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CHAPTER
7
Net Present Value
and Capital Budgeting
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Chapter Outline
Incremental Cash Flows
The Baldwin Company: An Example
The Boeing 777: A Real-World Example
Inflation and Capital Budgeting
Investments of Unequal Lives: The
Equivalent Annual Cost Method
Summary and Conclusions
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Incremental Cash Flows
Cash flows matter—not accounting earnings.
Sunk costs don’t matter.
Incremental cash flows matter.
Opportunity costs matter.
Side effects like synergy and erosion matter.
Taxes matter: we want incremental after-tax cash
flows.
Inflation matters.
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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.
3
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Incremental Cash Flows
Sunk costs
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.
4
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Incremental Cash Flows
Side effects matter.
Erosion ( If our new product causes existing
customers to demand less of current products,
we need to recognize that.)
Synergy
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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).
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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.
7
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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.
8
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The Worksheet for Cash Flows
of the Baldwin Company
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
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 0 (end of
year)
(6) Change in net – – –
working capital
(7) Total cash flow of – – –
investment
[(1) + (4) + (6)]
* 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 [ ($30,000 – $5,760)]. The after-tax salvage value is $30,000 – [ ($30,000 – $5,760)] = 21,760.
($ thousands) (All cash flows occur at the end of the year.)
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The Worksheet for Cash Flows of the Baldwin Company
($ thousands) (All cash flows occur at the end of the year.)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
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 0
(end of year)
(6) Change in net – – –
working capital
(7) Total cash flow of – – –
investment
[(1) + (4) + (6)]
150
At the end of the project, the warehouse is unencumbered, so we can sell it if we want to.
10
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The Worksheet for Cash Flows of the
Baldwin Company (continued)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Income:
(8) Sales Revenues
($ thousands) (All cash flows occur at the end of the year.)
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×[$20×()2] = 12,000×$ = $249,720.
11
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The Worksheet for Cash Flows of the Baldwin
Company (continued)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Income:
(8) Sales Revenues
(9) Operating costs
($ thousands) (All cash flows occur at the end of the year.)
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] = $88,000
12
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The Worksheet for Cash Flows of the Baldwin
Company (continued)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Income:
(8) Sales Revenues
(9) Operating costs
(10) Depreciation
($ thousands) (All cash flows occur at the end of the year.)
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) = $11,520.
Year ACRS %
1 %
2 %
3 %
4 %
5 %
6 %
Total %
13
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The Worksheet for Cash Flows of the
Baldwin Company (continued)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Income:
(8) Sales Revenues
(9) Operating costs
(10) Depreciation
(11) Income before taxes
[(8) – (9) - (10)]
(12) Tax at 34 percent
(13) Net Income
($ thousands) (All cash flows occur at the end of the year.)
14
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Incremental After Tax Cash Flows
of the Baldwin Company
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
(1) Sales
Revenues
$ $ $ $ $
(2) Operating
costs
(3) Taxes
(4) OCF
(1) – (2) – (3)
(5) Total CF of
Investment
–260. – –
(6) IATCF
[(4) + (5)]
–260.
,51$
)(
$
)(
$
)(
$
)(
$
)(
$
260$ 5432
=
+++++-=
NPV
NPV
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NPV Baldwin Company
1
51,
–260
CF1
F1
CF0
I
NPV
10
1
F2
1
F3
1
F4
1
F5
16
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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 . 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.
17
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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.
18
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Example of Capital Budgeting under Inflation
The riskless nominal discount rate is 4%.
The real discount rate for costs and revenues is 8%.
Calculate the NPV.
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
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CF0
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
Annual depreciation expense:
Depreciation tax shield = $8,000,000 × .34 = $2,720,000
4
2,720,000
0
CF1
F1 9,873,315
I
NPV
4
$8,000,000 = $32,000,000
4 years
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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 – .34) = $20,196,000
After-tax energy costs =
$5 × 2,00,000 × × (1 – .34) = $679,800
After-tax net operating CF =
$26,400,000 – $20,196,000 – $679,800 = $5,524,200
21
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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 × ()2 × (1 – .34) = $20,599,920
After-tax energy costs =
$5 × 2,00,000 × ()2 × (1 – .34) = $700,194
After-tax net operating CF =
$26,400,000 – $ 20,599,920– $ 700,194 = $ 31,499,886
22
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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 × ()3 × (1 – .34) = $21,
After-tax energy costs =
$5 × 2,00,000 × ()3 × (1 – .34) = $721,
After-tax net operating CF =
$26,400,000 – $ 21,– $ 721, = $31,066,882
23
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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 × ()4 × (1 – .34) = $21,
After-tax energy costs =
$5 × 2,00,000 × ()4 × (1 – .34) = $742,
After-tax net operating CF =
$26,400,000 – $21,– $742, = $17,425,007
24
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Example of Capital Budgeting under Inflation
$5,524,200 $31,499,886 $31,066,882 $17,425,007
-$32,000,000
0 1 2 3 4
1
5,524,000
–32 m
CF1
F1
CF0
1
31,499,886CF2
F2
1
31,066,882CF3
F3
1
17,425,007CF4
F4
69,590,868I NPV8
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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
26
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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.
27
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Table Incremental Cash Flows: Boeing 777
Year Units
Sales
Revenue
Operating
Costs Dep. Taxes DNWC
Capital
Spending
Invest-
ment
Net Cash
Flow
1991 $ $ $() $ $ $()
1992 1, () (1,)
1993 1, () (1,)
1994 () ()
1995 14 $1, 1, () ()
1996 145 19, 17, 1, 1,
1997 140 19, 16, () 1,
Net Cash Flow can be determined in three steps:
Taxes ($19, – $16, – $)× = $
Investment –$ + $ = $
NCF $19, – $16, – $ – $ = $1,
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1991 $ () 2002 $ 1, 2013 $ 2,
1992 $ (1,) 2003 $ 1, 2014 $ 2,
1993 $ (1,) 2004 $ 1, 2015 $ 2,
1994 $ () 2005 $ 2016 $ 2,
1995 $ () 2006 $ 1, 2017 $ 2,
1996 $ 2007 $ 2, 2018 $ 2,
1997 $ 1, 2008 $ 1, 2019 $ 2,
1998 $ 1, 2009 $ 2020 $ 2,
1999 $ 1, 2010 $ 1, 2021 $ 2,
2000 $ 1, 2011 $ 2, 2022 $ 2,
2001 $ 1, 2012 $ 2, 2023 $ 2,
2024 $ 2,
Year Year Year NCFNCFNCF
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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
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NPV Profile of the Boeing 777 Project
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.
IRR = %
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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.
32
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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?
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EAC with a Calculator
At first glance, the Cheapskate cleaner has a lower NPV
10
–100
–4,
–4,000
CF1
F1
CF0
I
NPV
10
5
–500
–2,
–1,000
CF1
F1
CF0
I
NPV
10
Cadillac Air Cleaner Cheapskate Air Cleaner
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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.
35
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The Cadillac cleaner time line of cash flows:
Investments of Unequal Lives: The
Equivalent Annual Cost Method
-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100
0 1 2 3 4 5 6 7 8 9 10
-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500
0 1 2 3 4 5 6 7 8 9 10
The Cheapskate cleaner time line of cash flows over ten years:
36
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The Equivalent Annual Cost Method
When we make a fair comparison, the Cadillac is cheaper:
10
–100
–4,
–4,000
CF1
F1
CF0
I
NPV
10
4
–500
–4,693
–1,000
CF1
F1
CF0
I
NPV
10
Cadillac Air Cleaner Cheapskate Air Cleaner
1
–1,500CF2
F1
5
–500CF3
F1
37
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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
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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 $
The EAC for the cheaper air cleaner is $ which confirms
our earlier decision to reject it.
39
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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.
10
–100
–4,
–4,000
CF1
F1
CF0
I
NPV
10
10
–4,
10
PMT
I/Y
FV
PV
N
PV
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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.
5
–500
–4,
–1,000
CF1
F1
CF0
I
NPV
10
10
–4,
10
PMT
I/Y
FV
PV
N
PV
41
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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 $2,
EAC of new autoclave = -$
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Example of Replacement Projects
Existing Autoclave
Year 0 1 2 3 4 5
Maintenance 0 200 275 325 450 500
Resale 900 850 775 700 600 500
Total Annual Cost
Total Cost for year 1 = (900 × – 850) + 200 = $340
340 435
Total Cost for year 2 = (850 × – 775) + 275 = $435
478
Total Cost for year 3 = (775 × – 700) + 325 = $478
620
Total Cost for year 4 = (700 × – 600) + 450 = $620
Total Cost for year 5 = (600 × – 500) + 500 = $660
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 $850 we have if we still own it at year 1.
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· New Autoclave
¨ EAC of new autoclave = -$
· Existing Autoclave
Year 0 1 2 3 4 5
Maintenance 0 200 275 325 450 500
Resale 900 850 775 700 600 500
Total Annual Cost
Example of Replacement Projects
340 435 478 620 660
•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 $ for the next year’s autoclaving and
the old one will cost $620 for one more year.
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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.
45
