Capital Budgeting Decision Rules
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.
When evaluating independent projects, take a
project if and only if it has a positive NPV.
When evaluating interdependent projects, take the
feasible combination with the highest total NPV.
The NPV rule appropriately accounts for the
opportunity cost of capital and so ensures the
project is more valuable than comparable
alternatives available in the financial market.
Internal Rate of Return




Definition: The discount rate that sets the NPV of a
project to zero is the project’s IRR.
 Conceptually, 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 NPV
0
$200
10
-$5.3
20
-$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



The IRR is an approximation for the return
generated over the life of a project on the
initial investment.
As with NPV, the IRR is based on incremental
cash flows, does not ignore any cash flows,
and (by comparison to the appropriate
discount rate, r) take proper account of the
time value of money and risk.
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%
-$2.00 $0.00 $0.19 $0.00 -$3.06
NPV
IRR2
IRR1
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:



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
• At low discount rates, B is better. At high discount
rates, A is better.
• 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.
Project Scale and the IRR


Because the IRR puts things in terms of
a “rate” it may not tell you what
interests you; which investment will
create the most “wealth”.
Example:
Project Investment
Time 1
IRR
NPV at 10%
A
-$1,000
+$1,500
50%
$363.64
B
-$10,000
+$13,000
30%
$1,1818.18
Summary of IRR vs. NPV

IRR analysis can be misleading if you don’t fully
understand its limitations.





For individual projects with normal cash flows 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 changes in sign of the cash
flows, multiple IRRs exist. Must compute the NPVs to see
what decision rule is appropriate.
IRR can give conflicting signals relative to NPV when ranking
projects.
I recommend NPV analysis, using others as backup.
Payback Period Rule

Frequently used as a check on NPV analysis or
by small firms or for small decisions.




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




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 one virtue.
At times the discounted payback period may be
valuable information but it is not often that this
information alone makes for good decision-making.
Economic Profit or EVA

EVA and Economic Profit

Economic Profit


The difference between revenue and the
opportunity cost of all resources consumed in
producing that revenue, including the opportunity
cost of capital
Economic Value Added (EVA)

The cash flows of a project minus a charge for the
opportunity cost of capital
Economic Profit or EVA

EVA When Invested Capital is Constant

EVA in Period n (when capital lasts forever)
EVAn  Cn  rI

where I is the project’s capital, Cn is the
project’s cash flow at time n, and r is the cost
of capital. (r × I ) is known as the capital
charge
Economic Profit or EVA

EVA When Invested Capital is Constant

EVA Investment Rule


Accept any investment for which the present
value (at the project’s cost of capital) of all
future EVAs is positive.
When invested capital is constant, the EVA rule
and the NPV rule will coincide.
Example

Problem




Ralph has an investment opportunity which
requires an upfront investment of $150 million.
The annual end-of-year cash flows of $14 million
dollars are expected to last forever.
The firm’s cost of capital is 8%.
Compute the annual EVA and the present
value of the project.
Example

Solution

EVA each year is:
EVAn  Cn  rI
EVAn  $14 million  8%  $150 million  $2 million

The present value of the EVA perpetuity is:
$2 million
PV 
 $25 million
8%
Economic Profit or EVA

EVA When Invested Capital Changes

EVA in Period n (when capital depreciates)
EVAn  Cn  rI n  1  (Depreciation in Period n)


Where Cn is a project’s cash flow in time period
n, In – 1 is the project’s capital at time n – 1,
and r is the cost of capital
When invested capital changes, the EVA rule
and the NPV rule continue to coincide.
Example




Ralph is considering an investment in a
machine to manufacture rubber chickens.
It will generate revenues of $20,000
each year for 4 years and cost $60,000.
The machine is expected to depreciate
evenly over the 4 years.
The current interest rate is 5%
Should he invest in the machine?
Example

Using the NPV rule we have a cost of
$60,000 and benefits that look like a 4
year annuity. The NPV is
$20,000 
1 
1 
  $10,919.01
NPV  $60,000 
4 
0.05  (1.05) 

Indicating that this is a valuable
endeavor.
Example

For EVA we calculate
Year
0
1
2
3
4
Capital
$60,000
$45,000
$30,000
$15,000
$0
Cash Flow
$20,000
$20,000
$20,000
$20,000
Capital Charge
($3,000)
($2,250)
($1,500)
($750)
Depreciation
($15,000) ($15,000) ($15,000) ($15,000)
EVAn
$2,000

$2,750
$3,500
$4,250
The present value of EVA is then:
$2,000 $2,750 $3,500 $4,250
PV ( EVA) 



 $10,919.01
2
3
4
1.05
1.05
1.05
1.05