This document provides solutions to multiple problems involving project evaluation techniques such as net present value (NPV), internal rate of return (IRR), payback period, and discounted payback period. It calculates the NPV, IRR, payback period, and discounted payback period for several hypothetical capital investment projects with different cash flow structures. It also explains why the IRR and NPV may provide different recommendations for mutually exclusive projects and determines which project a company should select based on the evaluation criteria.

1. CHAPTER 10 - Solutions
Project Decision Rules (NPV, IRR, Payback, Discounted Payback)
10.1 Net present value: Riggs Corp. management is planning to spend $650,000 on a new
marketing campaign. They believe that this action will result in additional cash flows of
$325,000 over the next three years. If the discount rate is 17.5 percent, what is the NPV
on this project?
LO 2
Solution:
Initial investment = $650,000
Annual cash flows = $325,000
Length of project = n = 3 years
Required rate of return = k = 17.5%
Net present value = NPV
$62,337
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341
,
200
$
401
,
235
$
596
,
276
000
,
650
$
)
175
.
1
(
000
,
325
$
)
175
.
1
(
000
,
325
$
)
175
.
1
(
000
,
325
$
000
,
650
$
)
k
1
(
NCF
NPV 3
2
1
n
0
t
t
t
10.5 Net present value: Blanda Incorporated management is considering investing in two
alternative production systems. The systems are mutually exclusive, and the cost of the
new equipment and the resulting cash flows are shown in the accompanying table. If the
firm uses a 9 percent discount rate for their production systems, in which system should
the firm invest?
LO 2
Year System 1 System 2
0 ‐15,000 ‐45,000
1 15,000 32,000

2. 2 15,000 32,000
3 15,000 32,000
Solution
The NPV of System 1 is $22,969.42 and the NPV of System 2 is $36,001.43. Since the
NPV of the System 2 is larger than the NPV for System 1, and the investments are
mutually exclusive, the firm should take System 2.
10.6 Payback: Refer to problem 10.5. What are the payback periods for production systems
1 and 2?
Solution
System 1 has a payback of exactly one year. System 2 has a payback of 1.41 years.
Given the shorter payback period for system 1, the investment should be made in System
1 based on the payback criteria.
10.12 Internal rate of return: Hathaway, Inc., a resort company, is refurbishing one of its
hotels at a cost of $7.8 million. The firm expects that this will lead to additional cash
flows of $1.8 million for the next six years. What is the IRR of this project? If the
appropriate cost of capital is 12 percent, should Hathaway go ahead with this project?
(Note that I would not have you solve this directly on a test – I would only ask for
the rate, when the problem is a single lump-sum (this is not) or a
perpetuity…you can try a 12% discount rate and based on the NPV, guess
where the IRR is relative to 12%....that would be the first step of a trial &
error – therefore, you still learn from doing this problem – to solve, you need
a financial calculator with a NPV function or Excel)
Solution:
Initial investment = $7,800,000
Annual cash flows = $1,800,000
Length of project = n = 6 years
Required rate of return = k = 12%
To determine the IRR, a trial-and-error approach can be used. Set NPV = 0.

3. Try IRR = 12%.
467
,
399
$
533
,
400
,
7
$
000
,
800
,
7
$
12
.
0
)
12
.
1
(
1
1
000
,
800
,
1
$
000
,
800
,
7
$
0
)
IRR
1
(
FCF
0
NPV
6
n
0
t
t
t
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
Since NPV < 0, try a lower rate, IRR = 10%.
469
,
39
$
469
,
839
,
7
$
000
,
800
,
7
$
10
.
0
)
10
.
1
(
1
1
000
,
800
,
1
$
000
,
800
,
7
$
0
)
IRR
1
(
FCF
0
NPV
6
n
0
t
t
t
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
Try IRR = 10.2%.
265
,
6
$
735
,
793
,
7
$
000
,
800
,
7
$
102
.
0
)
102
.
1
(
1
1
000
,
800
,
1
$
000
,
800
,
7
$
0
)
IRR
1
(
FCF
0
NPV
6
n
0
t
t
t
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Try IRR = 10.15%.
129
,
5
$
129
,
805
,
7
$
000
,
800
,
7
$
1015
.
0
)
1015
.
1
(
1
1
000
,
800
,
1
$
000
,
800
,
7
$
0
)
IRR
1
(
FCF
0
NPV
6
n
0
t
t
t
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The IRR of the project is between 10.15 and 10.2 percent. Using a financial calculator,
we find that the IRR is 10.1725 percent. Since IRR < k, reject the project.

4. 10.15 Net present value: Cranjet Industries is expanding its product line and its production
capacity. The costs and expected cash flows of the two independent projects are given in
the following table. The firm typically uses a discount rate of 16.4 percent.
a. What are the NPVs of the two projects?
b Should both projects be accepted? Or either? Or neither? Explain your reasoning.
Year
Product Line
Expansion
Production Capacity
Expansion
0 $(2,575,000) $(8,137,250)
1 $600,000 $2,500,000
2 $875,000 $2,500,000
3 $875,000 $2,500,000
4 $875,000 $3,250,000
5 $875,000 $3,250,000
LO 2
Solution:
a. Required rate of return = 16.4%
Product Line Expansion:
Cost of product line expansion = $2,575,000
$27,222
0
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490
,
409
646
,
476
816
,
554
$
806
,
645
$
464
,
515
$
000
,
575
,
2
$
)
164
.
1
(
000
,
875
$
)
164
.
1
(
000
,
875
$
)
164
.
1
(
000
,
875
$
)
164
.
1
(
000
,
875
$
)
164
.
1
(
000
,
600
$
00
,
575
,
2
$
)
k
1
(
FCF
NPV
5
4
3
2
1
n
0
t
t
t
Production Capacity Expansion:
Cost of production capacity expansion = $8,137,250

5. $732,228
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962
,
520
,
1
$
400
,
770
,
1
$
116
,
578
,
5
$
250
,
137
,
8
$
)
164
.
1
(
000
,
250
,
3
$
)
164
.
1
(
000
,
250
,
3
$
164
.
0
)
164
.
1
(
1
1
000
,
500
,
2
$
250
,
137
,
8
$
)
k
1
(
FCF
NPV
5
4
3
n
0
t
t
t
b. Since they are independent, and both have NPV > 0, both projects should be
accepted.
10.18 Discounted payback: Timeline Manufacturing Co. is evaluating two projects. It uses
payback criteria of three years or less. Project A has a cost of $912,855, and project B’s
cost is $1,175,000. Cash flows from both projects are given in the following table. What
are their discounted payback periods, and which will be accepted with a discount rate of 8
percent? (We may not get to discounted payback on Thurs. 11/14 – if so, this would be
good practice)
Year Project A Project B
1 $ 86,212 $586,212
2 $313,562 $413,277
3 $427,594 $231,199
4 $285,552
LO 3
Solution:
Project A
Year CF
Cumulative
CF PVCF
Cumulative
PVCF
0 $(912,855) $(912,855) $(912,855) $(912,855)
1 86,212 (826,643) 79,826 (833,029)
2 313,562 (513,081) 268,829 (564,200)

6. 3 427,594 (85,487) 339,438 (224,762)
4 285,552 200,065 209,889 (14,873)
The payback period exceeds four years.
Project B
Year CF
Cumulative
CF PVCF
Cumulative
PVCF
0 $(1,175,000) $(1,175,000) $(1,175,000) $(1,175,000)
1 586,212 (588,788) 542,789 (632,211)
2 413,277 (175,511) 354,318 (277,893)
3 231,199 55,688 183,533 (94,359)
PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year)
= 3 + years
Since the firm’s acceptance criteria is three years, neither project will be accepted.
10.25 Internal rate of return: Ancala Corporation is considering investments in two new golf
apparel lines for next season: golf hats and belts. Due to a funding constraint, these lines
are mutually exclusive. A summary of each project’s estimated cash flows over its three -
year life, as well as the IRRs and NPVs of each are outlined below. The CFO of the firm
has decided to manufacture the belts; however, the CEO of Ancala is questioning this
decision given that the IRR is higher for manufacturing hats. Explain to the CEO why the
IRRs and NPVs of the belt and hat projects disagree? Is the CFO’s decision the correct?
(Note that in this IRR problem, you are interpreting results – not calculating IRR)
Year Golf Belts Golf Hats
0 -$1,000 -$500
1 1,000 500
2 500 300
3 500 300
NPV $697.97 $427.87
IRR 54% 61%

7. LO 5
Solution
The IRRs and NPVs of the belt and hat lines disagree because of the differences in the
scale of the project. Hats deliver a higher IRR because they require a lower initial
investment. Thus, even with lower cash inflows in the years after startup, the hat project
is able to deliver a higher return on the initial investment. While the golf belts project
does cost more, it delivers a higher net cash flow for Ancala investors. This NPV factors
in the initial cost of the project, and reflects the total net cash flow for the firm’s
shareholders.
The CFO’s decision to choose the golf belts project is the right choice because it yields
the higher net cash flows for Ancala’s investors.
10.40. Given the following cash flows for a capital project, calculate the NPV and IRR. The
required rate of return is 8 percent. (For the IRR answer, just try each one)
Year
0 1 2 3 4 5
CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000
NPV IRR
a. $1,905 10.9%
b. $1,905 26.0%
c. $3,379 10.9%
d. $3,379 26.0%
LO 2
SOLUTION:
c is correct.

8. NPV = –50,000 + 13,888.89 + 12,860.08 + 15,876.64 + 7,350.30 + 3,402.92
NPV = –50,000 + 53,378.83 = $3,378.83
The IRR, found with a financial calculator, is 10.88 percent.
10.41. Given the following cash flows for a capital project, calculate its payback period and
discounted payback period. The required rate of return is 8 percent.
Year
0 1 2 3 4 5
CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000
The discounted payback period is
a. 0.16 years longer than the payback period.
b. 0.80 years longer than the payback period.
c. 1.01 years longer than the payback period.
d. 1.85 years longer than the payback period.
LO 3
SOLUTION:
c is correct.
YEAR 0 1 2 3 4 5
CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000
CUMULATIVE CASH
FLOW –50,000 –35,000 –20,000 0 10,000 15,000
DISCOUNTED CASH
FLOW –50,000 13,888.89 12,860.08 15,876.64 7,350.30 3,402.92
CUMULATIVE DCF –50,000 –36,111.11 –23,251.03 –7,374.38 –24.09 3,378.83
2 3 4 5
15,000 15,000 20,000 10,000 5,000
NPV 50,000
1.08 1.08 1.08 1.08 1.08
      

9. As the table shows, the cumulative cash flow offsets the initial investment in
exactly three years. The payback period is 3.00 years. The discounted payback
period is between four and five years. The discounted payback period is 4 years
plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The
discounted payback period is 4.01 – 3.00 = 1.01 years longer than the payback
period.
.