Chapter 13 – Weighing Net Present Value and Other Capital Budgeting Criteria
CHAPTER 13 – WEIGHING NET PRESENT VALUE AND OTHER CAPITAL
BUDGETING CRITERIA
questions
LG1 1. Is the set of cash flows depicted in the following table normal or non-normal? Explain.
Time 0 1 2 3 4 5
Cash
Flow
–
$100
–
$50
–
$80
$
0
$10
0
$10
0
LG1 2. Derive an accept/reject rule for IRR similar to equation 13-8 that would make the correct
decision on cash flows that are non-normal, but that always have one large positive cash
flow at time zero followed by a series of negative cash flows:
Time 0 1 2 3 4 5
Cash
Flow + – – – – –
LG1 3. Is it possible for a company to initiate two products that target the same market that are
LG2 4. Suppose that your company used “APV,” or “All-the-Present Value-Except-CF0”, to
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Chapter 13 – Weighing Net Present Value and Other Capital Budgeting Criteria
LG3 5. Under what circumstances could payback and discounted payback be equal?
LG5 6. Could a project’s MIRR ever exceed its IRR?
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?
LG7 8. Suppose a company wanted to double their firm’s value with the next round of capital
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?
problems
basic problems
LG2 13-1 NPV with Normal Cash Flows Compute the NPV for Project M and accept or reject the
project with the cash flows shown as follows if the appropriate cost of capital is 8
percent.
Project M
Using equation 13-2:
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Education.
Chapter 13 – Weighing Net Present Value and Other Capital Budgeting Criteria
( ) ( ) ( ) ( ) ( )
1 2 3 4 5
$350 $480 $520 $600 $100
$1, 000 1.08 1.08 1.08 1.08 1.08
$657.47
NPV =– + + + + +
=
The project should be accepted.
LG2 13-2 NPV with Normal Cash Flows Compute the NPV statistic for Project Y and note
whether the firm should accept or reject the project with the cash flows shown as follows
if the appropriate cost of capital is 12 percent.
Project Y
Using equation 13-2:
( ) ( ) ( ) ( )
1234
$3,350 $4,180 $1,520 $300
$8,000 1.12 1.12 1.12 1.12
$404.10
NPV =– + + + +
=–
The project should be rejected.
LG2 13-3 NPV with Non-normal Cash Flows Compute the NPV statistic for Project U and
recommend whether the firm should accept or reject the project with the cash flows
shown as follows if the appropriate cost of capital is ten percent.
Project U
LG3 13-4 NPV with Non-normal Cash Flows Compute the NPV statistic for Project K and
recommend whether the firm should accept or reject the project with the cash flows
shown as follows if the appropriate cost of capital is six percent.
Project K
LG3 13-5 Payback Compute the payback statistic for Project B and decide whether the firm should
accept or reject the project with the cash flows shown as follows if the appropriate cost of
capital is 12 percent and the maximum allowable payback is three years.
Project B
LG3 13-6 Payback Compute the payback statistic for Project A and recommend whether the firm
should accept or reject the project with the cash flows shown as follows if the appropriate
cost of capital is 8 percent and the maximum allowable payback is four years.
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Chapter 13 – Weighing Net Present Value and Other Capital Budgeting Criteria
Project A
LG3 13-7 Discounted Payback Compute the discounted payback statistic for Project C and
recommend whether the firm should accept or reject the project with the cash flows
shown as follows if the appropriate cost of capital is 8 percent and the maximum
allowable discounted payback is three years.
Project C
Solving equation 13-5 for N, cumulative PV of cash flow will switch from negative and
positive between years 2 and 3:
LG3 13-8 Discounted Payback Compute the discounted payback statistic for Project D and
recommend whether the firm should accept or reject the project with the cash flows
shown as follows if the appropriate cost of capital is 12 percent and the maximum
allowable discounted payback is four years.
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Chapter 13 – Weighing Net Present Value and Other Capital Budgeting Criteria
Project D
LG5 13-9 IRR Compute the IRR statistic for Project E and note whether the firm should accept or
reject the project with the cash flows shown as follows if the appropriate cost of capital is
8 percent.
Project E
0 1 2 3 4 5
01 1 1 1 1 1
25.49%
IRR
=
LG5 13-10 IRR Compute the IRR statistic for project F and note whether the firm should accept or
reject the project with the cash flows shown as follows if the appropriate cost of capital is
12 percent.
Project F
The IRR for this project will be the solution to equation 13-7:
( ) ( ) ( ) ( ) ( )
0 1 2 3 4
$11, 000 $3,350 $4,180 $1,520 $2,000
01 1 1 1 1
0.21%
IRR IRR IRR IRR IRR
IRR
–
= + + + +
+ + + + +
=
Since IRR < i, this project should be rejected..
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LG5 13-11 MIRR Compute the MIRR statistic for Project I and tell whether to accept or reject the
project with the cash flows shown as follows if the appropriate cost of capital is 12
Year 0 1 2 3 4
Cash Flow -$11,000 $5,330 $4,180 $1,520 $2,000
LG5 13-12 MIRR Compute the MIRR statistic for Project J and advise whether to accept or reject
the project with the cash flows shown as follows if the appropriate cost of capital is 10
percent.
Year 0 1 2 3 4 5
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Chapter 13 – Weighing Net Present Value and Other Capital Budgeting Criteria
Present
3
$520
–
5
$100
–
LG5 13-14 PI Compute the PI statistic for Project Q and tell whether you would accept or reject the
project with the cash flows shown as follows if the appropriate cost of capital is 12
percent.
Project Q
LG1 13-15 Multiple IRRs How many possible IRRs could you find for the following set of cash
flows?
Time 0 1 2 3 4
Cash Flow -$11,000 $3,35
0
$4,18
0
$1,52
0
$2,00
0
LG1 13-16 Multiple IRRs How many possible IRRs could you find for the following set of cash
flows?
Time 0 1 2 3 4
Cash Flow -$211,000 –
$39,350
$440,18
0
$217,52
0
–
$2,000
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Chapter 13 – Weighing Net Present Value and Other Capital Budgeting Criteria
intermediate problems
Use this information to answer the next six 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 as
follows, that the required rate of return on projects of this risk class is 8 percent, and that
the maximum allowable payback and discounted payback statistics for the project are 3.5
and 4.5 years, respectively.
Time0123456
Cash
Flow -$5,000 $1,200 $2,400 $1,600 $1,600 $1,400 $1,200
LG3 13-17 Payback Use the payback decision rule to evaluate this project; should it be accepted or
rejected?
LG3 13-18 Discounted Payback 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 to positive between years 3 and 4:
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