T9.1 Chapter Outline
Chapter 9
Net Present Value and Other Investment Criteria
Chapter Organization
 9.1 Net Present Value
 9.2 The Payback Rule
 9.3 The Average Accounting Return
 9.4 The Internal Rate of Return
 9.5 The Profitability Index
 9.6 The Practice of Capital Budgeting
 9.7 Summary and Conclusions
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Capital Budgeting
 In Chapter 1 we defined capital budgeting as ‘the process of
planning and managing a firm’s investment in fixed assets’



...probably the most or at least one of the most important issues in
corporate finance.
Identifying investment opportunities which offer more value to the
firm than their cost - the value of the future cash flows need to be
greater than the investment required
estimating the size, timing and risk of future cash flows is the most
challenging aspect of capital budgeting
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Slide 2
Investment Criteria
 NPV - Net Present Value
 the difference between an investment’s market value and its cost
 Payback  the length of time it takes to recover the initial investment
 Discounted Payback
 the length of time required for an investment’s discounted cash
flows to equal its initial cost
 Average Accounting Return - AAR
 an investment’s average net income divided by its average book
value
 Internal Rate of Return
 the discount rate that makes the NPV of an investment equal to
zero
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Slide 3
Investment Critieria cont’d
 The Profitability Index- “PI’
 ‘The present value of an investment’s future cash flows divided by
its initial cost
- also known as the benefit/cost ratio
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Slide 4
T9.2 NPV Illustrated

Estimate future cash flows, calculate the PV of these cash
flows and then compare to cost of project to arrive at NPV

Assume you have the following information on Project X:
Initial outlay -$1,100
Required return = 10%
Annual cash revenues and expenses are as follows:

Year
Revenues
Expenses
1
2
$1,000
2,000
$500
1,000
Draw a time line and compute the NPV of project X.
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Slide 5
T9.2 NPV Illustrated (concluded)
0
Initial outlay
($1,100)
1
Revenues
Expenses
$1,000
500
Cash flow
$500
– $1,100.00
$500 x
+454.55
2
Revenues
Expenses
Cash flow $1,000
1
1.10
$1,000 x
+826.45
$2,000
1,000
1
1.10 2
+$181.00 NPV
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Slide 6
T9.3 Underpinnings of the NPV Rule
 The foundation of the NPV approach:
A “firm” is created when securityholders supply the funds to acquire
assets that will be used to produce and sell a good or a service;
The market value of the firm is based on the present value of the
cash flows it is expected to generate;
Additional investments are “good” if the present value of the
incremental expected cash flows exceeds their cost;
Thus, “good” projects are those which increase firm value - or, put
another way, good projects are those projects that have positive
NPVs!
Conclusion - Invest only in projects with positive NPV’s.
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Slide 7
Payback Rule
 ‘length of time it takes to recover the initial investment’
 how long does the investment take before I recover my initial
investment? - a break-even in an accounting sense but not in an
economic sense
 The Payback ‘Rule’ - an investment is considered acceptabe if
the payback is less than some prespecified time frame
 shortcomings of the payback rule vs the NPV
 ignores time value of money - simply adds up future cash flows
 ignores risk differences - payback is calculated the same way for
projects that are risky and ‘safe’ projects
 determining the cut-off - what should the payback be??
 Ignores the cash flows beyond the payback cut-off
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Slide 8
T9.4 Payback Rule Illustrated
Initial outlay -$1,000
Year
1
2
3
Year
1
2
3
Cash flow
$200
400
600
Accumulated
Cash flow
$200
600
1,200
Payback period = 2 2/3 years
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Slide 9
Discounted Payback
 The same basic concept in how long does it take to recover the
original investment but in this case the future cash flows are
discounted.
‘the length of time it takes for an investment’s discounted cash
flows to equal its initial cost.’
 break-even in an economic sense
 What are its shortcomings?
 Cash flows beyond the cut-off point are ignored
 the cut-off point still has to be arbitrarily established
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Slide 10
T9.5 Discounted Payback Illustrated
Year
1
2
3
4
Year
1
2
3
4
Initial outlay -$1,000
R = 10%
PV of
Cash flow
Cash flow
$ 200
400
700
300
$ 182
331
526
205
Accumulated
discounted cash flow
$ 182
513
1,039
1,244
Discounted payback period is just under 3 years
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Slide 11
T9.6 Ordinary and Discounted Payback (Table 9.3)
Cash Flow
Year
Accumulated Cash Flow
Undiscounted Discounted
Undiscounted
Discounted
1
$100
$89
$100
$89
2
100
79
200
168
3
100
70
300
238
4
100
62
400
300
5
100
55
500
355
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Slide 12
Average Accounting Return
‘An investment’s average net income divided by its average
book value’ or
‘Some measure of average accounting profit/some measure
of average accounting value’

....’a project is acceptable if its average accounting return exceeds
a target average accounting return
 Advantages
 easy to calculate
 readily available accounting information
 What are its shortcomings?
 Ignores time value of money - the average return does not
differentiate between near term returns vs. Returns in the distant
future
 focuses on net income and book value instead of cash flow and
market value
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Slide 13
T9.7 Average Accounting Return Illustrated
 Average net income:
Year
1
2
3
Sales
$440
$240
$160
Costs
220
120
80
Gross profit
220
120
80
Depreciation
80
80
80
140
40
0
35
10
0
$105
$30
$0
Earnings before taxes
Taxes (25%)
Net income
Average net income = ($105 + 30 + 0)/3 = $45
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Slide 14
T9.7 Average Accounting Return Illustrated (concluded)
 Average book value:
Initial investment = $240
Average investment = ($240 + 0)/2 = $120
 Average accounting return (AAR):
Average net income
AAR =
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Average book value
$45
=
$120
= 37.5%
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Slide 15
Internal Rate of Return or ‘IRR’
‘the discount rate that makes the NPV of an investment equal
to zero’
- sometimes called the discounted cash flow or ‘DCF return’
 The IRR ‘rule’ suggest that an investment is acceptable if
the IRR exceeds the required return.



A viable alternative to the NPV model
Used extensively in practice - provides a return figure when
analyzing investments as opposed to a $ figure
more difficult to calculate - requires trial and error
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Slide 16
Internal Rate of Return
 What are the shortcomings of the IRR approach?
 Non -conventional cash flows make the calculation much more
difficult
 Mutually exclusive Investments - meaning we can accept one
project but not another that is under consideration
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Slide 17
T9.8 Internal Rate of Return Illustrated
Initial outlay = -$200
Year
Cash flow
1
2
3
$ 50
100
150
 Find the IRR such that NPV = 0
50
0 = -200 +
100
(1+IRR)1
50
200 =
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(1+IRR)1
+
(1+IRR)2
100
+
150
(1+IRR)2
+
(1+IRR)3
150
+
(1+IRR)3
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Slide 18
T9.8 Internal Rate of Return Illustrated (concluded)
 Trial and Error
Discount rates
NPV
0%
$100
5%
68
10%
41
15%
18
20%
-2
IRR is just under 20% -- about 19.44%
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 19
T9.9 Net Present Value Profile
Net present value
120
100
80
Year
Cash flow
0
1
2
3
4
– $275
100
100
100
100
60
40
20
0
– 20
– 40
Discount rate
2%
6%
10%
14%
18%
22%
IRR
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Slide 20
T9.10 Multiple Rates of Return
 Assume you are considering a project for
which the cash flows are as follows:
Year
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Cash flows
0
-$252
1
1,431
2
-3,035
3
2,850
4
-1,000
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Slide 21
T9.10 Multiple Rates of Return (continued)
 What’s the IRR? Find the rate at which
the computed NPV = 0:
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at 25.00%:
NPV = _______
at 33.33%:
NPV = _______
at 42.86%:
NPV = _______
at 66.67%:
NPV = _______
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Slide 22
T9.10 Multiple Rates of Return (continued)
 What’s the IRR? Find the rate at which
the computed NPV = 0:
at 25.00%:
NPV =
0
at 33.33%:
NPV =
0
at 42.86%:
NPV =
0
at 66.67%:
NPV =
0
 Two questions:


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1. What’s going on here?
2. How many IRRs can there be?
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Slide 23
T9.10 Multiple Rates of Return (concluded)
NPV
$0.06
$0.04
IRR = 1/4
$0.02
$0.00
($0.02)
IRR = 1/3
IRR = 2/3
IRR = 3/7
($0.04)
($0.06)
($0.08)
0.2
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0.28
0.36
0.44
0.52
Discount rate
0.6
0.68
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Slide 24
T9.11 IRR, NPV, and Mutually Exclusive Projects
Net present value
Year
0
160
140
120
100
80
60
40
20
0
1
2
3
4
Project A:
– $350
50
100
150
200
Project B:
– $250
125
100
75
50
Crossover Point
– 20
– 40
– 60
– 80
– 100
Discount rate
0
2%
6%
10%
14%
IRR A
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18%
22%
26%
IRR B
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 25
Profitability Index - ‘PI’
‘The present value of an investment’s future cash flows
divided by its initial cost’
 measures ‘bang for the buck’ or the value created per dollar
invested
 Shortcomings
 does not recognize total market value added (as does the NPV
approach) - thus when comparing mutually exclusive investments it
can lead to incorrect decisions
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 26
T9.12 Profitability Index Illustrated

Now let’s go back to the initial example - we assumed the
following information on Project X:
Initial outlay -$1,100Required return = 10%
Annual cash benefits:
Year
1
2

Cash flows
$ 500
1,000
What’s the Profitability Index (PI)?
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 27
T9.12 Profitability Index Illustrated (concluded)
 Previously we found that the NPV of Project X is equal to:
($454.55 + 826.45) - 1,100 = $1,281.00 - 1,100 = $181.00.
 The PI = PV inflows/PV outlay = $1,281.00/1,100 = 1.1645.
 This is a good project according to the PI rule. Can you explain
why?
It’s a good project because the present value of the inflows
exceeds the outlay.
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 28
T9.13 Summary of Investment Criteria
 I. Discounted cash flow criteria
A. Net present value (NPV). The NPV of an investment is the
difference between its market value and its cost. The NPV
rule is to take a project if its NPV is positive. NPV has no
serious flaws; it is the preferred decision criterion.
B. Internal rate of return (IRR). The IRR is the discount rate that
makes the estimated NPV of an investment equal to zero. The IRR
rule is to take a project when its IRR exceeds the required return. When
project cash flows are not conventional, there may be no IRR or there
may be more than one.
C. Profitability index (PI). The PI, also called the benefit-cost ratio, is
the ratio of present value to cost. The profitability index rule is to
take an investment if the index exceeds 1.0. The PI
measures the present value per dollar invested.
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Slide 29
T9.13 Summary of Investment Criteria (concluded)
 II. Payback criteria
A. Payback period. The payback period is the length of time until the
sum of an investment’s cash flows equals its cost. The payback period
rule is to take a project if its payback period is less than some
prespecified cutoff.
B. Discounted payback period. The discounted payback period is the
length of time until the sum of an investment’s discounted cash flows
equals its cost. The discounted payback period rule is to take an
investment if the discounted payback is less than some prespecified
cutoff.
 III. Accounting criterion
A. Average accounting return (AAR). The AAR is a measure of
accounting profit relative to book value. The AAR rule is to
take an investment if its AAR exceeds a benchmark.
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Slide 30
T9.14 The Practice of Capital Budgeting
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Slide 31
T9.15 Chapter 9 Quick Quiz
1. Which of the capital budgeting techniques do account for both the time
value of money and risk?
2. The change in firm value associated with investment in a project is
measured by the project’s _____________ .
a. Payback period
b. Discounted payback period
c. Net present value
d. Internal rate of return
3. Why might one use several evaluation techniques to assess a given
project?
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Slide 32
T9.15 Chapter 9 Quick Quiz
1. Which of the capital budgeting techniques do account for both the time
value of money and risk?
Discounted payback period, NPV, IRR, and PI
2. The change in firm value associated with investment in a project is
measured by the project’s Net present value.
3. Why might one use several evaluation techniques to assess a given
project?
To measure different aspects of the project; e.g., the payback period
measures liquidity, the NPV measures the change in firm value, and the
IRR measures the rate of return on the initial outlay.
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Slide 33
T9.16 Solution to Problem 9.3
 Offshore Drilling Products, Inc. imposes a payback cutoff of 3
years for its international investment projects. If the company
has the following two projects available, should they accept
either of them?
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Year
Cash Flows A
Cash Flows B
0
-$30,000
-$45,000
1
15,000
5,000
2
10,000
10,000
3
10,000
20,000
4
5,000
250,000
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 34
T9.16 Solution to Problem 9.3 (concluded)
 Project A:
Payback period
= 1 + 1 + ($30,000 - 25,000)/10,000
= 2.50 years
 Project B:
Payback period
= 1 + 1 + 1 + ($45,000 - 35,000)/$250,000
= 3.04 years
 Project A’s payback period is 2.50 years and project B’s
payback period is 3.04 years. Since the maximum acceptable
payback period is 3 years, the firm should accept project A and
reject project B.
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 35
T9.17 Solution to Problem 9.7
 A firm evaluates all of its projects by applying the IRR
rule. If the required return is 18 percent, should the firm
accept the following project?
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Year
Cash Flow
0
-$30,000
1
25,000
2
0
3
15,000
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Slide 36
T9.17 Solution of Problem 9.7 (concluded)
 To find the IRR, set the NPV equal to 0 and solve for the
discount rate:
NPV = 0 = -$30,000 + $25,000/(1 + IRR)1 + $0/(1 + IRR) 2
+$15,000/(1 + IRR)3
 At 18 percent, the computed NPV is ____.
 So the IRR must be (greater/less) than 18 percent. How did
you know?
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Slide 37
T9.17 Solution of Problem 9.7 (concluded)
 To find the IRR, set the NPV equal to 0 and solve for the
discount rate:
NPV = 0 = -$30,000 + $25,000/(1 + IRR)1 + $0/(1 + IRR)2
+$15,000/(1 + IRR)3
 At 18 percent, the computed NPV is $316.
 So the IRR must be greater than 18 percent. We know this
because the computed NPV is positive.
 By trial-and-error, we find that the IRR is 18.78 percent.
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Slide 38