Level of Difficulty: 3
Learning Goal: 4
Topic: Risk-Adjusted Discount Rate (Equation 10.2 and Equation 10.5)
3.
A firm is evaluating two mutually exclusive projects that have unequal lives. The firm must evaluate the
projects using the annualized net present value approach and recommend which project they should select.
The firm’s cost of capital has been determined to be 18 percent, and the projects have the following initial
investments and cash flows:
Project W
Project Y
Initial investment:
$40,000
$58,000
Cash flows:
1
$20,000
$30,000
2
20,000
35,000
3
20,000
40,000
4
20,000
5
20,000

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The Role and Environment of Managerial Finance
83
Answer:
Project W: NPV
$20,000(3.127)
–
$40,000
$22,540
Project Y: $30,000(0.847)
$25,410
35,000(0.718)
25,130
40,000(0.609)
24,360
$74,900
58,000
NPV
$16,900
ANPV of Project W: $22,540/3.127
$7,208
ANPV of Project Y: $16,900/2.174
$7,774
Select Project Y, highest ANPV.
Level of Difficulty: 4
Learning Goal: 5
Topic: Annualized Net Present Value (Equation 10.6)
Nico Manufacturing is considering investment in one of two mutually exclusive projects X and Y which are
described below. Nico Manufacturing’s overall cost of capital is 15 percent, the market return is
15 percent and the risk-free rate is 5 percent. Nico estimates that the beta for project X is 1.20 and the beta for project
Y is 1.40.
Table 10.6
Project X
Project Y
Initial Investment
$3,500,000
$3,900,000
Year
Cash Inflows (CF)
1
$1,500,000
$1,100,000
2
1,500,000
1,600,000
3
1,500,000
1,900,000
4
1,500,000
2,300,000
4.
Calculate the risk-adjusted discount rates for project X and project Y. (See Table 10.6)
Answer:
k
X
5%
1.20 (15%
–
5%)
17%
k
Y
5%
1.40 (15%
–
5%)
19%
Level of Difficulty: 2
Learning Goal: 4
Topic: Risk-Adjusted Discount Rate (Equation 10.2 and Equation 10.5)
5.
Using the risk-adjusted discount rate method of project evaluation, find the NPV for projects X and Y. Which
project should Nico select using this method? (See Table 10.6)

Chapter 1
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84
Answer:
Time
Project X
PVIF @ 17%
PV of CFs
0
$(3,500,000)
1.0000
$(3,500,000)
1
1,500,000
0.8547
1,282,051
2
1,500,000
0.7305
1,095,770
3
1,500,000
0.6244
936,556
4
1,500,000
0.5337
800,475
NPV
x
$614,853
Time
Project Y
PVIF @ 19%
PV of CFs
0
$(3,900,000)
1.0000
$(3,900,000)
1
1,100,000
0.8403
924,370
2
1,600,000
0.7062
1,129,864
3
1,900,000
0.5934
1,127,490
4
2,300,000
0.4987
1,146,938
NPV
Y
$428,662
Level of Difficulty: 2
Learning Goal: 4
Topic: Risk-Adjusted Discount Rate (Equation 10.2 and Equation 10.5)
6.
Calculate the NPV of projects X and Y assuming that the firm did not employ the RADR method and instead
used the firm’s overall cost of capital to evaluate projects X and Y. (See Table 10.6)
Answer:
Time
Project X
PVIF @ 16%
PV of CFs
0
$(3,500,000)
1.0000
$(3,500,000)
1
1,500,000
0.8696
1,304,348
2
1,500,000
0.7561
1,134,216
3
1,500,000
0.6575
986,274
4
1,500,000
0.5718
857,630
NPV
x
$782,468
Time
Project Y
PVIF @ 15%
PV of CFs
0
$(3,900,000)
1.0000
$(3,900,000)
1
1,100,000
0.8696
956,522
2
1,600,000
0.7561
1,209,830
3
1,900,000
0.6575
1,249,281
4
2,300,000
0.5718
1,315,032
NPV
Y
$830,665
The NPV of X is less than the NPV of Y using the firms overall cost of capital. Choose
Project Y.
Level of Difficulty: 2
Learning Goal: 4
Topic: Risk-Adjusted Discount Rate (Equation 10.2 and Equation 10.5)

Chapter 1
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85
7.
What potential biases exist in project selection if Nico Manufacturing did not adjust for the difference in risk
between projects X and Y (See Table 10.6).
Answer:
The danger of not accounting for differences in project risk is that the firm may potentially
unacceptable high-risk projects (with negative NPVs) may be chosen over potentially
acceptable low-risk projects (with positive NPVs).