### Chapter 6: Investment decision rules

```Chapter 6
Investment
Decision Rules
Chapter Outline
6.1 NPV and Stand-Alone Projects
6.2 Alternative Decision Rules
6.3 Mutually Exclusive Investment Opportunities
6.4 Project Selection with Resource Constraints
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6-2
Learning Objectives
1. Define net present value, payback period, internal rate of
return, profitability index, and incremental IRR.
2. Describe decision rules for each of the tools in objective
1, for both stand-alone and mutually exclusive projects.
3. Given cash flows, compute the NPV, payback period,
internal rate of return, profitability index, and incremental
IRR for a given project.
4. Compare each of the capital budgeting tools above, and
tell why NPV always gives the correct decision.
5. Define Economic Value Added, and describe how it can
be used in capital budgeting.
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6-3
6.1 NPV and Stand-Alone Projects
• Consider a take-it-or-leave-it investment decision
involving a single, stand-alone project for Fredrick
Feed and Farm (FFF).
 The project costs \$250 million and is expected to
generate cash flows of \$35 million per year, starting at
the end of the first year and lasting forever.
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6-4
NPV Rule
• The NPV of the project is calculated as:
35
NPV   250 
r
• The NPV is dependent on the discount rate.
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6-5
Figure 6.1 NPV of FFF’s New Project
•
If FFF’s cost of capital is 10%, the NPV is \$100 million and they should
undertake the investment.
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6-6
Measuring Sensitivity with IRR
• At 14%, the NPV is equal to 0, thus the project’s
IRR is 14%. For FFF, if their cost of capital
estimate is more than 14%, the NPV will be
negative, as illustrated on the previous slide.
 In general, the difference between the cost of capital
and the IRR is the maximum amount of estimation error
in the cost of capital estimate that can exist without
altering the original decision.
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6-7
Alternative Rules Versus the NPV Rule
• Sometimes alternative investment rules may give
the same answer as the NPV rule, but at other
times they may disagree.
 When the rules conflict, the NPV decision rule should
be followed.
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6-8
6.2 Alternative Decision Rules
• The Payback Rule
 The payback period is amount of time it takes to
recover or pay back the initial investment. If the
payback period is less than a pre-specified length of
time, you accept the project. Otherwise, you reject
the project.
• The payback rule is used by many companies because of
its simplicity.
• However, the payback rule does not always give a reliable
decision since it ignores the time value of money.
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6-9
Example 6.1
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6-10
Example 6.1 (cont'd)
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6-11
Alternative Example 6.1
• Problem
 Projects A, B, and C each have an expected life
of 5 years.
 Given the initial cost and annual cash flow
information below, what is the payback period
for each project?
A
B
C
Cost
\$80
\$120
\$150
Cash Flow
\$25
\$30
\$35
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6-12
Alternative Example 6.1
• Solution
 Payback A
• \$80 ÷ \$25 = 3.2 years
 Project B
• \$120 ÷ \$30 = 4.0 years
 Project C
• \$150 ÷ \$35 = 4.29 years
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6-13
The Internal Rate of Return
• Internal Rate of Return (IRR) Investment Rule
 Take any investment where the IRR exceeds the cost of
capital. Turn down any investment whose IRR is less
than the cost of capital.
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6-14
The Internal Rate of Return (cont'd)
• The IRR Investment Rule will give the same
answer as the NPV rule in many, but not all,
situations.
• In general, the IRR rule works for a stand-alone
project if all of the project’s negative cash flows
precede its positive cash flows.
 In Figure 6.1, whenever the cost of capital is below the
IRR of 14%, the project has a positive NPV and you
should undertake the investment.
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6-15
The Internal Rate of Return (cont'd)
• In other cases, the IRR rule may disagree with the
NPV rule and thus be incorrect.
 Situations where the IRR rule and NPV rule may be
in conflict:
• Delayed Investments
• Nonexistent IRR
• Multiple IRRs
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6-16
The Internal Rate of Return (cont'd)
• Delayed Investments
 Assume you have just retired as the CEO of a
successful company. A major publisher has offered you
a book deal. The publisher will pay you \$1 million
upfront if you agree to write a book about your
experiences. You estimate that it will take three years to
write the book. The time you spend writing will cause
you to give up speaking engagements amounting to
\$500,000 per year. You estimate your opportunity cost
to be 10%.
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6-17
The Internal Rate of Return (cont'd)
• Delayed Investments
 Should you accept the deal?
• Calculate the IRR.
 The IRR is greater than the cost capital. Thus, the IRR
rule indicates you should accept the deal.
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6-18
Financial Calculator Solution
1000000
CFj
-500000
CFj
3
Gold
Gold
IRR
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Nj
23.38
6-19
The Internal Rate of Return (cont'd)
• Delayed Investments
 Should you accept the deal?
NPV  1,000,000 
500, 000
500, 000
500, 000


  \$243,426
2
3
1.1
1.1
1.1
 Since the NPV is negative, the NPV rule indicates you
should reject the deal.
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6-20
Figure 6.2
NPV of Star’s \$1 million Book Deal
•
When the benefits of an investment occur before the costs, the NPV is an
increasing function of the discount rate.
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6-21
The Internal Rate of Return (cont'd)
• Nonexistent IRR
 Assume now that you are offered \$1 million per year if
you agree to go on a speaking tour for the next three
years. If you lecture, you will not be able to write the
book. Thus your net cash flows would look like:
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6-22
The Internal Rate of Return (cont'd)
• Nonexistent IRR
500, 000
500, 000
500, 000
NPV 


2
1  r
(1  r )
(1  r )3
 By setting the NPV equal to zero and solving for r, we
find the IRR. In this case, however, there is no discount
rate that will set the NPV equal to zero.
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6-23
Figure 6.3 NPV of Lecture Contract
•
No IRR exists because the NPV is positive for all values of the discount rate.
Thus the IRR rule cannot be used.
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6-24
The Internal Rate of Return (cont'd)
• Multiple IRRs
 Now assume the lecture deal fell through. You inform
the publisher that it needs to increase its offer before
you will accept it. The publisher then agrees to make
royalty payments of \$20,000 per year forever, starting
once the book is published in three years.
 Should you accept or reject the new offer?
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6-25
The Internal Rate of Return (cont'd)
• Multiple IRRs
 The cash flows would now look like:
 The NPV is calculated as:
NPV  1,000, 000 
 1,000, 000 
500, 000
500, 000
20, 000
20, 000
20, 000





1  r
(1  r ) 2
(1  r )3
(1  r ) 4
(1  r ) 5

500, 000 
1
1
 20, 000 
1






r
(1  r )3 
(1  r )3  r 

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6-26
The Internal Rate of Return (cont'd)
• Multiple IRRs
 By setting the NPV equal to zero and solving for r, we
find the IRR. In this case, there are two IRRs: 4.723%
and 19.619%. Because there is more than one IRR, the
IRR rule cannot be applied.
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6-27
Figure 6.4 NPV of Star’s
Book Deal with Royalties
• If the opportunity cost of capital is either below 4.723% or above
19.619%, you should accept the deal.
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6-28
The Internal Rate of Return (cont'd)
• Multiple IRRs
 Between 4.723% and 19.619%, the book deal has a
negative NPV. Since your opportunity cost of capital is
10%, you should reject the deal.
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6-29
The Internal Rate of Return (cont'd)
• IRR Versus the IRR Rule
 While the IRR rule has shortcomings for making
investment decisions, the IRR itself remains useful. IRR
measures the average return of the investment and the
sensitivity of the NPV to any estimation error in the cost
of capital.
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6-30
Economic Profit or EVA
• EVA and Economic Profit
 Economic Profit
• The difference between revenue and the opportunity cost of
all resources consumed in producing that revenue, including
the opportunity cost of capital
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6-31
Economic Profit or EVA (cont'd)
• EVA and Economic Profit
 Economic Value Added (EVA)
• The cash flows of a project minus a charge for the
opportunity cost of capital
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6-32
Economic Profit or EVA (cont'd)
• EVA When Invested Capital is Constant
 EVA in Period n (When Capital Lasts Forever)
EVAn  Cn  rI
• where I is the project’s capital, Cn is the project’s cash flow
in time period n, and r is the cost of capital. r × I is known
as the capital charge
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6-33
Economic Profit or EVA (cont'd)
• EVA When Invested Capital is Constant
 EVA Investment Rule
• Accept any investment in which the present value (at the
project’s cost of capital) of all future EVAs is positive.
• When invested capital is constant, the EVA rule and the
NPV rule will coincide.
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6-34
Example 6.2
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6-35
Example 6.2 (cont'd)
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6-36
Alternative Example 6.2
• Problem
 Ranger has an investment opportunity which requires
an upfront investment of \$150 million.
 The annual end-of-year cash flows of \$14 million
dollars are expected to last forever.
 The firm’s cost of capital is 8%.
 Compute the annual EVA and the present value of
the project.
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6-37
Alternative Example 6.2
• Solution
 Using Eq. 6.1, the EVA each year is:
EVAn  Cn  rI
EVAn  \$14 million  8%  \$150 million  \$2 million
 The present value of the EVA perpetuity is:
\$2 million
PV 
 \$25 million
8%
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6-38
Economic Profit or EVA (cont'd)
• EVA When Invested Capital Changes
 EVA in Period n (When Capital Depreciates)
EVAn  Cn  rI n  1  (Depreciation in Period n)
• Where Cn is a project’s cash flow in time period n, In – 1 is
the project’s capital at time period n – 1, and r is the cost
of capital
• When invested capital changes, the EVA rule and the NPV
rule coincide.
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6-39
Example 6.3
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6-40
Example 6.3
(cont'd)
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6-41
6.3 Mutually Exclusive
Investment Opportunities
• Mutually Exclusive Projects
 When you must choose only one project among several
possible projects, the choice is mutually exclusive.
 NPV Rule
• Select the project with the highest NPV.
 IRR Rule
• Selecting the project with the highest IRR may lead
to mistakes.
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6-42
Differences in Scale
• If a project’s size is doubled, its NPV will double.
This is not the case with IRR. Thus, the IRR
rule cannot be used to compare projects of
different scales.
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6-43
Differences in Scale (cont'd)
• Identical Scale
 Consider two projects:
Girlfriend’s
Business
Laundromat
Initial Investment
\$1,000
\$1,000
Cash FlowYear 1
\$1,100
\$400
Annual Growth Rate
-10%
-20%
Cost of Capital
12%
12%
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6-44
Differences in Scale (cont'd)
• Identical Scale
 Girlfriend’s Business
NPV   1000 
1100
1100
  1000 
 \$4000
r  0.1
0.12  0.1
1000 
1100
implies r  100%
r  0.1
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6-45
Differences in Scale (cont'd)
• Identical Scale
 Laundromat
NPV   1000 
400
400
  1000 
 \$250
r  0.2
0.12  0.2
• IRR = 20%
 Both the NPV rule and the IRR rule indicate the
girlfriend’s business is the better alternative.
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6-46
Figure 6.5
NPV of Investment Opportunities
•
The NPV of the girlfriend’s business is always larger than the NPV of the
single machine laundromat. The IRR of the girlfriend’s business is 100%, while
the IRR for the laundromat is 20%.
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6-47
Differences in Scale (cont'd)
• Changes in Scale
 What if the laundromat project was 20 times larger?
400


NPV  20  1000 
  \$5000
0.12  0.2 

• The NPV would be 20 times larger, but the IRR remains the
same at 20%.

Give an discount rate of 12%, the NPV rule indicates you should
choose the 20-machine laundromat (NPV = \$5,000) over the
girlfriend’s business (NPV = \$4,000).
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6-48
Figure 6.6 NPV of Investment Opportunities
with the 20-Machine Laundromat
• The NPV of the 20-machine laundromat is larger than the NPV of the
girlfriend’s business only for discount rates less than 13.9%.
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6-49
Differences in Scale (cont'd)
• Percentage Return Versus Impact on Value
 The girlfriend’s business has an IRR of 100%, while the
20-machine laundromat has an IRR of 20%, so why not
choose the girlfriend’s business?
• Because the 20-machine laundromat makes more money

It has a higher NPV.
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6-50
Differences in Scale (cont'd)
• Percentage Return Versus Impact on Value
 Would you prefer a 200% return on \$1 dollar or a 10%
return on \$1 million?
• The former investment makes only \$2, while the latter
opportunity makes \$100,000.
• The IRR is a measure of the average return, but NPV is a
measure of the total dollar impact on value.
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6-51
Timing of Cash Flows
• Another problem with the IRR is that it can be
affected by changing the timing of the cash flows,
even when that change in timing does not affect
the NPV.
 It is possible to alter the ranking of projects’ IRRs
without changing their ranking in terms of NPV.
 Hence you cannot use the IRR to choose between
mutually exclusive investments.
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6-52
Timing of Cash Flows (cont'd)
• Assume you are offered a maintenance contract
on the laundromat machines which would cost
\$250 per year per machine. With this contract,
you would not have to pay for maintenance
and so the cash flows from the machines would
not decline.
 The expected cash flows would then be:
\$400 – \$250 = \$150 per year per machine
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6-53
Timing of Cash Flows (cont'd)
• The time line would now be:
150 

NPV  20  1000 
  \$5000
r 

 The NPV of the project remains \$5,000 but the IRR falls
to 15%.
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6-54
Figure 6.7 NPV With and Without
the Maintenance Contract
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6-55
Timing of Cash Flows (cont'd)
• The NPV without the maintenance contract
exceeds the NPV with the contract for discount
rates that are greater than 12%.
 The IRR without the maintenance contract (20%)
is larger than the IRR with the maintenance
contract (15%).
• The correct decision is to agree to the contract if
the cost of capital is less than 12% and to decline
the contract if the cost of capital exceeds 12%.
With a 12% cost of capital, you are indifferent.
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6-56
The Incremental IRR Rule
• Incremental IRR Investment Rule
 Apply the IRR rule to the difference between the
cash flows of the two mutually exclusive alternatives
(the increment to the cash flows of one investment
over the other).
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6-57
The Incremental IRR Rule (cont'd)
• Incremental IRR Rule Application
 The following timeline illustrates the incremental cash
flows of the maintenance contract laundromat over the
laundromat without the contract.
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6-58
The Incremental IRR Rule (cont'd)
• Incremental IRR Rule Application
NPV 
150
400

r
r  0.2
 Setting this equation equal to zero and solving for r
gives an IRR of 12%.
• Applying the incremental IRR rule, you should take the
contract when the cost of capital is less than 12%. Because
your cost of capital is 12%, you are indifferent. This finding
concurs with the NPV rule.
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6-59
The Incremental IRR Rule (cont'd)
• Shortcomings of the Incremental IRR Rule
 The fact that the IRR exceeds the cost of capital for
both projects does not imply that both projects have a
positive NPV.
 The incremental IRR may not exist.
 Multiple incremental IRRs could exist.
 You must ensure that the incremental cash flows are
initially negative and then become positive.
 The incremental IRR rule assumes that the riskiness of
the two projects is the same.
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6-60
6.4 Project Selection
with Resource Constraints
• Evaluation of Projects with Different Resource
Constraints
 Consider three possible projects that require
warehouse space.
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6-61
Profitability Index
• The profitability index can be used to identify
the optimal combination of projects to undertake.
Value Created
NPV
Profitability Index 

Resource Consumed
Resource Consumed
 From Table 6.1, we can see it is better to take projects
B & C together and forego project A.
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6-62
Example 6.4
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6-63
Example 6.4 (cont'd)
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6-64
Shortcomings of the Profitability Index
• In some situations the profitability Index does not
give an accurate answer.
 Suppose in Example 6.4 that NetIt has an additional
small project with a NPV of only \$100,000 that requires
3 engineers. The profitability index in this case is
0.1 / 3 = 0.03, so this project would appear at the
bottom of the ranking. However, 3 of the 190
employees are not being used after the first four
projects are selected. As a result, it would make
sense to take on this project even though it would
be ranked last.
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6-65
Shortcomings of the Profitability
Index (cont'd)
• With multiple resource constraints, the profitability
index can break down completely.
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6-66
Questions?
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6-67
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