T9.1 Chapter Outline
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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Irwin/McGraw-Hill

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 2005 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 2005 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
Irwin/McGraw-Hill 2005 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 2005 Slide 5

NPV Illustrated (concluded)
0
Initial outlay
($1,100)
– $1,100.00
+454.55
+826.45
+$ 181.00
NPV
1
Revenues $1,000
Expenses 500
Cash flow $500
1
$500 x
1.10
1
$1,000 x
1.10
2
2
Revenues $2,000
Expenses 1,000
Cash flow $1,000
Irwin/McGraw-Hill 2005 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 2005 Slide 7

Net Present Value Profile
Net present value
60
40
20
0
– 20
– 40
120
100
80
2% 6%
Irwin/McGraw-Hill
2
3
4
0
1
Year Cash flow
– $275
100
100
100
100
2005
10% 14% 18%
IRR
Slide 8
22%
Discount rate

NPV - Incremental Well Case
CAPEX
Year
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2003
2004
2005
2006
2007
2008
2009
2010
2002 -300,000
Total -300,000
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
208
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
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 2403190
434940
324220
267000
224280
192240
160200
145340
125730
105120
95440
85260
74580
63400
52720
52720
Net of Royalties at 20%
347952
259376
213600
179424
153792
128160
116272
100584
84096
76352
68208
59664
50720
42176
42176
1922552
Fixed Well
Costs
Variable
Costs
Total Well
Costs
30000
30000
30000
31000
31500
32000
32000
32500
33000
33500
34000
34500
35500
36000
36500
492000
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
263000 755000
Irwin/McGraw-Hill 2005
NPV at 15%
NPV at 10%
Slide 9
$394,442.02
$505,363.01
Net Cash
Flow
-300,000
265452
181376
145600
118424
98292
77660
69772
58084
43596
37852
31208
22164
12220
3176
2676
1167552

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 2005 Slide 10

Payback Rule Illustrated
Irwin/McGraw-Hill
Year
1
2
3
Initial outlay -$1,000
Cash flow
$200
400
600
Year
1
2
3
Accumulated
Cash flow
$200
600
1,200
Payback period = 2 2/3 years
2005 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
1167552
Irwin/McGraw-Hill 2005
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 2005 Slide 13

Discounted Payback Illustrated
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
Year
3
4
1
2
Accumulated discounted cash flow
$ 182
513
1,039
1,244
Discounted payback period is just under 3 years
Irwin/McGraw-Hill 2005 Slide 14

Ordinary and Discounted Payback (Table 9.3)
Cash Flow Accumulated Cash Flow
Year Undiscounted Discounted Undiscounted Discounted
1
4
5
2
3
$100
100
100
100
100
$89
79
70
62
55
$100
200
300
400
500
$89
168
238
300
355
Irwin/McGraw-Hill 2005 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
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
1167552
Irwin/McGraw-Hill
$394,442.00
2005
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 2005 Slide 17

Average Accounting Return Illustrated
 Average net income:
Sales
Costs
Gross profit
Depreciation
Earnings before taxes
Taxes (25%)
Net income
1
$440
220
220
80
140
35
$105
Year
2 3
$240
120
120
80
40
10
$30
$160
80
80
80
0
0
$0
Average net income = ($ 105 + 30 + 0 )/3 = $45
Irwin/McGraw-Hill 2005 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):
AAR =
Average net income
Average book value
=
$45
$120
= 37.5%
Irwin/McGraw-Hill 2005 Slide 19

Return on Capital Employed/investment
 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
 similar to the ‘average accounting return’ -
 average book value is the average investment
Irwin/McGraw-Hill 2005 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
Irwin/McGraw-Hill 2005 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
50 100 150
0 = -200 + + +
(1+IRR) 1 (1+IRR) 2 (1+IRR) 3
50 100 150
200 = + +
(1+IRR) 1 (1+IRR) 2 (1+IRR) 3
Irwin/McGraw-Hill 2005 Slide 22

Internal Rate of Return Illustrated (concluded)
 Trial and Error
Discount rates NPV
0%
5%
10%
15%
20%
$100
68
41
18
-2
IRR is just under 20% -- about 19.44
%
Irwin/McGraw-Hill 2005 Slide 23

Net Present Value Profile
Net present value
60
40
20
0
– 20
– 40
120
100
80
2% 6%
Irwin/McGraw-Hill
2
3
4
0
1
Year Cash flow
– $275
100
100
100
100
2005
10% 14% 18%
IRR
Slide 24
22%
Discount rate

IRR - Incremental Well Case
Net Cash
Flow
-300,000
265452
181376
145600
118424
98292
77660
69772
58084
43596
37852
31208
22164
12220
3176
2676
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
1167552
Irwin/McGraw-Hill
$394,442.00
2005
NPV at 15%
NPV at 10%
NPV at 50%
IRR
$394,442.02
$505,363.01
$52,626.17
63%
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
– IRR may give an ‘incorrect signal’
Not covered in the text
 IRR assumes annual cash flows earn the IRR rate over the life of the investment ( remember the bond coupon re-investment risk!)
Irwin/McGraw-Hill 2005 Slide 26

Multiple Rates of Return – a shortcoming
 Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
0
3
4
1
2
-$252
1,431
-3,035
2,850
-1,000
Irwin/McGraw-Hill 2005 Slide 27

Multiple Rates of Return (continued)
 What’s the IRR? Find the rate at which the computed NPV = 0: at 25.00%: NPV = _______ at 33.33%: NPV = _______ at 42.86%: NPV = _______ at 66.67%: NPV = _______
Irwin/McGraw-Hill 2005 Slide 28

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 = 0 at 33.33%: NPV = 0 at 42.86%: NPV = 0 at 66.67%: NPV = 0
 Two questions:
 1.
What’s going on here?
 2. How many IRRs can there be?
2005 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)
Irwin/McGraw-Hill
0.2
0.28
2005
0.36
0.44
Discount rate
0.52
Slide 30
0.6
0.68

IRR, NPV, and Mutually Exclusive Projects
Net present value
60
40
20
0
– 20
– 40
– 60
– 80
– 100
160
140
120
100
80
Crossover Point
0 2% 6%
0
Project A: – $350 50
Project B: – $250 125
Year
1 2
100
100
10% 14% 18% 22%
3 4
150 200
75 50
26%
Discount rate
Irwin/McGraw-Hill 2005
IRR
A
IRR
B
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
•
Only looks at the value per dollar invested
Irwin/McGraw-Hill 2005 Slide 32

Profitability Index Illustrated
 Now let’s go back to the initial example - we assumed the following information on Project X:
Initial outlay -$1,100
Annual cash benefits:
Required return = 10%
Year
1
2
Cash flows
$ 500
1,000
 What’s the Profitability Index (PI)?
Irwin/McGraw-Hill 2005 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 2005 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
$394,442.00
Irwin/McGraw-Hill
What is the Profitability 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!!
2005 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 2005 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 2005 Slide 37

Key concepts
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 2005 Slide 38

Examples
 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?
Year Cash Flows A Cash Flows B
2
3
0
1
4
-$30,000
15,000
10,000
10,000
5,000
-$45,000
5,000
10,000
20,000
250,000
Irwin/McGraw-Hill 2005 Slide 39

Examples
 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 2005 Slide 40

Examples
 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?
Year
0
1
2
3
Cash Flow
-$30,000
25,000
0
15,000
Irwin/McGraw-Hill 2005 Slide 41

Examples
 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 2005 Slide 42

Examples
 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/calculator/spreadsheet , we find that the
IRR is 18.78 percent.
Irwin/McGraw-Hill 2005 Slide 43