C would have a
slower payback than D.
19. Project selection Answer: a Diff: M This is the only project with either a positive NPV or an IRR which
exceeds the cost of capital. Chapter 10 Page 21 20. Payback period
Time line: Answer: b Diff: E ( In thousands ) 0 1
2
3
4
5
6
7
8
9
10 Yrs
k = 10%
_________________________________________________________________________________________
CFs 150
30
30
30
30
35
35
35
35
35
40
Cumulative
CFs 150
120
90
60
30
5 Using the even cash flow distribution assumption, the project will
completely recover initial investment after 30/35 = 0.86 of Year 5:
Payback = 4 +
21. 30
= 4.86 years.
35 NPV Answer: a Time line:
0
CFX Project X (In thousands)
1
2
k = 15% 100 50 3 40 Diff: E 4 Years 30 10 k = 15% NPVx = 43.478
30.246
19.725
5.718
0.833 = $833 k = 15%
k = 15%
k = 15% Project Z (In thousands)
0
1
k = 15%
CFX 100
8.696
22.684
26.301
34.305 NPVZ = 2
30 10 3 4 Years 40 60 k = 15%
k = 15%
k = 15%
k = 15% 8.014 = $8,014. At a cost of capital of 15%, both projects have negative NPVs and,
thus, both would be rejected.
Numerical solution: (In thousands)
NPVX = 100 + 50(1/1.15) + 40(1/1.15 2) + 30(1/1.153) + 10(1/1.154)
= 100 + 50(0.8696) + 40(0.7561) + 30(0.6575) + 10(0.5718)
= 0.833 = $833.
NPVZ = 100 + 10(1/1.15) + 30(1/1.15 2) + 40(1/1.153) + 60(1/1.154)
= 100 + 10(0.8696) + 30(0.7561) + 40(0.6575) + 60(0.5718)
= 8.013 = $8,013.
Financial calculator solution: (In thousands)
Project X Inputs: CF0 = 100; CF1 = 50; CF2 = 40; CF3 = 30;
CF 4 = 10; I = 15.
Output: NPV X = 0.833 = $833.
Project Z Inputs: CF0 = 100; CF1 = 10; CF2 = 30; CF3 = 40;
CF 4 = 60; I = 15.
Output: NPV Z = 8.014 = $8,014.
Chapter 10 Page 22 22. NPV
Time line:
0 Answer: a k = 10% CFA 50,000
NPV A = ?
CFB 50,000
NPV B = ? 1 2 15,625 3 15,625 4 15,625 Diff: E 5 Years 15,625 15,625
99,500 Numerical solution:
NPVA = $15,625[(1/0.10)(1/(0.10*(1+0.10) 5)]  $50,000
= $15,625(3.7908)  $50,000
= $59,231.25  $50,000 = $9,231.25.
NPVB = $99,500(1/1.10 5)  $50,000 = $99,500(0.6209)  $50,000
= $61,779.55  $50,000 = $11,779.55.
NPVB > NPVA; $11,779.55 > $9,231.25; Choose Project B.
Financial calculator solution:
Project A Inputs: N = 5; I = 10; PMT = 15,625.
Output: PV = 59,231.04.
NPV A = $59,231.04  $50,000 = $9,231.04.
Project B Inputs: N = 5; I = 10; FV = 99,500.
Output: PV = 61,781.67.
NPV B = $61,781.67  $50,000 = $11,781.67.
Alternate method by cash flows:
Project A Inputs: CF0 = 50,000; CF 1 = 15,625; Nj = 5; I = 10.
Output: NPV = $9,231.04.
Project B Inputs: CF0 = 50,000; CF 1 = 0; Nj = 4; CF2 = 99,500; I = 10.
Output: NPV = $11,781.67.
23. Payback period Time line: Answer: c (In thousands)
0 CF
Cumulative
NCF Diff: M 1 2 100 500 100 600 Payback = 5 + 3 4 5 6 10 100 110 121 133.1 146.41 500 390 269 135.9 Years 10.51 $135.9
= 5.928 years ≈ 6 years.
$146.41 Chapter 10 Page 23 24. Payback period Answer: c Diff: M Step 1 Calculate the PV of the cash flows:
PVA5 = $60,000[(1/0.10)(1/(0.10*(1.10) 5)]
= $60,000(3.7908)
= $227,448. Step 2 Calculate the Year 0 outflow:
The outflow at t = 0 is X where $227,448  X = $75,000.
CF0 = $152,448. Step 3 Calculate the regular payback:
Year
CF
0
$152,448
1
60,000
2
60,000
3
60,000
4
60,000
5
60,000
So the payback is 2 + 25. Cumulative CF
$152,448
92,448
32,448
27,552
87,552
147,552 $32 448
,
= 2.54 years.
$60, 00
0 Discounted payback
0 Answer: e 3
4
5 3 50,000 100,000 150,000 40,000 25,000 50,000
1 .1
Discounted
CFs 200,000 100,000
(1.1) 2 1 50,000
( 1.1) 3 4 0,000
( 1.1) 4 2 5,000
( 1.1) 5 27,320.54 15,523.03 45,454.55 Discounted CF
200,000.00
45,454.55
82,644.63
Payback
112,697.22
27,320.54
15,523.03 Cumulative CF
200,000.00
154,545.45
71,900.82 Payback period = 2 years + Chapter 10 Page 24 82,644.63 112,697.22 4 Diff: M 2 k = 1 0% CFs 200,000 0
1
2 1 X or +40,796.40
+68,116.94
+83,639.97
$71,900.82
= 2.638 years.
$112,697.22 5 26. Discounted payback Year
0
1
2
3
4 Answer: b Answer: d Cash Flow
$100,000
40,000
90,000
30,000
60,000 Discounted Payback = 1 +
27. Discounted
Cash Flow
$100,000.00
36,363.64
74,380.17
22,539.44
40,980.81 Diff: M Diff: M Cumulative
Cash Flow
$100,000.00
63,636.36
10,743.81
33,283.25
74,264.06 $63,636.36
= 1.86 years.
$74,380.17 Discounted payback The sum of the PVs of the t = 1, t = 2, and t = 3 cash flows at t = 0
for Project A is $99,474.08.
Thus, the discounted payback period of
Project A exceeds 3 years and Project A is not acceptable. The PVs of
the t = 1, t = 2, and t = 3 cash flows at t = 0 for Project B are
$45,454.55, $16,528.93, and $22,539.44, respectively. These PVs sum to
$84,522.92, which is greater than the cost of the project, indicating
that the discounted payback period is less than 3 years. Thus, Project
B will be undertaken.
28. NPV Answer: d T ime line:
0 k = 10% 150 Diff: M (In thousands) 1 2 3 4 5 6 7 8 9 10 Yrs. 30 30 30 30 35 35 35 35 35 40 NPV = ? Numerical solution:
NPV = $30,000[(1/0.10)(1/(0.10*(1+0.10) 4)]
+ $35,000[(1/0.10)(1/(0.10*(1+0.10) 5)](1/1.104)
+ $40,000(1/1.10 10)  $150,000
= $30,000(3.1699) + $35,000(3.7908)(0.6830)
+ $40,000(0.3855)  $150,000 = $51,136.07 ≈ $51,136.
Financial calculator solution: (In thousands)
Inputs: CF0 = 150; CF1 = 30; Nj = 4; CF 2 = 35; Nj = 5; CF3 = 40; I = 10.
Output: NPV = $51.13824 = $51,138.24 ≈ $51,138. Chapter 10 Page 25 29. NPV Answer: b Diff: M Time line: (In thousands)
0 k = 14% PV = ? 1 2 3 4 5 6 7 8 9 5 5 5 5 5 3 3 3 10 Yrs. 2 2 Numerical solution:
PV = $5,000[(1/0.14)(1/(0.14*(1+0.14) 5
+ $3,000[(1/0.14)(1/(0.14*(1+0.14) 3 (1/1.145)
+ $2,000[(1/0.14)(1/(0.14*(1+0.14) 2 (1/1.148)
= $5,000(3.4331) + $3,000(2.3216)(0.5194) + $2,000(1.6467)(0.3506)
= $17,165.50 + $3,617.52 + $1,154.67 = $21,937.69.
Financial calculator solution: (In thousands)
Inputs:
CF0 = 0; CF1 = 5; Nj = 5; CF2 = 3; Nj = 3; CF3 = 2; Nj = 2;
I = 14.
Output: NPV = 21.93726 = $21,937.26.
Note:
Numerical solution differs from calculator solution due to
rounding.
30. NPV and payback Answer: b Diff: M First, find the missing t = 0 cash flow. If payback = 2.5 years, this
implies t = 0 cash flow must be $2,000  $3,000 + (0.5)$3,000 =
$6,500.
$2 000
,
$3,
000
$3,
000
$1,
500
NPV = $6,500 +
+
+
+
2
3
4
(1.12)
(1.12)
(1.12)
1.12
= $765.91.
31. Beforetax cash flows
T ime line:
0
1
IRR = 15%
10,000 PMT = ? Answer: b 2 3 4 PMT PMT PMT Numerical solution:
X = aftertax cash flow.
Y = beforetax cash flow.
X = Y(1  T).
$10,000
$10,000
X
$1,992.51
Y =
=
=
=
= X[(1/0.15)(1/(0.15*(1+0.15) 10)]
X(5.0188)
$1,992.51.
Y(1  0.40)
$3,320.85 ≈ $3,321. Financial calculator solution:
Inputs: N = 10; I = 15; PV = 10,000. Output: PMT = $1,992.52.
Beforetax CF = $1,992.52/0.6 = $3,320.87 ≈ $3,321.
Chapter 10 Page 26 Diff: M 10 Years PMT 32. IRR Answer: c T ime line:
k = 14%
0 IRR = ?
200,000 1 2 44,503 33. 10 Years 44,503 Financial calculator solution:
Inputs: CF0 = 200,000; CF 1 = 44,503; Nj = 10. Diff: E 44,503 Output: IRR = 18%. IRR Answer: c T i me l i ne :
0
IRR = ? 1 2 PMT = 100 Diff: E 2 0 Y e a rs  10 0 100
FV = 3,310 Financial calculator solution:
Inputs: CF0 = 0; CF1 = 100; Nj = 19; CF2 = 3,210. Output: IRR = 5.0%.
Alternate method annuity calculation
Inputs: N = 20; PMT = 100; FV = 3,310. Output: I = 5.0%
34. IRR and mutually exclusive projects Answer: d Diff: E Because the two projects are mutually exclusive, the project with the
higher positive NPV is the "better" project.
0
S k 1 0 2 3 1,000 12% 1,100 NPVS = $107.46. L = 350 50 IRR S = 20.46%.
k 1,100 = 12% 1 2 0 3 300 1,500 NPVL = $206.83.
IRR L = 19.08%.
Project L is the "better" project; its IRR = 19.08%.
35. NPV and IRR Answer: b Diff: E NPVS = $243.43; IRR S = 23.38%.
NPVL = $535.13; IRR L = 20.00%.
Value sacrificed: $535.13  $243.43 = $291.70. Chapter 10 Page 27 36. NPV and IRR Answer: e Diff: E Enter the cash flows for each project into the cash flow register on
the calculator and get the NPV and IRR.
NPVA = $15,200; IRR A = 21.3811%.
NPVB = $7,092; IRR B = 19.2783%.
Project A has the highest IRR, so the answer is $15,200.
37. NPV, IRR, and payback Answer: d Diff: E 38. Payback = 2 + 300/500 = 2.6 years.
Using the cash flow register, calculate NPV and IRR:
IRR = 21.22%.
NPV = $260.43 ≈ $260.
Replacement chain Answer: d Diff: E 0 k = 1 10% 2 3 4 S
8,000 5,000 IRRS = 16.26%.
NPVS = $1,237.76.
0 k = 5,000
8,000
3,000 5,000 (extended NPV)
1 10% 5,000 2 3 4 L
11,500 4,000 4,000 4,000 4,000 IRRL = 14.66%.
NPVL = $1,179.46.
39. Mutually exclusive projects Answer: b Diff: M T ime line:
0
CF A
CF B IRR A = ?
I RR B = ?  100,000
 100,000 1
39,500
0 Financial calculator solution:
Project A: Inputs: CF0 = 100,000;
Output: IRR A = 8.992% ≈
Project B: Inputs: CF0 = 100,000;
Output: IRR B = 9.972% ≈ Chapter 10 Page 28 2
39,500
0 3 Y ears 39,500
133,000 CF 1 = 39,500; Nj = 3.
9.0%.
CF 1 = 0; Nj = 2; CF2 = 133,000.
10.0%. 40. IRR Answer: d Diff: M T ime line:
IRR A 0 IRR B
CF A
CF B 41. =
= ?
?1  2,000
 2,000 0
832 2 3 0
832 4 Y ears 0
832 3,877
832 Financial calculator solution:
Machine A Inputs: CF0 = 2,000; CF 1 = 0; Nj = 3; CF2 = 3877.
Output: IRR = 17.996% ≈ 18%.
Machine B Inputs: CF0 = 2,000; CF 1 = 832; Nj = 4.
Output: IRR = 24.01% ≈ 24%.
IRR
Answer: c Diff: M Financial calculator solution:
Project A
Inputs: N = 1; PV = 10,000; FV = 11,800.
Output: I = 18% = IRR A.
Project C
Inputs: N = 3; PV = 12,000; PMT = 5,696.
Output: I = 19.99% ≈ 20% = IRRC.
42. NPV and IRR Answer: a Diff: M Time line:
0 k = 12% 1 Cash flows S 1,100
NPV S = ?
Cash flows L 1,100
NPV L = ? 900
IRR S = ?
0
IRR L = ? 2 3 4 350 50 10 300 500 Years 850 Financial calculator solution:
Calculate the NPV and IRR of each project then select the IRR of the
higher NPV project
Project S; Inputs: CF0 = 1,100; CF1 = 900; CF2 = 350; CF3 = 50; CF4 = 10;
I = 12
Output: NPV S = 24.53; IRR S = 13.88%.
Project L; Inputs: CF0 = 1,100; CF1 = 0; CF2 = 300; CF3 = 500; CF4 = 850;
I = 12
Output: NPV L = 35.24; IRR L = 13.09%.
Project L has the higher NPV and its IRR = 13.09%. Chapter 10 Page 29 43. IRR of uneven CF stream
T ime line:
0
1 Answer: d 2 3 IRR = ? 4 5 6 Diff: M Years 3,000,000 2,000,000 2,000,000 500,000 Financial calculator solution: (In millions)
Inputs: CF0 = 3; CF1 = 2; Nj = 2; CF2 = .5.
Output: IRR% = 12.699 ≈ 12.70%.
44. IRR of uneven CF stream Answer: e T ime line: ( In millions)
0 IRR = ? 1
2 3 4 5 5 2 2 Diff: M 2 1 1.5 Years Financial calculator solution: (In millions)
Inputs: CF0 = 5; CF1 = 1.0; CF2 = 1.5; CF3 = 2.0; Nj = 3.
Output: IRR% = 18.37%.
45. NPV profiles Answer: d Diff: M First, solve for the crossover rate.
If you subtract the cash flows
(CFs) of Project A from the CFs of Project B, then the differential CFs
are CF0 = $10,000, CF1 = $40,000, CF2 = 0, CF3 = $20,000, and CF4 =
$40,000. Entering these CFs and solving for IRR/YR yields a crossover
rate of 6.57%. Thus, if the cost of capital is 6.57%, then Projects A
and B have the same NPV.
If the cost of capital is less than 6.57%,
then Project B has a higher NPV than Project A, since Project B's cash
inflows come comparatively later in the project life.
For lower
discount rates, Project B's NPV is not penalized as much for having
large cash inflows farther in the future than Project A.
46. Replacement chain Answer: c Diff: M To find the NPV of the system we must use the replacement chain approach.
Time
0
1
2
3
4
5
6 System A
100,000
60,000
60,000  100,000 = 40,000
60,000
60,000  100,000 = 40,000
60,000
60,000 System B
100,000
48,000
48,000
48,000  110,000 = 62,000
52,800
52,800
52,800 Use the CF key to enter the cash flows for each period.
I/YR = 11.
This should give the following NPVs:
NPV A = $6,796.93.
NPV B = $31,211.52.
Computer system B creates the most value for the firm, so the correct
answer is c. Chapter 10 Page 30 47. Replacement chain Answer: e Diff: M The CFs and NPVs (calculated with I = k = 10.5%) are as follows:
t
0
1
2
3
4
5
6
NPV Project A
100,000
40,000
40,000
40,000
40,000
40,000
40,000
$71,687.18 ≈
$71,687 Project B
50,000
30,000
30,000
30,000  55,000 = 25,000
32,000
32,000
32,000
$41,655.58 ≈
$41,656 Chapter 10 Page 31 ...
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 Spring '12
 Rhee
 International Finance

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