Capital Budgeting Decision Rules
What real investments should
firms make?
Alternative Rules in Use Today

NPV
IRR
Profitability Index

Payback Period
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Discounted Payback Period
Accounting Rate of Return
What Provides Good Decision-Making?

Our work has shown that several criteria
must be satisfied by any good decision rule:
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The decision rule must be based on cash flow.
The rule should incorporate all the incremental
cash flows attributable to the project.
The rule should discount cash flows appropriately
taking into account the time value of money
and properly adjusting for the risk inherent in the
project. - Opportunity cost of capital.
When forced to choose between projects, the
choice should be governed by maximizing
shareholder wealth given any relevant constraints.
NPV Analysis

The recommended approach to any
significant capital budgeting decision is NPV
analysis.


NPV = PV of the incremental benefits – PV of
the incremental costs.
NPV based decision rule:
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
When evaluating independent projects, take those
with positive NPVs, reject those with negative
NPVs.
When evaluating interdependent projects, take the
feasible combination with the highest combined
NPV.
Lockheed Tri-Star



As an example of the use of NPV analysis we
will use the Lockheed Tri-Star case.
To examine the decision to invest in the TriStar project, we first need to forecast the
cash flows associated with the Tri-Star project
for a volume of 210 planes.
Then we can ask: What is a valid estimate of
the NPV of the Tri-Star project at a volume of
210 planes as of 1967.
Internal Rate of Return

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Definition: The discount rate that sets the NPV of a
project to zero (essentially project YTM) is the
project’s IRR.
 IRR asks: “What is the project’s rate of return?”
Standard Rule: Accept a project if its IRR is greater
than the appropriate market based discount rate,
reject if it is less. Why does this make sense?
For independent projects with “normal cash flow
patterns” IRR and NPV give the same conclusions.
IRR is completely internal to the project. To use the
rule effectively we compare the IRR to a market rate.
IRR – “Normal” Cash Flow Pattern

Consider the following stream of cash flows:
0
-$1,000


1
$400
2
$400
3
$400
Calculate the NPV at different discount rates
until you find the discount rate where the
NPV of this set of cash flows equals zero.
That’s all you do to find IRR.
IRR – NPV Profile Diagram

Evaluate the NPV at various discount rates:
Rate
0
10
20

NPV
$200
-$5.3
-$157.4
At r = 9.7%,
NPV = 0
250
200
150
100
NPV 50
0
-50 0
-100
-150
-200
10
20
Discount Rate
The Merit to the IRR Approach

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The IRR can be interpreted as the answer to the
following question. Suppose that the initial
investment is placed in a bank account instead of this
project. What interest rate must the bank account
pay in order that we may make withdrawals equal to
the cash flows generated by the project?
As with NPV, the IRR is also based on incremental
cash flows, does not ignore any cash flows, and (by
comparison to the appropriate discount rate, r)
accounts for the time value of money and risk (the
opportunity cost of capital).
In short, it can be useful.
Pitfalls of the IRR Approach

Multiple IRRs


There can be as many solutions to the IRR
definition as there are changes of sign in the time
ordered cash flow series.
Consider:
0
1
2
-$100

$230
-$132
This can (and does) have two IRRs.
Pitfalls of IRR cont…
Disc.Rate 0.00% 10.00% 15.00% 20.00% 40.00%
NPV
-$2.00 $0.00 $0.19 $0.00 -$3.06
IRR1
IRR2
0.5
0
NPV
-0.5 0
10
15
-1
-1.5
-2
-2.5
-3
Discount Rate
20
40
Pitfalls of IRR cont…
3
2.5
NPV
2
1.5
1
0.5
0
-0.5 0
10
15
Discount Rate
20
40
Pitfalls of IRR cont…
Mutually exclusive projects:
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IRR can lead to incorrect conclusions
about the relative worth of projects.
Ralph owns a warehouse he wants to fix
up and use for one of two purposes:
A.
B.
Store toxic waste.
Store fresh produce.
Let’s look at the cash flows, IRRs and NPVs.
Mutually Exclusive Projects and IRR
Project
A
B
Year 0 Year 1 Year 2 Year 3
-10,000 10,000 1,000
1,000
-10,000 1,000
1,000
12,000
Project
NPV @
0%
$2000
$4000
A
B
NPV @ NPV@
10%
15%
$669
$109
$751
-$484
IRR
16.04%
12.94%
5000
A
B
4000
NPV
3000
2000
1000
0
-1000
0%
10%
15%
Discount Rate
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At low discount rates, B is better. At high discount rates,
project A is a better choice.
But A always has the higher IRR. A common mistake to
make is choose A regardless of the discount rate.
Simply choosing the project with the larger IRR would be
justified only if the project cash flows could be reinvested
at the IRR instead of the actual market rate, r, for the life
of the project.
Summary of IRR vs. NPV

IRR analysis can be misleading if you don’t fully
understand its limitations.
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For individual projects with a normal cash flow pattern NPV
and IRR provide the same conclusion.
For projects with inflows followed by outlays, the decision
rule for IRR must be reversed.
For Multi-period projects with several changes in sign of the
cash flows multiple IRRs exist. Must compute the NPVs to
see what is appropriate decision rule.
IRR can give conflicting signals relative to NPV when ranking
projects.
I recommend NPV analysis, using others as backup.
Profitability Index


Definition: The present value of the cash
flows that accrue after the initial outlay
divided by the initial cash outlay.
Rule: Take any/only projects with a PI>1.

The PI does a benefit/cost (bang for the buck)
analysis. When the PV of the future benefits is
larger than the current cost PI > 1. If this is true
what is true of the NPV? Thus for independent
projects the rules make exactly the same decision.
N
PI 
t
CF
/(
1

r
)
 t
t 1
CF0
PI and Mutually Exclusive
Projects
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Example:
Project
CF0
CF1
NPV @ 10%
PI
A
-$1,000 $1,500
$364
1.36
B
-$10,000 $13,000
$1,818
1.18
 Since you can only take one and not both the NPV rule says
B, the PI rule would suggest A. Which is right?

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The projects are mutually exclusive so the NPV of
one is an opportunity cost to the other. We must
take B; in this respect A has a negative NPV.
PI treats scale strangely. It measures the bang per
buck invested. This is larger for A but since we
invest more in B it will create more wealth for us.
Payback Period Rule
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Frequently used as a check on NPV analysis
or by small firms or for small decisions.
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Payback period is defined as the number of years
before the cumulative cash inflows equal the initial
outlay.
Provides a rough idea of how long invested capital
is at risk.
Example: A project has the following cash flows
Year 0 Year 1 Year 2 Year 3 Year 4
-$10,000 $5,000 $3,000 $2,000 $1,000
The payback period is 3 years. Is that good or
bad?
Payback Period Rule
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An adjustment to the payback period rule that is
sometimes made is to discount the cash flows and
calculate the discounted payback period.
This “new” rule continues to suffer from the problem
of ignoring cash flows received after an arbitrary
cutoff date.
If this is true, why mess up the simplicity of the rule?
Simplicity is its only virtue.
At times the payback or discounted payback period
may be valuable information but it is not often that
this information alone makes for good decisionmaking.
Average Accounting Return
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Definition: The average net income
after depreciation and taxes (before
interest) divided by the average book
value of the investment.
Rule: If the AAR is above some cutoff
take the project.
This is essentially a measure of return
on assets (ROA).
AAR
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Issues
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Doesn’t use cash flows but rather
accounting numbers.
Ignores the time value of money.
Does not adjust for risk.
Uses an arbitrarily specified cutoff rate.
Other than that it’s a beautiful decisionmaking tool.
Applying the NPV Method
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While other approaches
(particularly IRR) can be of use, I
recommend NPV.
The three steps to apply NPV:
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Estimate the incremental cash flows (today).
Select the appropriate discount rate to
reflect current capital market conditions and
risk.
Compute the present value of the cash
flows.
For now, we will continue to assume that
firms are all equity financed. To be
continued…
Our Golden Rules
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Cash flows are the concern.
Consider only incremental cash flows.
Don’t forget induced changes in NWC.
Don’t ignore opportunity costs.
Never, never, never neglect taxes.
Don’t include financing costs in cash flow.
Treat inflation consistently.
Recognize project interactions.
Incremental Cash Flow
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The incremental cash flow is the company’s
total free cash flow with the proposed project
minus the company’s total cash flow without
the project.
Some issues that arise:
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Sunk costs. These are costs, related to the
project, that have already been incurred.
Opportunity costs. What else could be done?
Capital expenditures versus depreciation expense.
Side effects. Does the new project affect other
cash flows of the firm?
Taxes.
Increased investment in working capital.
Sunk Costs vs. Opportunity
Costs
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Last year, you purchased a plot of land
for $2.5 million.
Currently, its market value is $2.0
million.
You are considering placing a new retail
outlet on this land. How should the land
cost be evaluated for purposes of
projecting the cash flows that will
become part of the NPV analysis?
Side Effects

A further difficulty in determining cash
flows from a project comes from effects
the proposed project may have on other
parts of the firm. The most important side
effect is called erosion. This is cash flow
transferred from existing operations to the
project.
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Chrysler’s introduction of the minivan.
What if a competitor would introduce the new
product if your company does not?
Taxes
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Typically,
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Revenues are taxable when accrued.
Expenses are deductible when accrued.
Capital expenditures are not deductible, but
 depreciation can be deducted as it is accrued,
 tax depreciation can differ from that reported
on financial statements.
Sale of an asset for a price other than its tax basis
(original price less accumulated tax depreciation)
leads to a capital gain/loss with tax implications.
Working Capital

Increases in Net Working Capital should
typically be viewed as requiring a net
cash outflow.

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increases in inventory and/or the cash
balance* require actual uses of cash.
increases in receivables mean that accrued
revenues exceed actual cash collections.
 If you are basing your measure of cash
flow on accrued revenues you need a
correcting adjustment.
 If you are basing your measure of cash
flow on cash revenues no adjustment is
required.