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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
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 or cost/benefit ratio
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 4
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 5
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 6
Underpinnings of the NPV Rule
 The foundation of the NPV approach:
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 7
Net Present Value Profile
Net present value
120
100
80
Year
Cash flow
0
1
2
3
4
– $275
100
100
100
100
60
40
20
0
– 20
– 40
Discount rate
2%
6%
10%
14%
18%
22%
IRR
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 8
NPV - Incremental Well Case
CAPEX
Year
2002
Net of Royalties
at 20%
Fixed Well
Costs
Variable
Costs
Total Well
Costs
Net Cash
Flow
434940
324220
267000
224280
192240
160200
145340
125730
105120
95440
85260
74580
63400
52720
52720
347952
259376
213600
179424
153792
128160
116272
100584
84096
76352
68208
59664
50720
42176
42176
30000
30000
30000
31000
31500
32000
32000
32500
33000
33500
34000
34500
35500
36000
36500
52500
48000
38000
30000
24000
18500
14500
10000
7500
5000
3000
3000
3000
3000
3000
82500
78000
68000
61000
55500
50500
46500
42500
40500
38500
37000
37500
38500
39000
39500
-300,000
265452
181376
145600
118424
98292
77660
69772
58084
43596
37852
31208
22164
12220
3176
2676
2403190
1922552
-300,000
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
Total
Incremental Price
WI @50%WI Revenues
Production$Cdn/bbl
$
m bbls
m bbls
33
29
25
21
18
15
13
11
9
8
7
6
5
4
4
-300,000
26.36
22.36
21.36
21.36
21.36
21.36
22.36
22.86
23.36
23.86
24.36
24.86
25.36
26.36
26.36
208
16.5
14.5
12.5
10.5
9
7.5
6.5
5.5
4.5
4
3.5
3
2.5
2
2
104
492000
NPV at 15%
NPV at 10%
Irwin/McGraw-Hill
263000
755000
$394,442.02
$505,363.01
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 9
116755
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 acceptable if
the payback is less than some pre specified 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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 10
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 11
Payback - Incremental Well Case
Net Cash
Flow
-300,000
265452
181376
145600
118424
98292
77660
69772
58084
43596
37852
31208
22164
12220
3176
2676
Payback occurs after year 1
- about 1 year and two months
1167552
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 12
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 – time value of money is
considered
 What are its shortcomings?
 Cash flows beyond the cut-off point are ignored
 the cut-off point still has to be arbitrarily established
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 13
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 14
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 15
Discounted Payback - Incremental Well Case
Net Cash
Flow
-300,000
265452
181376
145600
118424
98292
77660
69772
58084
43596
37852
31208
22164
12220
3176
2676
1167552
Irwin/McGraw-Hill
NPV at
15%
-300000
$230,828.00
$137,147.00
$95,735.00
$67,709.00
$48,868.00
$33,574.00
$26,228.00
$18,988.00
$12,393.00
$9,357.00
$6,708.00
$4,142.00
$1,987.00
$449.00
$329.00
Using discounted cash
flows - payback takes
a few months longer
$394,442.00
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 16
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 17
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 18
Average Accounting Return Illustrated (concluded)
 Average book value:
Initial investment = $240
Average investment = ($240 + 0)/2 = $120
(assuming st. line depreciation)
 Average accounting return (AAR):
Average net income
AAR =
Irwin/McGraw-Hill
Average book value
$45
=
$120
= 37.5%
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 19
Return on Capital Employed/investment
Return on Capital Employed - (ROCE)
 Ratio at a particular point in time
 Earnings plus after tax interest on long term debt/average capital
employed
 Capital employed is total equity plus total long term debt
including the current portion of long term debt
Return on Investment - (ROI)
 similar to the ‘average accounting return’  average book value is the average investment
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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 20
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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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 21
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 =
Irwin/McGraw-Hill
(1+IRR)1
+
(1+IRR)2
100
+
150
(1+IRR)2
+
(1+IRR)3
150
+
(1+IRR)3
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 22
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 23
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 24
IRR - Incremental Well Case
Net Cash
Flow
-300,000
265452
181376
145600
118424
98292
77660
69772
58084
43596
37852
31208
22164
12220
3176
2676
1167552
Irwin/McGraw-Hill
NPV at
15%
-300000
$230,828.00
$137,147.00
$95,735.00
$67,709.00
$48,868.00
$33,574.00
$26,228.00
$18,988.00
$12,393.00
$9,357.00
$6,708.00
$4,142.00
$1,987.00
$449.00
$329.00
NPV at 15%
NPV at 10%
$394,442.02
$505,363.01
NPV at 50%
IRR
$52,626.17
63%
IRR for this incremental well
project is 63% - the discount
rate where the NPV is zero
$394,442.00
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 25
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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copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 26
Multiple Rates of Return – a shortcoming
 Assume you are considering a project for
which the cash flows are as follows:
Year
Irwin/McGraw-Hill
Cash flows
0
-$252
1
1,431
2
-3,035
3
2,850
4
-1,000
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 27
Multiple Rates of Return (continued)
 What’s the IRR? Find the rate at which
the computed NPV = 0:
Irwin/McGraw-Hill
at 25.00%:
NPV = _______
at 33.33%:
NPV = _______
at 42.86%:
NPV = _______
at 66.67%:
NPV = _______
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 28
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:


Irwin/McGraw-Hill
1. What’s going on here?
2. How many IRRs can there be?
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 29
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
Irwin/McGraw-Hill
0.28
0.36
0.44
0.52
Discount rate
0.6
0.68
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 30
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
Irwin/McGraw-Hill
18%
22%
26%
IRR B
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 31
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 32
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)?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 33
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……It’s a good
project because the present value of the inflows exceeds the
outlay.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 34
Profitability Index- Incremental Well Case
NPV at
15%
-300000
$230,828.00
$137,147.00
$95,735.00
$67,709.00
$48,868.00
$33,574.00
$26,228.00
$18,988.00
$12,393.00
$9,357.00
$6,708.00
$4,142.00
$1,987.00
$449.00
$329.00
What is the Profitablity Index if the firm has
a required rate of return of 15%?
PV of cash inflows at 15% = $694,442
$694,442/$300,000 = 2.31
....for every $1 invested, the project is returning $2.31
....a healthy return!!
$394,442.00
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 35
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 36
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 37
A few questions
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?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 38
A few questions
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 39
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?
Irwin/McGraw-Hill
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 40
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 41
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?
Irwin/McGraw-Hill
Year
Cash Flow
0
-$30,000
1
25,000
2
0
3
15,000
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 42
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?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 43
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 44