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g. (1) The net present value (NPV) is simply the sum of the present values of a project’s cash
flows:
( )
n
t
t
t0
ˆ
CF
1r
=
We refer to the completed cash flow time line and explain how each of the indicators is
calculated. We base our explanation on financial calculators, but it would be equally easy
to explain using a regular calculator. The cash flow time line and the NPV computation are:
(2) The rationale behind the NPV method is straightforward: If a project has NPV = $0, then
the project generates exactly enough cash flows (1) to recover the cost of the investment
h. (1) The internal rate of return (IRR) is the discount rate that forces the NPV of a project to
equal zero; it is the rate of return the project is expected to generate:
(260.00) 79.7 91.2 62.4 89.7
72.45
75.37
46.88
61.27
( 4.03)
0 1 2 3 4
10%
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Expressed as an equation, we have:
( )
=
+
0t t
IRR1
Note that the IRR equation is the same as the NPV equation, except that to find the
IRR, the equation is solved for the particular discount rate that forces the project’s NPV
to equal zero (the IRR) rather than using the cost of capital (k) in the denominator and
(2) The IRR is to a capital project what the YTM is to a bond—it is the expected rate of return
on the project, just as the YTM is the promised rate of return on a bond.
(3) IRR measures a project’s profitability in the rate of return sense: If a project’s IRR equals
its required rate of return, then its cash flows are just sufficient to provide investors with
(4) The IRR is independent of the required rate of return. Therefore, the IRR would not change
(260.00) 79.7 91.2 62.4 89.7
PV of CF1
PV of CF2
PV of CF3
PV of CF4
NPV= 0
0 1 2 3 4
IRR
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i. (1) The MIRR is the rate of return that equates a project’s terminal value to the present value
of its cash outflows. Cash inflows are compounded to the end of the project’s life at the
firm’s required rate of return, cash outflows are discounted at the firm’s required rate of
return, and then the rate at which these two value are equal is the MIRR. To compute the
MIRR, solve this equation:
n
n
)MIRR1(
TV
+
=
outflows cash of PV
(2) The modified IRR has a significant advantage over the traditional IRR measure. MIRR
assumes that cash flows are reinvested at the required rate of return, whereas the
(3) The cash outflows are discounted at the firm’s required rate of return, and the cash
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j. The NPV profile is plotted in the figure below.
k. In a replacement analysis, we must find differences in cash flows—that is, the cash flows that
l. It is apparent from the data in the previous table that inflation has not been reflected in the
13-36 Integrative Problem
a. (1) We used a spreadsheet model to develop the scenarios (in thousands of dollars), which
are summarized below:
Case Probability NPV (000s)
NPV
r
IRR = 9.3%
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( )
NPV
E NPV $1.7
b. (1) The project has a CV of 14.6, which is much higher than the average range of 2.0 to 3.0,
(2) It is reasonable to assume that if the economy is strong and people are buying a lot of
(3) If the project’s cash flows are highly correlated with the firm’s aggregate cash flows, which
generally is a reasonable assumption, then the project would have high corporate risk.
c. (1) Because the project is judged to have above-average risk, its differential risk-adjusted, or
(2) A numerical analysis such as this one might not capture all of the risk factors inherent in
d. The SML can be used to estimate the project’s required rate of return on equity:
13–41
13-37 Computer-Related Problem
a. & b.
INPUT DATA: KEY OUTPUT:
Expected Cash Flows
Year Proj. A Proj. B Proj. A Proj. B
0 (45,000) (50,000) NPV 2,600 2,758
MODEL-GENERATED DATA:
NPV profile:
Proj. A Proj. B
r NPV NPV
0.00% 41,000 25,000
Crossover rate calculation:
Delta’s Required NPV of
Year CFs Return Delta
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c. Because the projects are mutually exclusive, only one can be chosen. Following are the
NPVs for the two projects at the different required rates of return:
r NPVA NPVB Project to Purchase
INPUT DATA: KEY OUTPUT:
Expected Cash Flows
Year Proj. A Proj. B Proj. A Proj. B
0 (45,000) (50,000) NPV –114 2,758
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e. (2) Year 4 cash flow = $50,000
INPUT DATA: KEY OUTPUT:
Expected Cash Flows
Year Proj. A Proj. B Proj. A Proj. B
0 (45,000) (50,000) NPV 5,314 2,758
13-38 Computer-Related Problem
a. The NPV of the project is positive (NPV = $57,186), so Golden State should purchase the
machine and expand its operations.
INPUT DATA: KEY OUTPUT:
Base price 260,000 NPV
MODEL-GENERATED DATA:
1.Cost of investment at t=0:
Depreciation schedule:
Basis = 275,000
Ending
Year MACRS Depreciation Book
Rate Allowance Value
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Annual cash flows:
0 1 2 3 4 5 6 7 8 9 10
Cash Outlay –297,500
Depr. tax savings 22,000 35,200 20,900 13,200 12,100 6,600 0 0 0 0
b. The NPV of the project is negative (NPV = -27,254), so Golden State should not purchase the
machine and expand its operations.
INPUT DATA: KEY OUTPUT:
Base price 260,000 NPV
Modifications 15,000 -27,254
MODEL-GENERATED DATA:
1.Cost of investment at t=0:
Depreciation schedule:
Ending
Year MACRS Depreciation Book
Rate Allowance Value
1 0.20 55,000 220,000
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Annual cash flows:
0 1 2 3 4 5
Cash Outlay -297,500
c. The NPV of the project is negative (NPV = -16,549), so Golden State should not purchase the
machine and expand its operations.
INPUT DATA: KEY OUTPUT:
Base price 260,000 NPV
MODEL-GENERATED DATA:
1.Cost of investment at t=0:
Depreciation schedule:
Basis = 275,000
Ending
Year MACRS Depreciation Book
Rate Allowance Value
1 0.20 55,000 220,000
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Annual cash flows:
0 1 2 3 4 5 6 7 8 9 10
Cash Outlay -297,500
Depr. tax savings 22,000 35,200 20,900 13,200 12,100 6,600 0 0 0 0
d. The NPV of the project is negative (NPV = 20,318.56), so Golden State should not purchase
the machine and expand its operations.
INPUT DATA: KEY OUTPUT:
Base price 260,000 NPV
MODEL-GENERATED DATA:
1.Cost of investment at t=0:
Depreciation schedule:
Basis = 275,000
Ending
Year MACRS Depreciation Book
Rate Allowance Value
1 0.20 55,000 220,000
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Annual cash flows:
0 1 2 3 4 5 6 7 8 9 10
Cash Outlay -297,500
Depr. tax savings 22,000 35,200 20,900 13,200 12,100 6,600 0 0 0 0
Solutions to Appendix Problem
13A-1 MACRS MACRS Straight-Line Difference in PV of
Year Rate Depreciation Depreciation Depreciation Tax Savings Savings
1 0.10 $ 10,000,000 $ 10,000,000 $ 0 $ 0 $ 0
2 0.18 18,000,000 10,000,000 8,000,000 2,720,000 2,289,370
ETHICAL DILEMMA
This Is a Good Investment—Be Sure the Numbers Show that It Is!
Ethical dilemma:
Oliver Greene is a relatively recent college graduate whose primary responsibility with Cybercomp, Inc. is to
evaluate capital budgeting projects and make recommendations to the board of directors. He is paid very
well in his current position. Oliver finds himself in a situation where the CEO of Cybercomp, Nadine Wilson,
insists that the proposal to purchase Netware Products be made to look good. Netware manufactures
circuitry that complements Cybercomp’s products. A preliminary appraisal report given to Oliver suggests
the purchase might not be very judicious; the report was completed two years ago. Nadine has made it clear
to Oliver that she wants his analysis to recommend that Netware be purchased by Cybercomp. To make
matters worse, the gossip at Cybercomp is that Mrs. Wilson is tied to the owners of Netware either through
friendship, ownership, or both. The suggestion is that a conflict of interest exists for Mrs. Wilson. Also, Oliver
has the impression that he could lose his job if he doesn’t make the “right” decision.
Discussion questions:
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• What is the ethical dilemma? Is there an ethical dilemma?
On the surface, it appears the ethical dilemma is that Mrs. Wilson, the CEO of Cybercomp, is pressuring
Oliver Greene to provide a favorable analysis of Netware Products so Cybercomp’s board of directors
• What should Oliver do?
Oliver should complete his analysis of Netware Products in an unbiased manner; he should disregard
any rumors and try not to let Mrs. Wilson’s comments influence his initial analysis. Perhaps Oliver’s
• Should rumors and innuendos be considered in the capital budgeting analysis?
• If Oliver was certain his job hinged on this capital budgeting decision, should he produce the results
requested by the CEO?
Ask the students what they would do in this situation. Oliver is in a position that pays very well, perhaps
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References:
Certainly there are countless examples of the situation described in this Ethical Dilemma, but, few, if any are
made public. An example of a capital budgeting project that parallels this scenario is described in the
Managerial Perspective in Chapter 10. RJR Nabisco invested in the smokeless cigarette because it was the
pet project of some top managers. Even though there is no indication that top managers pressured RJR’s
capital budgeting analysts to “manipulate” the results so a favorable decision could be reached, it is thought
that the company knew the project had serious flaws and many were afraid to voice their concerns because
they didn’t want to offend top management. The smokeless cigarette turned out to be a $300 million disaster
that lasted less than one year.
Interestingly, RJR currently is testing whether a new smokeless cigarette can be marketed under different
conditions. For more information about RJR’s smokeless cigarette projects, see the following articles:
“RJR Is Testing a ‘Smokeless Cigarette’ After Attempt Failed Five Years Ago,” The Wall Street Journal,
November 28, 1994, p. A5.
“RJR Smokeless Cigarette Test Is Snuffed Out,” Los Angeles Times, March 1, 1989, p. 1+.
“Fire Without Smoke,” The Economist, September 17, 1988, p. 33+.
For examples of some product ideas that were flops, see the following articles:1
“Ford’s Edsel Drives Pack of Marketing Misses: A Look at the Century’s Hyped Products,” Chicago Tribune,
June 13, 1999, p. 12.
“The Museum of Dumb Ideas,” National Post, July 1, 1999, p. 10.
1 The fact that a product flops does not mean that the firm did not conduct a proper capital budgeting analysis.