7-0
Chapter Seven
Net Present Value
andFinance
Corporate
Ross Westerfield Jaffe
Capital Budgeting


7
Seventh Edition
Seventh Edition
McGraw-Hill/Irwin
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7-1
Chapter Outline
7.1 Incremental Cash Flows
7.2 The Baldwin Company: An Example
7.3 The Boeing 777: A Real-World Example
7.4 Inflation and Capital Budgeting
7.5 Investments of Unequal Lives: The Equivalent
Annual Cost Method
7.6 Summary and Conclusions
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7-2
7.1 Incremental Cash Flows
•
•
•
•
•
•
Cash flows matter—not accounting earnings.
Sunk costs don’t matter.
Incremental cash flows matter.
Opportunity costs matter.
Side effects like cannibalism and erosion matter.
Taxes matter: we want incremental after-tax cash
flows.
• Inflation matters.
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7-3
Cash Flows—Not Accounting Earnings.
• Consider depreciation expense.
• You never write a check made out to “depreciation”.
• Much of the work in evaluating a project lies in
taking accounting numbers and generating cash
flows.
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7-4
Incremental Cash Flows
• Sunk costs are not relevant
– Just because “we have come this far” does not
mean that we should continue to throw good
money after bad.
• Opportunity costs do matter. Just because a project
has a positive NPV that does not mean that it should
also have automatic acceptance. Specifically if
another project with a higher NPV would have to be
passed up we should not proceed.
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7-5
Incremental Cash Flows
• Side effects matter.
– Erosion and cannibalism are both bad things. If
our new product causes existing customers to
demand less of current products, we need to
recognize that.
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7-6
Estimating Cash Flows
• Cash Flows from Operations
– Recall that:
Operating Cash Flow = EBIT – Taxes +
Depreciation
• Net Capital Spending
– Don’t forget salvage value (after tax, of course).
• Changes in Net Working Capital
– Recall that when the project winds down, we
enjoy a return of net working capital.
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7-7
Interest Expense
• Later chapters will deal with the impact that the
amount of debt that a firm has in its capital structure
has on firm value.
• For now, it’s enough to assume that the firm’s level
of debt (hence interest expense) is independent of
the project at hand.
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7-8
Project Cash Flows
• T=0: Cost of new asset.
– Sale of old asset.
– Change in Net Working Capital.
• T=1,n: Operating Cash Flows (in the
simplest case)
• T=n: Terminal Cash Flows
– Salvage value
– Change in Net Working Capital.
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7-9
Modified ACRS Depreciation
McGraw-Hill/Irwin
Class
Examples
3-Year
Equipment used in research
5-Year
Autos, computers
7-Year
Most industrial equipment
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7-10
Modified ACRS Depreciation Allowances
Year
3-year class 5-year class
7-year class
1
33.33%
20.00%
14.29%
2
44.44%
32.00%
24.49%
3
14.82%
19.20%
17.49%
4
7.41%
11.52%
12.49%
5
11.52%
12.49%
6
5.76%
8.93%
7
8.93%
8
4.45%
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7-11
Problem 7.3
• The Best Manufacturing Company is considering a
new investment. Financial projections for the
investment are tabulated below. (Cash flows are in
$ thousands and the corporate tax rate is 34
percent.)
Year 0
Year 1
Year 2
Year 3
Year 4
Sales revenue
7,000
7,000
7,000
7,000
Operating costs
2,000
2,000
2,000
2,000
2,500
2,500
2,500
2,500
250
300
200
0
Investment
-10,000
Depreciation
NWC (End of year)
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7-12
Problem 7.3: Compute OCF
• Compute the incremental cash flow of the
investment.
• OCF = (R-C-D)(1-T)+D
• The incremental cash flow is the same for each year.
• OCF = (7,000-2,000-2,500)(1-.34)+2,500=$4,150
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7-13
Problem 7.3: Cash Flow from Assets
• CFA = OCF – Net Capital Spending – Net Working
Capital Spending
Year
OCF
0
4,150
4,150
Addition
to assets
10,000
0
0
Addition
CFA
to NWC
200
-10,200
50
4,100
50
4,100
0
1
2
3
4,150
0
-100
4,250
4
4,150
0
-200
4,350
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7-14
Problem 7.3: Compute NPV
Year
CFA
0
-10,200
1
4,100
2
4,100
3
4,250
4
4,350
McGraw-Hill/Irwin
• NPV(12%) =
$2,518.78
• NPV >0
• Project is acceptable.
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7-15
7.2 The Baldwin Company: An Example
Costs of test marketing (already spent): $250,000.
Current market value of proposed factory site (which we
own): $150,000.
Cost of bowling ball machine: $100,000 (depreciated
according to ACRS 5-year life).
Increase in net working capital: $10,000.
Production (in units) by year during 5-year life of the
machine: 5,000, 8,000, 12,000, 10,000, 6,000.
Price during first year is $20; price increases 2% per year
thereafter.
Production costs during first year are $10 per unit and
increase 10% per year thereafter.
Annual inflation rate: 5%
Working Capital: initially $10,000 changes with sales.
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7-16
Depreciation
• Cost of machine = $100,000
Dep. %
Depreciation Book Value
End of Year
Acc. Dep.
Year 1
20%
$20,000
$80,000
$20,000
Year 2
32%
$32,000
$48,000
$52,000
Year 3
19.2%
$19,200
$28,800
$71,200
Year 4
11.52%
$11,520
$17,280
$82,720
Year 5
11.52%
$11,520
$5,760
$94,240
Year 6
5.76%
$5,760
0
$100,000
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7-17
The Worksheet for Cash Flows of the
Baldwin Company
($ thousands) (All cash flows occur at the end of the year.)
Year 0
Investments:
(1) Bowling ball machine
(2) Accumulated
depreciation
(3) Adjusted basis of
machine after
depreciation (end of year)
(4) Opportunity cost
(warehouse)
(5) Net working capital
(end of year)
(6) Change in net
working capital
(7) Total cash flow of–260.00
[(1) + (4) + (6)]
Year 1
Year 2
Year 3
Year 4
Year 5
21.76*
94.24
–100.00
80.00
20.00
52.00
71.20
82.72
48.00
28.80
17.28
5.76
–150.00
10.00
150.00
10.00
–10.00
–6.32
16.32
24.97
21.22
–6.32
–8.65
3.75
–8.65
3.75
0
21.22
192.98 investment
* We assume that the ending market value of the capital investment at year 5 is $30,000. Capital gain is the difference between
ending market value and adjusted basis of the machine. The adjusted basis is the original purchase price of the machine less
depreciation. The capital gain is $24,240 (= $30,000 – $5,760). We will assume the incremental corporate tax for Baldwin on
this project is 34 percent. Capital gains are now taxed at the ordinary income rate, so the capital gains tax due is $8,240 [0.34 
($30,000 – $5,760)]. The after-tax salvage value is $30,000 – [0.34  ($30,000 – $5,760)] = 21,760.
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
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7-18
Salvage Value
• Cash Flow from Salvage Value = Market Value – (Market
Value – Book Value)*Tax Rate
• CF(SV) = MV- (MV-BV)*T
• At the end of year 5, the book value = $5,760. The machine
can be sold for $30,000 and the tax rate is 34%.
• CF(SV) = $30,000 – ($30,000-$5,760)*.34 = $21,758.40
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7-19
The Worksheet for Cash Flows of the
Baldwin Company
($ thousands) (All cash flows occur at the end of the year.)
Year 0
Investments:
(1) Bowling ball machine
(2) Accumulated
depreciation
(3) Adjusted basis of
machine after
depreciation (end of year)
(4) Opportunity cost
(warehouse)
(5) Net working capital
(end of year)
(6) Change in net
working capital
(7) Total cash flow of–260.00
[(1) + (4) + (6)]
Year 1
Year 2
Year 3
Year 4
Year 5
21.76*
94.24
–100.00
80.00
20.00
52.00
71.20
82.72
48.00
28.80
17.28
5.76
–150.00
10.00
150.00
10.00
–10.00
–6.32
16.32
24.97
21.22
–6.32
–8.65
3.75
–8.65
3.75
0
21.22
192.98 investment
At the end of the project, the warehouse is unencumbered, so we can sell it if we want to.
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7-20
Working Capital
Year 0
Sales
NWC
$10,000
Year 1
Year 2
Year 3
Year 4
Year 5
$100,000 $163,000 $249,720
$212,200 $129,900
$10,000
$16,300
$24,720
$21,220
0
0
$6,300
$8,420
-$3,500
-$21,220
10% of
Sales
ΔNWC $10,000
• NWC initially increases by $10,000.
• In years 1-4, it is 10% of sales.
• The assumption is made that at the end of the project’s life (end of year
5), NWC goes back to its prior level.
• The row of changes in NWC should add to zero.
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7-21
The Worksheet for Cash Flows of the
Baldwin Company (continued)
($ thousands) (All cash flows occur at the end of the year.)
Year 0
Income:
(8) Sales Revenues
Year 1
Year 2
Year 3
Year 4
Year 5
100.00
163.00
249.72
212.20 129.90
Recall that production (in units) by year during 5-year life of the machine is
given by:
(5,000, 8,000, 12,000, 10,000, 6,000).
Price during first year is $20 and increases 2% per year thereafter.
Sales revenue in year 3 = 12,000×[$20×(1.02)2] = 12,000×$20.81 = $249,720.
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7-22
The Worksheet for Cash Flows of the
Baldwin Company (continued)
($ thousands) (All cash flows occur at the end of the year.)
Income:
(8) Sales Revenues
(9) Operating costs
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
50.00
100.00
88.00
163.00
145.20
249.72
212.20 129.90
133.10 87.84
Again, production (in units) by year during 5-year life of the machine is given
by:
(5,000, 8,000, 12,000, 10,000, 6,000).
Production costs during first year (per unit) are $10 and (increase 10% per
year thereafter).
Production costs in year 2 = 8,000×[$10×(1.10)1] = $88,000
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7-23
The Worksheet for Cash Flows of the
Baldwin Company (continued)
($ thousands) (All cash flows occur at the end of the year.)
Income:
(8) Sales Revenues
(9) Operating costs
(10) Depreciation
Year 0
Year 1
Year 2
Year 3
50.00
20.00
100.00
88.00
32.00
163.00
145.20
19.20
249.72
212.20 129.90
133.10 87.84
11.52 11.52
Depreciation is calculated using the Accelerated
Cost Recovery System (shown at right)
Our cost basis is $100,000
Depreciation charge in year 4
= $100,000×(.1152) = $11,520.
McGraw-Hill/Irwin
Year
1
2
3
4
5
6
Total
Year 4
Year 5
ACRS %
20.00%
32.00%
19.20%
11.52%
11.52%
5.76%
100.00%
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7-24
The Worksheet for Cash Flows of the
Baldwin Company (continued)
($ thousands) (All cash flows occur at the end of the year.)
Year 0
Income:
(8) Sales Revenues
(9) Operating costs
(10) Depreciation
(11) Income before taxes
[(8) – (9) - (10)]
(12) Tax at 34 percent
(13) Net Income
McGraw-Hill/Irwin
Year 1
Year 2
Year 3
Year 4
100.00
50.00
20.00
30.00
163.00
88.00
32.00
43.20
249.72
145.20
19.20
85.32
212.20 129.90
133.10 87.84
11.52 11.52
67.58 30.54
10.20
19.80
14.69
28.51
29.01
56.31
22.98
44.60
Year 5
10.38
20.16
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7-25
Incremental After Tax Cash Flows
of the Baldwin Company
Year 0
(1) Sales
Revenues
(2) Operating
costs
(3) Taxes
(4) OCF
(1) – (2) – (3)
(5) Total CF of
Investment
(6) IATCF
[(4) + (5)]
Year 1
Year 2
Year 3
Year 4
Year 5
$100.00
$163.00
$249.72
$212.20
$129.90
-50.00
-88.00
-145.20
133.10
-87.84
-10.20
-14.69
-29.01
-22.98
-10.38
39.80
60.51
75.51
56.12
31.68
–6.32
–8.65
3.75
192.98
54.19
66.86
59.87
224.66
–260.
–260.
39.80
$39.80 $54.19 $66.86 $59.87 $224.66
NPV  $260 




2
3
4
(1.10) (1.10) (1.10) (1.10)
(1.10)5
NPV  $51,588.05
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7-26
Total Cash Flow of Investment
Year 0
Capital
Spending
-100
NWC
Spending
-10
Year 1
Year 2
Year 3
Year 4
+21.76
0
-6.3
-8.42
+3.75
Opportunity -150
Cost
CFFI
-260
Year 5
+21.220
+150
0
-6.3
-8.42
+3.75
+192.98
• CFA = OCF – Net Capital Spending – Net Working Capital Spending
• CFA = OCF – Cash flow from investment
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7-27
NPV Baldwin Company
CF0
–260
CF1
39.80
F1
CF4
F4
F2
CF3
F3
McGraw-Hill/Irwin
1
1
CF5
CF2
59.87
224.66
54.19
F5
1
I
10
1
66.86
1
NPV
51,588.05
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7-28
7.3 Inflation and Capital Budgeting
• Inflation is an important fact of economic life and must be
considered in capital budgeting.
• Consider the relationship between interest rates and inflation,
often referred to as the Fisher relationship:
(1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate)
• For low rates of inflation, this is often approximated as
Real Rate  Nominal Rate – Inflation Rate
• While the nominal rate in the U.S. has fluctuated with
inflation, most of the time the real rate has exhibited far less
variance than the nominal rate.
• When accounting for inflation in capital budgeting, one must
compare real cash flows discounted at real rates or nominal
cash flows discounted at nominal rates.
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7-29
Example of Capital Budgeting under Inflation
Sony International has an investment opportunity to produce
a new stereo color TV.
The required investment on January 1 of this year is $32
million. The firm will depreciate the investment to zero
using the straight-line method. The firm is in the 34% tax
bracket.
The price of the product on January 1 will be $400 per unit.
The price will stay constant in real terms.
Labor costs will be $15 per hour on January 1. The will
increase at 2% per year in real terms.
Energy costs will be $5 per TV; they will increase 3% per
year in real terms.
The inflation rate is 5% Revenues are received and costs are
paid at year-end.
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7-30
Example of Capital Budgeting under Inflation
Year 1
Year 2
Year 3
Year 4
Physical
Production
(units)
100,000
200,000
200,000
150,000
Labor Input
(hours)
2,000,000
2,000,000
2,000,000
2,000,000
Energy input,
physical units
200,000
200,000
200,000
200,000
The riskless nominal discount rate is 4%.
The real discount rate for costs and revenues is 8%. Calculate the
NPV.
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7-31
Example of Capital Budgeting under Inflation
The depreciation tax shield is a risk-free nominal cash flow,
and is therefore discounted at the nominal riskless rate.
Cost of investment today = $32,000,000
Project life = 4 years
$32,000,000
Annual depreciation expense: $8,000,000 =
4 years
Depreciation tax shield = $8,000,000 × .34 = $2,720,000
CF0
0
CF1
2,720,000
F1
McGraw-Hill/Irwin
4
I
NPV
4
9,873,315
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7-32
Year 1 After-tax Real Risky Cash Flows
• Risky Real Cash Flows
– Price: $400 per unit with zero real price increase
– Labor: $15 per hour with 2% real wage increase
– Energy: $5 per unit with 3% real energy cost increase
• Year 1 After-tax Real Risky Cash Flows:
After-tax revenues =
$400 × 100,000 × (1 – .34) = $26,400,000
After-tax labor costs =
$15 × 2,000,000 × 1.02 × (1 – .34) = $20,196,000
After-tax energy costs =
$5 × 2,00,000 × 1.03 × (1 – .34) = $679,800
After-tax net operating CF =
$26,400,000 – $20,196,000 – $679,800 = $5,524,200
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7-33
Year 2 After-tax Real Risky Cash Flows
• Risky Real Cash Flows
– Price: $400 per unit with zero real price increase
– Labor: $15 per hour with 2% real wage increase
– Energy: $5 per unit with 3% real energy cost increase
• Year 1 After-tax Real Risky Cash Flows:
After-tax revenues =
$400 × 100,000 × (1 – .34) = $26,400,000
After-tax labor costs =
$15 × 2,000,000 × (1.02)2 × (1 – .34) = $20,599,920
After-tax energy costs =
$5 × 2,00,000 × (1.03)2 × (1 – .34) = $700,194
After-tax net operating CF =
$26,400,000 – $ 20,599,920– $ 700,194 = $ 31,499,886
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7-34
Year 3 After-tax Real Risky Cash Flows
• Risky Real Cash Flows
– Price: $400 per unit with zero real price increase
– Labor: $15 per hour with 2% real wage increase
– Energy: $5 per unit with 3% real energy cost increase
• Year 1 After-tax Real Risky Cash Flows:
After-tax revenues =
$400 × 100,000 × (1 – .34) = $26,400,000
After-tax labor costs =
$15 × 2,000,000 × (1.02)3 × (1 – .34) = $21,011.92
After-tax energy costs =
$5 × 2,00,000 × (1.03)3 × (1 – .34) = $721,199.82
After-tax net operating CF =
$26,400,000 – $ 21,011.92– $ 721,199.82 = $31,066,882
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7-35
Year 4 After-tax Real Risky Cash Flows
• Risky Real Cash Flows
– Price: $400 per unit with zero real price increase
– Labor: $15 per hour with 2% real wage increase
– Energy: $5 per unit with 3% real energy cost increase
• Year 1 After-tax Real Risky Cash Flows:
After-tax revenues =
$400 × 100,000 × (1 – .34) = $26,400,000
After-tax labor costs =
$15 × 2,000,000 × (1.02)4 × (1 – .34) = $21,432.16
After-tax energy costs =
$5 × 2,00,000 × (1.03)4 × (1 – .34) = $742,835.82
After-tax net operating CF =
$26,400,000 – $21,432.16– $742,835.82 = $17,425,007
McGraw-Hill/Irwin
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7-36
Example of Capital Budgeting under Inflation
$5,524,200
0
$31,499,886
1
$31,066,882
2
3
$17,425,007
4
-$32,000,000
CF0
–32 m
CF1
5,524,000
F1
CF2
F2
McGraw-Hill/Irwin
1
31,499,886
1
CF3
F3
CF4
31,066,882
1
17,425,007
F4
1
I
8
NPV
69,590,868
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7-37
Example of Capital Budgeting under Inflation
The project NPV can now be computed as the sum of the PV
of the cost, the PV of the risky cash flows discounted at the
risky rate and the PV of the risk-free cash flows discounted at
the risk-free discount rate.
NPV = –$32,000,000 + $69,590,868 + $9,873,315 = $47,464,183
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7-38
7.3 The Boeing 777: A Real-World Example
• In late 1990, the Boeing Company announced its intention to
build the Boeing 777, a commercial airplane that could carry
up to 390 passengers and fly 7,600 miles.
• Analysts expected the up-front investment and R&D costs
would be as much as $8 billion.
• Delivery of the planes was expected to begin in 1995 and
continue for at least 35 years.
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7-39
Table 7.5 Incremental Cash Flows: Boeing 777
Sales Operating
Year Units Revenue Costs Dep.
Taxes
Capital Invest- Net Cash
Flow
DNWC Spending ment
1991
$865.00 $40.00 $(307.70)
1992
1993
1,340.00
1,240.00
96.00
116.40
(488.24)
(461.18)
600.00
300.00
600.00 (1,451.76)
300.00 (1,078.82)
1994
840.00
124.76
(328.02)
200.00
200.00
(711.98)
$1,847.55
1,976.69
112.28
(82.08)
181.06
1.85
182.91
(229.97)
1996 145 19,418.96
17,865.45
101.06
493.83
1,722.00
1997 140 19,244.23
16,550.04
90.95
885.10
1995
14
$400.00 $400.00 $(957.30)
(17.12)
19.42 1,741.42
19.42
681.74
2.30 1,806.79
Net Cash Flow can be determined in three steps:
Taxes ($19,244.23 – $16,550.04 – $90.95)×0.34 = $885.10
Investment
NCF
–$17.12 + $19.42 = $2.30
$19,244.23 – $16,550.04 – $885.10 – $2.30 = $1,806.79
McGraw-Hill/Irwin
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7-40
Year
NCF
Year
NCF
Year NCF
1991 $ (957.30)
1992 $ (1,451.76)
1993 $ (1,078.82)
2002 $ 1,717.26
2003 $ 1,590.01
2004 $ 1,798.97
2013 $ 2,213.18
2014 $ 2,104.73
2015 $ 2,285.77
1994 $ (711.98)
1995 $ (229.97)
1996 $ 681.74
2005 $ 616.79
2006 $ 1,484.73
2007 $ 2,173.59
2016 $ 2,353.81
2017 $ 2,423.89
2018 $ 2,496.05
1997 $ 1,806.79
1998 $ 1,914.06
1999 $ 1,676.05
2008 $ 1,641.97
2009 $ 677.92
2010 $ 1,886.96
2019 $ 2,568.60
2020 $ 2,641.01
2021 $ 2,717.53
2000 $ 1,640.25
2001 $ 1,716.80
2011 $ 2,331.33
2012 $ 2,576.47
2022 $ 2,798.77
2023 $ 2,882.44
2024 $ 2,964.45
McGraw-Hill/Irwin
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7-41
7.3 The Boeing 777: A Real-World Example
• Prior to 1990, Boeing had invested several hundred
million dollars in research and development.
• Since these cash outflows were incurred prior to the
decision to build the plane, they are sunk costs.
• The relevant costs were the at the time the decision
was made were the forecasted Net Cash Flows
McGraw-Hill/Irwin
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7-42
NPV
NPV Profile of the Boeing 777 Project
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
($10,000)0%
IRR = 21.12%
10%
20%
30%
40%
50%
Discount Rate
• This graph shows NPV as a function of the discount rate.
• Boeing should accept this project at discount rates less than
21 percent and reject the project at higher discount rates.
McGraw-Hill/Irwin
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7-43
Boeing 777
• As it turned out, sales failed to meet expectations.
• In fairness to the financial analysts at Boeing, there
is an important distinction between a good decision
and a good outcome.
McGraw-Hill/Irwin
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7-44
7.4 Investments of Unequal Lives: The
Equivalent Annual Cost Method
• There are times when application of the NPV rule
can lead to the wrong decision. Consider a factory
which must have an air cleaner. The equipment is
mandated by law, so there is no “doing without”.
• There are two choices:
– The “Cadillac cleaner” costs $4,000 today, has
annual operating costs of $100 and lasts for 10
years.
– The “Cheapskate cleaner” costs $1,000 today,
has annual operating costs of $500 and lasts for 5
years.
• Which one should we choose?
McGraw-Hill/Irwin
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7-45
EAC with a Calculator
At first glance, the Cheapskate cleaner has a lower NPV
Cadillac Air Cleaner
Cheapskate Air Cleaner
CF0
–4,000
CF0
–1,000
CF1
–100
CF1
–500
F1
10
F1
5
I
10
I
10
NPV
McGraw-Hill/Irwin
–4,614.46
NPV
–2,895.39
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
7-46
7.4 Investments of Unequal Lives: The
Equivalent Annual Cost Method
• This overlooks the fact that the Cadillac cleaner
lasts twice as long.
• When we incorporate that, the Cadillac cleaner is
actually cheaper.
McGraw-Hill/Irwin
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7-47
7.4 Investments of Unequal Lives: The
Equivalent Annual Cost Method
The Cadillac cleaner time line of cash flows:
-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100
0
1
2
3
4
5
6
7
8
9
10
The Cheapskate cleaner time line of cash flows over ten years:
-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500
0
McGraw-Hill/Irwin
1
2
3
4
5
6
7
8
9
10
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7-48
The Equivalent Annual Cost Method
When we make a fair comparison, the Cadillac is cheaper:
Cadillac Air Cleaner
Cheapskate Air Cleaner
CF0
–4,000
CF0
–1,000
CF1
–100
CF1
–500
F1
F1
10
CF2
I
10
F1
NPV
–4,614.46
CF3
F1
McGraw-Hill/Irwin
4
–1,500
1
–500
5
I
NPV
10
–4,693
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
7-49
Investments of Unequal Lives
• Replacement Chain
– Repeat the projects forever, find the PV of that
perpetuity.
– Assumption: Both projects can and will be
repeated.
• Matching Cycle
– Repeat projects until they begin and end at the
same time—like we just did with the air
cleaners.
– Compute NPV for the “repeated projects”.
• The Equivalent Annual Cost Method
McGraw-Hill/Irwin
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7-50
Investments of Unequal Lives: EAC
The Equivalent Annual Cost Method
• Applicable to a much more robust set of circumstances than
replacement chain or matching cycle.
• The Equivalent Annual Cost is the value of the level payment
annuity that has the same PV as our original set of cash
flows.
• NPV = EAC × ArT
• Where ArT is the present value of $1 per period for T periods
when the discount rate is r.
– For example, the EAC for the Cadillac air cleaner is
$750.98
– The EAC for the cheaper air cleaner is $763.80 which
confirms our earlier decision to reject it.
McGraw-Hill/Irwin
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7-51
Cadillac EAC with a Calculator
Use the cash flow menu to find the PV of the “lumpy” cash flows.
Then use the time value of money keys to find a payment with
that present value.
CF0
–4,000
CF1
N
10
–100
I/Y
10
F1
10
PV
–4,614.46
I
10
PMT
750.98
NPV
McGraw-Hill/Irwin
–4,614.46
FV
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
7-52
Cheapskate EAC with a Calculator
Use the cash flow menu to find the PV of the cash flows.
Then use the time value of money keys to find a payment with
that present value.
CF0
–1,000
CF1
N
10
–500
I/Y
10
F1
5
PV
–4,693.21
I
10
PMT
763.80
NPV
McGraw-Hill/Irwin
–4,693.21
FV
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
7-53
Example of Replacement Projects
Consider a Belgian Dentist’s office; he needs an autoclave to
sterilize his instruments. He has an old one that is in use, but
the maintenance costs are rising and so is considering
replacing this indispensable piece of equipment.
New Autoclave
– Cost = $3,000 today,
– Maintenance cost = $20 per year
– Resale value after 6 years = $1,200
– NPV of new autoclave (at r = 10%) is $2,409.74
6
$20
$1,200
 $2,409.74  $3,000  

t
(1.10) 6
t 1 (1.10)
EAC of new autoclave = -$553.29
 $553.29
 $2,409.74  
t
(
1
.
10
)
t

1
McGraw-Hill/Irwin
6
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7-54
Example of Replacement Projects
• Existing Autoclave
Year
0
Maintenance
0
Resale
900
Total Annual Cost
1
200
850
340
2
275
775
435
3
325
700
478
4
450
600
620
5
500
500
660
Total Cost for year 1 = (900 × 1.10 – 850) + 200 = $340
Total Cost for year 2 = (850 × 1.10 – 775) + 275 = $435
Total Cost for year 3 = (775 × 1.10 – 700) + 325 = $478
Total Cost for year 4 = (700 × 1.10 – 600) + 450 = $620
Total Cost for year 5 = (600 × 1.10 – 500) + 500 = $660
Note that the total cost of keeping an autoclave for the first year
includes the $200 maintenance cost as well as the opportunity cost of
the foregone future value of the $900 we didn’t get from selling it in
year 0 less the $850 we have if we still own it at year 1.
McGraw-Hill/Irwin
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7-55
Example of Replacement Projects
 New Autoclave

EAC of new autoclave = -$553.29
 Existing Autoclave
Year
0
1
2
3
Maintenance
0
200
275
325
Resale
900
850
775
700
Total Annual Cost
435
478
340
4
450
600
620
5
500
500
660
•We should keep the old autoclave until it’s cheaper to buy
a new one.
•Replace the autoclave after year 3: at that point the new
one will cost $553.29 for the next year’s autoclaving and
the old one will cost $620 for one more year.
McGraw-Hill/Irwin
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7-56
7.5 Summary and Conclusions
• Capital budgeting must be placed on an incremental basis.
– Sunk costs are ignored
– Opportunity costs and side effects matter
• Inflation must be handled consistently
– Discount real flows at real rates
– Discount nominal flows at nominal rates.
• When a firm must choose between two machines of unequal
lives:
– the firm can apply either the matching cycle approach
– or the equivalent annual cost approach.
McGraw-Hill/Irwin
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7-57
Dorm Beds Example
Consider a project to supply the University of
Missouri with 10,000 dormitory beds annually for
each of the next 3 years.
Your firm has half of the woodworking equipment to
get the project started; it was bought years ago for
$200,000: is fully depreciated and has a market
value of $60,000. The remaining $60,000 worth of
equipment will have to be purchased.
The engineering department estimates you will need
an initial net working capital investment of
$10,000.
McGraw-Hill/Irwin
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7-58
Dorm Beds Example
The project will last for 3 years. Annual fixed costs
will be $25,000 and variable costs should be $90
per bed.
The initial fixed investment will be depreciated
straight line to zero over 3 years. It also estimates
a (pre-tax) salvage value of $10,000 (for all of the
equipment).
The marketing department estimates that the selling
price will be $200 per bed.
You require an 8% return and face a marginal tax
rate of 34%.
Compute the NPV.
McGraw-Hill/Irwin
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