Chapter 13, Solutions
Cornett, Adair, and Nofsinger
CHAPTER 13 - WEIGHING NET PRESENT VALUE AND OTHER CAPITAL
BUDGETING CRITERIA
Questions
LG1
1.
Is the set of cash flows depicted below normal or non-normal? Explain.
0
1
2
3
4
5
Time
Cash Flow -$100 -$50 $80 $0 $100 $100
They’re normal: there is only one change in cash flows from negative to positive.
LG1
2.
Derive an accept/reject rule for IRR similar to 13-8 that would make the correct
decision on cash flows that are non-normal, but which always have one large
positive cash flow at time zero followed by a series of negative cash flows:
0 1 2 3 4 5
Time
Cash Flow Sign + - - - - With one positive at the beginning and all future cash flows negative, this type of
project would be worth more if rates were higher, implying that the NPV profile
would be upward-sloping. So the appropriate accept/reject decision rule would look
like
Accept Project if IRR ≤ Cost of Capital
Reject Project if IRR > Cost of Capital
LG1
3.
Is it possible for a company to initiate two products that target the same market and
are not mutually exclusive?
Sure, as long as the market has room for both products.
LG2
4.
Suppose that your company used “APV”, or “All-the-Present Value-Except-CF0”, to
analyze capital budgeting projects. What would this rule’s benchmark value be?
Accept Project if APV ≥ -CF0
Reject Project if APV < -CF0
LG3
5.
Under what circumstances could Payback and Discounted Payback be equal?
They would be equal if i = 0.
LG5
6.
Could a project’s MIRR ever exceed its IRR?
13-1
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
MIRR would be greater than IRR if a project with normal cash flows had a negative
NPV.
LG6
7.
If you had two mutually exclusive, normal-cash-flow projects whose NPV profiles
crossed at all points, for which range of interest rates would IRR give the right
accept/reject answer?
At all rates, because we would be indifferent between the two projects at any rate.
LG7
8.
Suppose a company wanted to double their firm’s value with the next round of
capital budgeting project decisions. To what would they set the PI benchmark to
make this goal?
They would set it equal to 1.
LG5
9.
Suppose a company faced different borrowing and lending rates: How would this
range change the way that you would compute the MIRR statistic?
We would want to use the borrowing rate to move the negative cash flows to time 0,
and the lending rate to move the positive cash flows to the end of the project.
Problems
Basic Problems
LG2
13-1
Compute the NPV for Project M and accept or reject the project with the cash flows
shown below if the appropriate cost of capital is 8 percent.
Project M
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $480 $520 $300 $100
Using equation 13-2:
NPV  $1,000 
$350
1.08
1

$480
1.08
2

$520
1.08
 $436.96
The project should be accepted.
13-2
3

$300
1.08 
4

$100
1.08 
5
Chapter 13, Solutions
LG2
13-2
Cornett, Adair, and Nofsinger
Compute the NPV statistic for Project Y and tell whether the firm should accept or
reject the project with the cash flows shown below if the appropriate cost of capital
is 12 percent.
Project Y
0
1
2
3
4
Time
Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000
Using equation 13-2:
NPV  $11,000 
$3,350
1.12 
1

$4,180
1.12 
2

$1,520
1.12 
3

$2,000
1.12 
4
 $2,323.72
The project should be rejected.
LG2
13-3
Compute the NPV statistic for Project U and recommend whether the firm should
accept or reject the project with the cash flows shown below if the appropriate cost
of capital is 10 percent.
Project U
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $1,480 -$520 $300 -$100
Using equation 13-2:
NPV  $1, 000 
$350
1.10 
1

$1, 480
1.10 
2

$520
1.10 
3

$300
1.10 
4

$100
1.10 
5
 $293.45
The project should be accepted.
LG3
13-4
Compute the Payback statistic for Project A and recommend whether the firm should
accept or reject the project with the cash flows shown below if the appropriate cost
of capital is 8 percent and the maximum allowable payback is 4 years.
Project A
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $480 $520 $300 $100
13-3
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
Solving equation 13-3 for N, cumulative cash flow will switch from negative and
positive between years 2 and 3:
LG3
13-5
Year
Cash Flow
Cumulative Cash
Flow
0
-$1,000
1
$350
2
$480
3
$520
4
$300
5
$100
-$1,000
-$650
-$170
$350
Specifically, PB  2 
$170
 2.3269 years so this project should be accepted.
$520
Compute the Payback statistic for Project B and decide whether the firm should
accept or reject the project with the cash flows shown below if the appropriate cost
of capital is 12 percent and the maximum allowable payback is 3 years.
Project B
0
1
2
3
4
5
Time
Cash Flow -$11,000 $3,350 $4,180 $1,520 $0 $1,000
Solving equation 13-3 for N:
Year
Cash Flow
Cumulative Cash Flow
0
-$11,000
-$11,000
1
$3,350
-$7,650
2
$4,180
-$3,470
3
$1,520
-$1,950
4
$0
-$1,950
5
$1,000
-$950
This project will never achieve payback, and should be rejected.
LG3
13-6
Compute the Discounted Payback statistic for Project C and recommend whether the
firm should accept or reject the project with the cash flows shown below if the
appropriate cost of capital is 8 percent and the maximum allowable discounted
payback is 3 years.
Project C
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $480 $520 $300 $100
Solving equation 13-5 for N, cumulative PV of cash flow will switch from negative
and positive between years 2 and 3:
13-4
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
Year
Cash Flow
0
-$1,000
Cash Flow PV
-$1,000
1.08 
1.08 
Cum. Cash Flow PV
-$1,000
 $324.07
-$675.93
 $411.52
-$264.41
Specifically, DPB  2 
LG3
13-7
1
$350
$350
2
$480
$480
1
3
$520
$520
1.08 
2
4
$300
5
$100
3
 $412.79
$148.38
$264.41
 2.64 years and this project should be accepted.
$412.79
Compute the Discounted Payback statistic for Project D and recommend whether
the firm should accept or reject the project with the cash flows shown below if the
appropriate cost of capital is 12 percent and the maximum allowable discounted
payback is 4 years.
Project D
0
1
2
3
4
5
Time
Cash Flow -$11,000 $3,350 $4,180 $1,520 $0 $1,000
The NPV for this project is negative, so discounted payback never occurs.
LG5
13-8
Compute the IRR statistic for Project E and note whether the firm should accept or
reject the project with the cash flows shown below if the appropriate cost of capital
is 8 percent.
Project E
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $480 $520 $300 $100
The IRR for this project will be the solution to equation 13-7:
0
$1,000
1  IRR 
0

$350
1  IRR 
1

$480
1  IRR 
2

$520
1  IRR 
IRR  .2549, or 25.49%
Since IRR > i, this project should be accepted.
13-5
3

$300
1  IRR 
4

$100
1  IRR 
5
Chapter 13, Solutions
LG5
13-9
Cornett, Adair, and Nofsinger
Compute the IRR statistic for project F and note whether the firm should accept or
reject the project with the cash flows shown below if the appropriate cost of capital
is 12 percent.
Project F
0
1
2
3
4
Time
Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000
The IRR for this project will be the solution to equation 13-7:
0
$11,000
1  IRR 
0

$3,350
1  IRR 
1

$4,180
1  IRR 
2

$1,520
1  IRR 
3

$2,000
1  IRR 
4
IRR  .2068, or 20.68%
Since IRR > i, this project should be accepted.
LG5
13-10 Compute the IRR statistic for Project G and note whether the firm should accept or
reject the project with the cash flows shown below if the appropriate cost of capital
is 10 percent.
Project G
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $1,480 -$520 $300 -$100
IRR for this project will be the solution to equation 13-7:
0
$1,000
1  IRR 
0

$350
1  IRR 
1

$1, 480
1  IRR 
2

$520
1  IRR 
3

$300
1  IRR 
4

$100
1  IRR 
5
However, since cash flows are not normal, there may be multiple solutions to this
problem, and IRR should not be used.
LG5
13-11 Compute the MIRR statistic for Project H and note whether to accept or reject the
project with the cash flows shown below if the appropriate cost of capital is 8
percent.
Project H
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $480 $520 $300 $100
13-6
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
Cash flows will be moved as shown below:
0
-$1,000
Year
Cash Flow
1
$350
2
$480
3
$520
4
$300
5
$100
$350  1.08 $480  1.08 $520  1.08 $300  1.08
4
Future
Value (If
Positive)
 $476.17
3
 $604.66
2
1
$100
 $324
 $606.53
$2,111.36
Sum of FV
Modified
CFs
-$1,000
$2,111.36
With this new set of modified cash flows, the MIRR is:
0
$1,000
1  IRR 
0

$2,111.36
1  IRR 
5
IRR  .1612, or 16.12%
Since our MIRR decision statistic exceeds the 8 percent cost of capital, we would
accept the project under the MIRR method.
.
LG5
13-12 Compute the MIRR statistic for Project I and tell whether to accept or reject the
project with the cash flows shown below if the appropriate cost of capital is 12
percent.
Project I
0
1
2
3
4
Time
Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000
Cash flows will be moved as shown below:
Year
Cash Flow
0
-$11,000
2
$4,180
$3,350  1.12  $4,180  1.12 
3
Future
Value (If
Positive)
Sum of FV
Modified
CFs
1
$3,350
 $4,706.51
 $5, 243.39
3
$1,520
2
4
$2,000
$1,520  1.12 
1
 $1,702.40
$2,000
$13,652.30
-$11,000
$13,652.30
13-7
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
With this new set of modified cash flows, the MIRR is:
0
$11,000
1  IRR 

0
$13,652.30
1  IRR 
4
IRR  .0555, or 5.55%
Since our MIRR decision statistic is less than the 12 percent cost of capital, we
would reject the project under the MIRR method.
LG5
13-13 Compute the MIRR statistic for Project J and advise whether to accept or reject the
project with the cash flows shown below if the appropriate cost of capital is 10
percent.
Project J
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $1,480 -$520 $300 -$100
Cash flows will be moved as shown below:
Year
Cash Flow
0
-$1,000
Present
Value (If
Negative)
-$1,000
1
$350
2
$1,480
3
-$520
$520
1.10 
4
$300
5
-$100
$100
1.10 
3
 $390.68
Sum of PV -$1,452.78
Future
Value (If
Positive)
Sum of FV
Modified
-$1,452.78
CFs
$350  1.10 
$1,480  1.10 
4
3
 $1,969.88
 $512.44
$300  1.10 
1
 $330
$2,812.32
$1, 452.78
1  IRR 
 $62.09
$2,812.32
With this new set of modified cash flows, the MIRR is:
0
5
0

$2,812.32
1  IRR 
5
IRR  .1412, or 14.12%
13-8
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
Since our MIRR decision statistic is greater than the 10 percent cost of capital, we
would accept the project under the MIRR method.
LG5
13-14 Compute the PI statistic for Project Z for and advise the firm whether to accept or
reject the project with the cash flows shown below if the appropriate cost of capital
is 8 percent.
Project Z
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $480 $520 $300 $100
Using equation 13-9:
NPV  $1, 000 
$350

1.08
1
$480
1.08
2

$520
1.08
3

$300
1.08
4

$100
1.08 
5
 $436.96
$436.96
PI 
 .4370, or 43.7%
$1, 000
Since PI > 0, the project should be accepted.
LG5
13-15 Compute the PI statistic for Project Q and tell whether you would accept or reject
the project with the cash flows shown below if the appropriate cost of capital is 12
percent.
Project Q
0
1
2
3
4
Time
Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000
Using equation 13-9:
NPV  $11, 000 
$3, 350
1.12 
1

$4,180
1.12 
2

$1, 520
1.12 
 $2, 323.72
$2, 323.72
PI 
 .2112, or -21.12%
$11, 000
Since PI < 0, the project should be rejected.
13-9
3

$2, 000
1.12 
4
Chapter 13, Solutions
LG5
Cornett, Adair, and Nofsinger
13-16 Compute the PI statistic for Project LL and decide whether to accept or reject the
project with the cash flows shown below if the appropriate cost of capital is 10
percent.
Project LL
0
1
2
3
4
5
Time
Cash Flow -$1,000 $350 $1,480 -$520 $300 -$100
Using equation 13-9:
NPV  $1, 000 
$350
1.10 
1

$1, 480
1.10 

2
$520
1.10 
3

$300
1.10 
4

$100
1.10 
5
 $293.45
$293.45
PI 
 .2935, or 29.35%
$1, 000
Since PI > 0, the project should be accepted.
LG1
13-17 How many possible IRRs could you find for the following set of cash flows?
0
1
2
3
4
Time
Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000
Since there’s only 1 change in sign, there can only be 1 IRR.
LG1
13-18 How many possible IRRs could you find for the following set of cash flows?
0
1
2
3
4
Time
Cash Flow -$211,000 -$39,350 $440,180 $217,520 -$2,000
Since there are 2 changes in sign, there could potentially be as many as 2 IRRs.
Intermediate Problems
***Use this information to answer the next 6 questions. If a particular decision
method should not be used, indicate why.***
Suppose your firm is considering investing in a project with the cash flows shown
below, that the required rate of return on projects of this risk class is 8 percent, and
13-10
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
that the maximum allowable payback and discounted payback statistics for the
project are 3.5 and 4.5 years, respectively.
Time
Cash
Flow
LG3
0
1
2
3
4
5
6
-$5,000
$1,200
$1,400
$1,600
$1,600
$1,400
$1,200
13-19 Use the payback decision rule to evaluate this project; should it be accepted or
rejected?
Cumulative cash flow will switch from negative and positive between years 3 and 4:
0
1
2
3
4
5
6
Year
$1,200
$1,400
$1,600 $1,600 $1,400 $1,200
Cash Flow -$5,000
-3,800
-2,400
-800
800
Cumulative Cash -$5,000
Flow
$800
Specifically, PB  3 
 3.5 years , which is equal to the maximum
$1, 600
allowable payback, so this project should be accepted.
LG3
13-20 Use the discounted payback decision rule to evaluate this project; should it be
accepted or rejected?
Cumulative PV of cash flow will switch from negative and positive between years 4
and 5:
Year
Cash Flow
Cash Flow PV
Cum. Cash Flow
PV
0
-$5,000
-$5,000
-$5,000
1
$1,200
$1,111
-$3,889
2
$1,400
$1,200
-$2,689
3
$1,600
$1,270
-$1,418
4
5
6
$1,600 $1,400 $1,200
$1,176
$953
$756
-$242
$710
$242
 4.25 years , which is less than the maximum
$953
allowable payback of 4.5 years, so this project should be accepted.
Specifically, DPB  4 
LG5
13-21 Use the IRR decision rule to evaluate this project; should it be accepted or rejected?
The IRR for this project will be the solution to:
0
$5, 000
1  IRR 
0

$1, 200
1  IRR 
1

$1, 400
1  IRR 
2

IRR  .1706, or 17.06%
Since IRR > i, this project should be accepted.
13-11
$1, 600
1  IRR 
3

$1, 600
1  IRR 
4

$1, 400
1  IRR 
5

$1, 200
1  IRR 
6
Chapter 13, Solutions
LG5
Cornett, Adair, and Nofsinger
13-22 Use the MIRR decision rule to evaluate this project; should it be accepted or
rejected?
Cash flows will be moved as shown below:
Year
Cash
Flow
Future
Value (If
Positive)
Sum of
FV
Modified
CFs
0
1
2
3
4
5
6
-$5,000
$1,200
$1,400
$1,600
$1,600
$1,400
$1,200
$1, 200  1.08 
$1, 400  1.08 
 $1, 763.19
 $1, 904.68
5
$1, 600  1.08
4
 $2, 015.54
3
$1, 600  1.08
 $1,866.24
2
$1, 400  1.08
1
 $1,512
$1, 200
$10,261.66
-$5,000
$10,261.66
With this new set of modified cash flows, the MIRR is:
0
$5, 000
1  IRR 
0

$10, 261.66
1  IRR 
6
IRR  .1273, or 12.73%
Since our MIRR decision statistic is greater than the 8 percent cost of capital, we
would accept the project under the MIRR method.
LG2
13-23 Use the NPV decision rule to evaluate this project; should it be accepted or rejected?
NPV  $5, 000 
$1, 200
1.08
1

$1, 400
1.08
2

$1, 600
1.08
3

$1, 600
1.08
4

$1, 400
1.08
5

$1, 200
1.08
6
 $1, 466.58
The project should be accepted.
LG7
13-24 Use the PI decision rule to evaluate this project; should it be accepted or rejected?
NPV  $5, 000 
$1, 200
1.08
1

$1, 400
1.08
2

$1, 600
1.08
 $1, 466.58
$1, 466.58
PI 
 .2933, or 29.33%
$5, 000
Since PI > 0, the project should be accepted.
13-12
3

$1, 600
1.08
4

$1, 400
1.08
5

$1, 200
1.08
6
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
***Use this information to answer the next 6 questions. If you should not use a
particular decision technique, indicate why.***
Suppose your firm is considering investing in a project with the cash flows shown
below, that the required rate of return on projects of this risk class is 11 percent, and
that the maximum allowable payback and discounted payback statistics for your
company are 3 and 3.5 years, respectively.
0
1
2
3
4
5
Time
Cash Flow -$235,000 $65,800 $84,000 $141,000 $122,000 $81,200
LG3
13-25 Use the payback decision rule to evaluate this project; should it be accepted or
rejected?
Cumulative cash flow will switch from negative and positive between years 2 and 3:
Year
Cash Flow
Cumulative
Cash Flow
0
-$235,000
-$235,000
Specifically, PB  2 
LG3
1
$65,800
-$169,200
2
3
$84,000 $141,000
-$85,200 $55,800
4
$122,000
$177,800
5
$81,200
$259,000
$85, 200
 2.6043 years so this project should be accepted.
$141, 000
13-26 Use the discounted payback decision rule to evaluate this project; should it be
accepted or rejected?
Cumulative PV of cash flow will switch from negative and positive between years 3
and 4:
Year
Cash
Flow
0
-$235,000
Cash
Flow
PV
-$235,000
Cum.
Cash
Flow
PV
-$235,000
1
$65,800
2
$84,000
3
$141,000
4
5
$122,000 $81,200
$65,800
$84, 000
$141, 000
$122, 000
1.11
1.11
1.11
1.11
1
2
3
4
 $59, 279.28
 $68,176.28
 $103, 097.98
 $80, 365.18
-$175,721
-$107,544
-$4,446
$75,919
$4, 446
 3.05 years , which is less than the maximum
$80, 365.18
allowable discounted payback, so project should be accepted.
Specifically, DPB  3 
13-13
Chapter 13, Solutions
LG5
Cornett, Adair, and Nofsinger
13-27 Use the IRR decision rule to evaluate this project; should it be accepted or rejected?
The IRR for this project will be the solution to:
0
$235, 000
1  IRR 
0

$65,800
1  IRR 
1
$84, 000

1  IRR 
2

$141, 000
1  IRR 
3

$122, 000
1  IRR 
4

$81, 200
1  IRR 
5
IRR  .2879, or 28.79%
Since IRR > i, this project should be accepted.
LG5
13-28 Use the MIRR decision rule to evaluate this project; should it be accepted or
rejected?
Cash flows will be moved as shown below:
0
Year
Cash
-$235,000
Flow
Future
Value (If
Positive)
Sum of
FV
Modified
-$235,000
CFs
1
2
3
4
5
$65,800
$84,000
$141,000
$122,000
$81,200
$65,800  1.11
4
 $99,889.03
$84, 000  1.11
3
$141, 000  1.11
$122, 000  1.11
2
1
 $173, 726.10
 $114,881
$81, 200
 $135, 420
$605,116.14
$605,116.14
With this new set of modified cash flows, the MIRR is:
0
$235, 000
1  IRR 
0

$605,116.14
1  IRR 
5
IRR  .2082, or 20.82%
Since our MIRR decision statistic is greater than the 11 percent cost of capital, we
would accept the project under the MIRR method.
LG2
13-29 Use the NPV decision rule to evaluate this project; should it be accepted or rejected?
NPV  $235, 000 
$65,800
1.11
1

$84, 000
1.11
2

$141, 000
1.11
 $124,106.98
Since NPV > 0, the project should be accepted.
13-14
3

$122, 000
1.11
4

$81, 200
1.11
5
Chapter 13, Solutions
LG7
Cornett, Adair, and Nofsinger
13-30 Use the PI decision rule to evaluate this project; should it be accepted or rejected?
NPV  $235, 000 
$65,800
1.11
1

$84, 000
1.11
2

$141, 000
1.11
3

$122, 000
 $124,106.98
$124,106.98
PI 
 .5281, or 52.81%
$235, 000
Since PI > 0, the project should be accepted.
Advanced Problems
***Use the project cash flows for the two mutually
exclusive projects shown to the right to answer the
following 4 questions.***
LG6
13-31 Graph the NPV profiles for both projects on a common
chart, making sure that you identify all of the “crucial”
points.
Since the two NPV profiles shown below do not cross in
the first quadrant, the only crucial points are the two
projects’ IRRs: IRRA = 13% and IRRB = 14.29%
13-15
1.11
4

$81, 200
1.11
5
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
NPV Profiles
$600.00
$500.00
$400.00
NPV
$300.00
$200.00
$100.00
20.00%
19.00%
18.00%
17.00%
16.00%
15.00%
14.00%
13.00%
12.00%
11.00%
-$200.00
10.00%
9.00%
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
-$100.00
0.00%
$-
r
A
LG6
B
13-32 For what range of possible interest rates would you want to use IRR to choose
between these two projects? For what range of rates would you NOT want to use
IRR?
Since the two projects’ NPV profiles do not cross in the first quadrant, IRR would
work for ALL possible rages of rates.
LG6
13-33 Assume that the expected cash flows for these
two projects have been revised as shown to the
right. Reconstruct the NPV profiles.
Now the two NPV profiles will cross in the first quadrant, so we will need to
compute the crossover rate as well as the two projects’ IRRs.
13-16
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
NPV Profiles
$500.00
$400.00
$300.00
NPV
$200.00
$100.00
-$300.00
r
A
B
As shown below, project A’s IRR will still be 13%, project B’s IRR will be 11.08%,
and the two profiles will cross at 6.03%.
LG6
13-34 With the new expected cash flows shown to the right, is there still a range of
possible interest rates where the 3-step decision process for choosing between
mutually exclusive projects using IRR will accept the wrong project? Explain your
answer.
Yes. If i < 6.03%, we should NOT use the IRR decision rule, as it will always want
to choose project A at step two of the runoff, even if project B is better (as measured
by a higher NPV at those lower interest rates).
13-17
20.00%
19.00%
18.00%
17.00%
16.00%
15.00%
14.00%
13.00%
12.00%
11.00%
9.00%
8.00%
10.00%
-$200.00
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
-$100.00
0.00%
$-
Chapter 13, Solutions
LG6
Cornett, Adair, and Nofsinger
13-35 Construct an NPV profile and determine EXACTLY how many nonnegative IRRs
you can find for the following set of cash flows:
As shown below, there appear to be only two.
NPV Profiles
$100.00
$80.00
$60.00
$40.00
2100.00%
2000.00%
1900.00%
1800.00%
1700.00%
1600.00%
1500.00%
1400.00%
1300.00%
1200.00%
1100.00%
900.00%
800.00%
700.00%
600.00%
500.00%
400.00%
1000.00%
-$60.00
300.00%
-$40.00
200.00%
$-$20.00
100.00%
NPV
$20.00
-$80.00
-$100.00
r
LG6
13-36 Construct an NPV profile and determine EXACTLY how many nonnegative IRRs
you can find for the following set of cash flows:
As shown below, there appears to be only one in the first quadrant.
13-18
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
NPV Profiles
$160.00
$140.00
$120.00
$100.00
NPV
$80.00
$60.00
$40.00
$20.00
2100.00%
2000.00%
1900.00%
1800.00%
1700.00%
1600.00%
1500.00%
1400.00%
1300.00%
1200.00%
1100.00%
900.00%
1000.00%
800.00%
700.00%
600.00%
500.00%
400.00%
-$60.00
300.00%
-$40.00
200.00%
-$20.00
100.00%
$-
r
Research It!
Business Valuation
The capital budgeting decision techniques that we’ve discussed all have strengths and
weaknesses, but they do comprise the most popular rules for valuing projects. Valuing
entire businesses, on the other hand, requires that some adjustments be made to various
pieces of these methodologies. For example, one alternative to NPV used quite frequently
for valuing firms is called Adjusted Present Value (APV).
To explore these alternative decision rules, do a web search for APV and answer the
following questions:
1. What is APV, and how does it differ from NPV?
13-19
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
2. What other business valuation models seem to be popular?
Solution:
The two main approaches to valuation used by practitioners are those involving
discounted cash flows, which we’ve discussed here, and those involving the
“multiples” method, which involves using a sample of ratios from comparable peer
groups to estimate an appropriate price for a firm.
Integrated Minicase
Suppose your firm is considering investing in a project with the cash flows shown below,
that the required rate of return on projects of this risk class is 11 percent, and that the
maximum allowable payback and discounted payback statistics for your company are 3 and
3.5 years, respectively.
Time
Cash Flow
0
-$175,000
1
-$65,800
2
$94,000
3
$41,000
4
$122,000
5
$81,200
Using every one of the capital budgeting decision methods discussed in this chapter,
evaluate this project, indicating whether each decision rule would call for acceptance or
rejection of the project.
Solution:
The decision statistics and the appropriate accept/reject decisions are shown below:
13-20
Chapter 13, Solutions
Cornett, Adair, and Nofsinger
13-21