Chapter 6
Investment Decision Rules
Chapter Outline
6.1 NPV and Stand-Alone Projects
6.2 Alternative Decision Rules
6.3 Mutually Exclusive Investment Opportunities
6.4 Project Selection with Resource Constraints
2
Learning Objectives
1.
Define net present value, payback period, internal rate
of return, profitability index, and incremental IRR.
2.
Describe decision rules for each of the tools in
objective 1, for both stand-alone and mutually exclusive
projects.
3.
Given cash flows, compute the NPV, payback period,
internal rate of return, profitability index, and
incremental IRR for a given project.
4.
Compare each of the capital budgeting tools above,
and tell why NPV always gives the correct decision.
5.
Define Economic Value Added, and describe how it can
be used in capital budgeting.
3
6.1 NPV and Stand-Alone Projects

Consider a take-it-or-leave-it investment
decision involving a single, stand-alone
project for Fredrick Feed and Farm (FFF).

The project costs $250 million and is expected to
generate cash flows of $35 million per year,
starting at the end of the first year and lasting
forever.
4
NPV Rule

The NPV of the project is calculated as:
35
NPV   250 
r

The NPV is dependent on the discount rate.
5
Figure 6.1 NPV of FFF’s New Project

If FFF’s cost of capital is 10%, the NPV is $100 million and they should
undertake the investment.
6
Measuring Sensitivity with IRR

At 14%, the NPV is equal to 0, thus the
project’s IRR is 14%. For FFF, if their cost of
capital estimate is more than 14%, the NPV
will be negative, as illustrated on the previous
slide.
7
Alternative Rules Versus the NPV Rule

Sometimes alternative investment rules may
give the same answer as the NPV rule, but at
other times they may disagree.

When the rules conflict, the NPV decision rule
should be followed.
8
6.2 Alternative Decision Rules

The Payback Rule

The payback period is amount of time it takes to
recover or pay back the initial investment. If the
payback period is less than a pre-specified length
of time, you accept the project. Otherwise, you
reject the project.

The payback rule is used by many companies because
of its simplicity.

However, the payback rule does not always give a
reliable decision since it ignores the time value of money.
9
Example 6.1
10
Example 6.1 (cont'd)
11
Alternative Example 6.1

Problem

Projects A, B, and C each have an expected life
of 5 years.

Given the initial cost and annual cash flow
information below, what is the payback period
for each project?
Cost
Cash
Flow
A
$80
B
$120
C
$150
$25
$30
$35
12
Alternative Example 6.1

Solution

Payback A


Project B


$80 ÷ $25 = 3.2 years
$120 ÷ $30 = 4.0 years
Project C

$150 ÷ $35 = 4.29 years
13
The Internal Rate of Return

Internal Rate of Return (IRR) Investment
Rule

Take any investment where the IRR exceeds the
cost of capital. Turn down any investment whose
IRR is less than the cost of capital.
14
The Internal Rate of Return (cont'd)

The IRR Investment Rule will give the same
answer as the NPV rule in many, but not all,
situations.

In general, the IRR rule works for a standalone project if all of the project’s negative
cash flows precede its positive cash flows.

In Figure 6.1, whenever the cost of capital is
below the IRR of 14%, the project has a positive
NPV and you should undertake the investment.
15
The Internal Rate of Return (cont'd)

In other cases, the IRR rule may disagree
with the NPV rule and thus be incorrect.

Situations where the IRR rule and NPV rule may
be in conflict:

Delayed Investments

Nonexistent IRR

Multiple IRRs
16
The Internal Rate of Return (cont'd)

Delayed Investments

Assume you have just retired as the CEO of a
successful company. A major publisher has
offered you a book deal. The publisher will pay
you $1 million upfront if you agree to write a book
about your experiences. You estimate that it will
take three years to write the book. The time you
spend writing will cause you to give up speaking
engagements amounting to $500,000 per year.
You estimate your opportunity cost to be 10%.
17
The Internal Rate of Return (cont'd)

Delayed Investments

Should you accept the deal?


Calculate the IRR.
The IRR is greater than the cost capital. Thus, the
IRR rule indicates you should accept the deal.
18
Financial Calculator Solution
CF
1000000
ENTER
↓
-500000
ENTER
↓
3
ENTER
IRR
CPT
23.38
19
The Internal Rate of Return (cont'd)

Delayed Investments

Should you accept the deal?
NPV  1,000,000 

500, 000
500, 000
500, 000


  $243,426
2
3
1.1
1.1
1.1
Since the NPV is negative, the NPV rule indicates
you should reject the deal.
20
Figure 6.2
NPV of Star’s $1 million Book Deal

When the benefits of an investment occur before the costs, the NPV is an
increasing function of the discount rate.
21
The Internal Rate of Return (cont'd)

Nonexistent IRR

Assume now that you are offered $1 million per
year if you agree to go on a speaking tour for the
next three years. If you lecture, you will not be
able to write the book. Thus your net cash flows
would look like:
22
The Internal Rate of Return (cont'd)

Nonexistent IRR
500, 000
500, 000
500, 000
NPV 


2
1  r
(1  r )
(1  r )3

By setting the NPV equal to zero and solving for r,
we find the IRR. In this case, however, there is no
discount rate that will set the NPV equal to zero.
23
Figure 6.3 NPV of Lecture Contract

No IRR exists because the NPV is positive for all values of the discount
rate. Thus the IRR rule cannot be used.
24
The Internal Rate of Return (cont'd)

Multiple IRRs

Now assume the lecture deal fell through. You
inform the publisher that it needs to increase its
offer before you will accept it. The publisher then
agrees to make royalty payments of $20,000 per
year forever, starting once the book is published
in three years.

Should you accept or reject the new offer?
25
The Internal Rate of Return (cont'd)

Multiple IRRs

The cash flows would now look like:

The NPV is calculated as:
NPV  1,000, 000 
 1,000, 000 
500, 000
500, 000
50, 000
20, 000
20, 000





1  r
(1  r ) 2
(1  r )3
(1  r ) 4
(1  r )5

500, 000 
1
1
 20, 000 
1






r
(1  r )3 
(1  r )3  r 

26
The Internal Rate of Return (cont'd)

Multiple IRRs

By setting the NPV equal to zero and solving for r,
we find the IRR. In this case, there are two IRRs:
4.723% and 19.619%. Because there is more
than one IRR, the IRR rule cannot be applied.
27
Figure 6.4 NPV of Star’s Book Deal with
Royalties

If the opportunity cost of capital is either below 4.723% or above
19.619%, you should accept the deal.
28
The Internal Rate of Return (cont'd)

Multiple IRRs

Between 4.723% and 19.619%, the book deal has
a negative NPV. Since your opportunity cost of
capital is 10%, you should reject the deal.
29
The Internal Rate of Return (cont'd)

IRR Versus the IRR Rule

While the IRR rule has shortcomings for making
investment decisions, the IRR itself remains
useful. IRR measures the average return of the
investment and the sensitivity of the NPV to any
estimation error in the cost of capital.
30
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
31
Economic Profit or EVA (cont'd)

EVA and Economic Profit

Economic Value Added (EVA)

The cash flows of a project minus a charge for the
opportunity cost of capital
32
Economic Profit or EVA (cont'd)

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 in time period n, and r is the cost of capital. r × I is
known as the capital charge
33
Economic Profit or EVA (cont'd)

EVA When Invested Capital is Constant

EVA Investment Rule

Accept any investment in 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.
34
Example 6.2
35
Example 6.2 (cont'd)
36
Alternative Example 6.2

Problem

Ranger 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.
37
Alternative Example 6.2

Solution

Using Eq. 6.1, the 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%
38
Economic Profit or EVA (cont'd)

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 period n – 1, and r is the cost
of capital

When invested capital changes, the EVA rule and the
NPV rule coincide.
39
Example 6.3
40
Example 6.3
(cont'd)
41
6.3 Mutually Exclusive Investment Opportunities

Mutually Exclusive Projects

When you must choose only one project among
several possible projects, the choice is mutually
exclusive.

NPV Rule


Select the project with the highest NPV.
IRR Rule

Selecting the project with the highest IRR may lead
to mistakes.
42
Differences in Scale

If a project’s size is doubled, its NPV will
double. This is not the case with IRR. Thus,
the IRR rule cannot be used to compare
projects of different scales.
43
Differences in Scale (cont'd)

Identical Scale

Consider two projects:
Initial Investment
Cash FlowYear 1
Annual Growth Rate
Cost of Capital
Girlfriend’s
Business
$1,000
$1,100
-10%
12%
Laundromat
$1,000
$400
-20%
12%
44
Differences in Scale (cont'd)

Identical Scale

Girlfriend’s Business
NPV   1000 
1100
1100
  1000 
 $4000
r  0.1
0.12  0.1
1000 
1100
implies r  100%
r  0.1
45
Differences in Scale (cont'd)

Identical Scale

Laundromat
NPV   1000 


400
400
  1000 
 $250
r  0.2
0.12  0.2
IRR = 20%
Both the NPV rule and the IRR rule indicate the
girlfriend’s business is the better alternative.
46
Figure 6.5 NPV of Investment Opportunities

The NPV of the girlfriend’s business is always larger than the NPV of the
single machine laundromat. The IRR of the girlfriend’s business is 100%,
while the IRR for the laundromat is 20%.
47
Differences in Scale (cont'd)

Changes in Scale

What if the laundromat project was 20 times larger?
400


NPV  20  1000 
  $5000
0.12  0.2 


The NPV would be 20 times larger, but the IRR remains
the same at 20%.

Give an discount rate of 12%, the NPV rule indicates you
should choose the 20-machine laundromat (NPV = $5,000)
over the girlfriend’s business (NPV = $4,000).
48
Figure 6.6 NPV of Investment Opportunities
with the 20-Machine Laundromat

The NPV of the 20-machine laundromat is larger than the NPV of
the girlfriend’s business only for discount rates less than 13.9%.
49
Differences in Scale (cont'd)

Percentage Return Versus Impact on Value

The girlfriend’s business has an IRR of 100%,
while the 20-machine laundromat has an IRR of
20%, so why not choose the girlfriend’s business?

Because the 20-machine laundromat makes more
money

It has a higher NPV.
50
Differences in Scale (cont'd)

Percentage Return Versus Impact on Value

Would you prefer a 200% return on $1 dollar or a
10% return on $1 million?

The former investment makes only $2, while the latter
opportunity makes $100,000.

The IRR is a measure of the average return, but NPV is
a measure of the total dollar impact on value.
51
Timing of Cash Flows

Another problem with the IRR is that it can be
affected by changing the timing of the cash
flows, even when that change in timing does
not affect the NPV.


It is possible to alter the ranking of projects’ IRRs
without changing their ranking in terms of NPV.
Hence you cannot use the IRR to choose between
mutually exclusive investments.
52
Timing of Cash Flows (cont'd)

Assume you are offered a maintenance
contract on the laundromat machines which
would cost $250 per year per machine. With
this contract, you would not have to pay for
maintenance and so the cash flows from the
machines would not decline.

The expected cash flows would then be:
$400 – $250 = $150 per year per machine
53
Timing of Cash Flows (cont'd)

The time line would now be:
150 

NPV  20  1000 
  $5000
r 


The NPV of the project remains $5,000 but the
IRR falls to 15%.
54
Figure 6.7 NPV With and Without
the Maintenance Contract
55
Timing of Cash Flows (cont'd)

The NPV without the maintenance contract
exceeds the NPV with the contract for
discount rates that are greater than 12%.


The IRR without the maintenance contract (20%)
is larger than the IRR with the maintenance
contract (15%).
The correct decision is to agree to the
contract if the cost of capital is less than 12%
and to decline the contract if the cost of
capital exceeds 12%. With a 12% cost of
capital, you are indifferent.
56
The Incremental IRR Rule

Incremental IRR Investment Rule

Apply the IRR rule to the difference between the
cash flows of the two mutually exclusive
alternatives (the increment to the cash flows of
one investment over the other).
57
The Incremental IRR Rule (cont'd)

Incremental IRR Rule Application

The following timeline illustrates the incremental
cash flows of the maintenance contract
laundromat over the laundromat without the
contract.
58
The Incremental IRR Rule (cont'd)

Incremental IRR Rule Application
150
400
NPV 

r
r  0.2

Setting this equation equal to zero and solving for
r gives an IRR of 12%.

Applying the incremental IRR rule, you should take the
contract when the cost of capital is less than 12%.
Because your cost of capital is 12%, you are indifferent.
This finding concurs with the NPV rule.
59
The Incremental IRR Rule (cont'd)

Shortcomings of the Incremental IRR Rule

The fact that the IRR exceeds the cost of capital
for both projects does not imply that both projects
have a positive NPV.

The incremental IRR may not exist.

Multiple incremental IRRs could exist.

You must ensure that the incremental cash flows
are initially negative and then become positive.

The incremental IRR rule assumes that the
riskiness of the two projects is the same.
60
6.4 Project Selection with Resource
Constraints

Evaluation of Projects with Different
Resource Constraints

Consider three possible projects that require
warehouse space.
61
Profitability Index

The profitability index can be used to
identify the optimal combination of projects to
undertake.
Value Created
NPV
Profitability Index 

Resource Consumed
Resource Consumed

From Table 6.1, we can see it is better to take
projects B & C together and forego project A.
62
Example 6.4
63
Example 6.4 (cont'd)
64
Shortcomings of the Profitability Index

In some situations the profitability Index does
not give an accurate answer.

Suppose in Example 6.4 that NetIt has an
additional small project with a NPV of only
$100,000 that requires 3 engineers. The
profitability index in this case is
0.1 / 3 = 0.03, so this project would appear at the
bottom of the ranking. However, 3 of the 190
employees are not being used after the first four
projects are selected. As a result, it would make
sense to take on this project even though it would
be ranked last.
65
Shortcomings of the Profitability
Index (cont'd)

With multiple resource constraints, the
profitability index can break down completely.
66