Capital Budgeting
FIN 461: Financial Cases & Modeling
George W. Gallinger
Associate Professor of Finance
W. P. Carey School of Business
Arizona State University
Typical Capital Budgeting
System
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Calculating Accounting Rate
of Return
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Calculating Payback Period
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Calculating Discounted
Payback Period
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Calculating NPV
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Calculating NPV…
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Use Nominal or Real WACC?

Nominal return reflects the actual dollar return; real return
measures the increase in purchasing power gained by holding a
certain investment
(1  nominal rate)  (1  inflation rate)  (1  real rate),
 1  nom 
or, real rate  
 1
 1  inf 

Common in capital budgeting is the use of market rates of return
at the time of the analysis


Market interest rates have embedded an assumption about inflation
Use nominal cash flows to reflect the same inflation rate as that
embedded in discount rate.
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Risk-Return Tradeoff for
Projects

Projects plotting above the
security market line (SML)
have rates of return in
excess of their required
market rates


Projects plotting below the
SML have rates of return
less than their required
market rates


Positive NPVs
Negative NPVs
Projects plotting on the
SML earn their market rates

Zero NPVs.
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Calculating IRR
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Illustration for Calculating
IRR
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IRR & Required RiskAdjusted Rate

Appropriate rates for
comparing project returns
are those falling on the
upward sloping market riskreturn trade-off curve


Not the firm’s horizontal
cost of capital line, WACC
WACC is only appropriate
for evaluating projects with
risk comparable to the level
of risk of the firm

“Carbon copy” projects.
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Size Problem
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Cash Flow Pattern Problems
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Multiple IRR Solutions
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Undervaluation of Later
Cash Flows
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Calculating the Profitability
Index
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Comparison of Project
Rankings

Project B is better than
project A


Project D is more
desirable than project C


Project B continues to
earn cash flows longer
Although both projects
generate the same
amount of cash flows,
project D does it
earlier
Unanswered question:

Is Project D better
than project B?
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Sunk Costs
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Salvage Value Comparisons
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Calculating Initial
Investment
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Calculating Annual
Operating Cash Flows
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Alternatively, Calculating
Annual Operating Cash Flows…
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Calculating Terminal Cash
Flows
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Salvage Value: Present vs.
Future
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Another Topic:
Competing Projects

Assume projects




Mutually exclusive
On-going
Different economic lives
How do you select the correct project?
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Example


There are times when application of the NPV rule
can lead to the wrong decision
Consider a factory which must have an air cleaner


There are two choices:



The equipment is mandated by law, so there is no “doing
without”
The “Cadillac cleaner” costs $4,000 today, has annual
operating costs of $100 and lasts for 10 years
The “cheaper 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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Example …

At first glance, the cheap cleaner has the “better”
NPV (r = 10%):
10
$100
NPVCadillac  $4,000  
 4,614.46
t
t 1 (1.10)
5
NPVcheap
$500
 $1,000  
 2,895.39
t
t 1 (1.10)
 Overlooks the fact that the Cadillac cleaner lasts twice as
long
 When we incorporate project life, the Cadillac cleaner is
actually cheaper.
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Example …

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
10
NPVCadillac  $4,000  
t 1

6
7
8
9
10
$100
 4,614.46
t
(1.10)
The “cheaper cleaner” time line of cash flows over ten years:
-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500
0
1
2
3
4
5
6
7
8
9
10
5
NPVcheap
$500 $1,000 10 $500
 $1,000  


 $4,693.20
t
5
t
(1.10) t 6 (1.10)
t 1 (1.10)
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Investments of Unequal Lives

Replacement Chain



Matching Cycle



Repeat the projects forever, find the PV of that perpetuity
Assumption: Both projects can and will be repeated
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 Annuity (EAA) Method.
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Equivalent Annual Cost
Method

Equivalent Annual Annuity Method



Provides the value of the level payment annuity that has the
same PV as the original set of cash flows
NPV = EAA × ArT
For example, the EAA for the Cadillac air cleaner is $750.98
10
 $4,000 
 (1.10)
10
$100
t 1
t
 4,614 .46 
 (1.10)
t 1
$750 .98
t
Annuity Table
10%, 10 years
= 6.1446
The EAA for the cheaper air cleaner is $763.80,
which confirms our earlier decision to reject it.
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Another Example:
Calculating EAA
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Human Face of Capital
Budgeting

NPV of a project  based on assumptions


Companies need control measures to remove bias



Managers must be aware of optimistic bias in these
assumptions made by supporters of the project
Analysis done by a group independent of individual or group
proposing the project
Analysts must have a sense of what is reasonable when
forecasting a project’s profit margin and its growth potential
Another side of determining which projects receive
funding – storytelling

Best analysts not only provide numbers to highlight a good
investment, but also can explain why this investment makes
sense.
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The End
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