### Chapter 6: Net present value and other investment rules

```Chapter 5: Net present value and
other investment rules
Corporate Finance
Ross, Westerfield, and
Jaffe
Outline
1. Net present value (NPV)
2. The payback period method
3. The discounted payback period method
4. The Internal rate of return (IRR)
5. The profitability index
Good decision criteria



Does the rule take the time value of money
into consideration?
Does the rule adjust for risk?
Does the rule tell us whether and by how
much the project add value to the firm?
A proposed project






Your company is looking at a new project
that has the following cash flows.
Year 0: initial cost, C0 = \$100,000.
Year 1: CF1 = \$30,000.
Year 2: CF2 = \$50,000.
Year 3: CF3 = \$60,000.
The applicable discount rate is 10%.
1st method: the NPV rule


NPV = PV – C0: the difference between the
present value of the investment’s future net
cash flows, i.e., benefits, and its initial cost.
Ideas: (1) an investment is worth undertaking
if it creates value for its owners, and (2) an
investment creates value if it worth more than
it costs within the time value of money
framework (Chapter 4).
Decision rule




If NPV > = 0, accept the project.
If NPV < 0, reject the project.
A positive NPV suggests that the project is expected
to add value to the firm, and the project should
improve shareholders’ wealth.
Because the goal of financial management is to
increase shareholders’ wealth, NPV is a good
measure of how well this project will meet this goal.
Project NPV
Year
0
1
2
3
CF
30000
50000
60000
Discount rate
0.1
C(0)
100000
PV
NPV
13674
27272.7
>0
41322.3 Accept!
45078.9
113674
Judging the NPV rule



Does the NPV rule take the time value of
money into consideration?
Does the NPV rule adjust for risk?
Does the NPV rule tell us whether and by
how much the project add value to the firm?
Finally, they listen


CFOs are using what academics consider better
measures in their capital-budgeting analysis.
According to a recent survey, more than 85 percent
say they use net present value (NPV) analysis in at
least three out of four decisions…."Finance
textbooks have taught for years that NPV is superior,
but this is the first known survey to show it's the
preferred tool," says co-author Patricia A. Ryan, a
professor of corporate finance at Colorado State
University.
Source: CFO.com.
2nd method: payback period

Payback period: the amount of time required
for an investment to generate after-tax cash
flows sufficient to recover its initial cost.
Decision rule


An investment is accepted (rejected), if
payback period < (>) some specified number
of time period.
The cutoff is arbitrarily chosen by the
manager or the entrepreneur.
Project payback period
Year
CF
C(0)
0
100000
1
30000
2
50000
3
60000
Accu. CF
\$ to be recoved
Payback period
30000
80000
140000
70000
20000
-40000
>2
<3
To be exact,
2+(20000/60000)
2.33 years
The decision



The payback period is longer than 2 years
and shorter than 3 years.
If the cutoff is 2 years, we’d reject the project.
If the cutoff is 3 years, we’d accept the
project.
Judging the payback period rule



Does the payback period rule take the time
value of money into consideration?
Does the payback period rule adjust for risk?
Does the payback period rule tell us whether
and by how much the project add value to
the firm?

–

Easy to understand and communicate.
–
–
–
–
–
Ignores the time value of money.
Fail to consider the riskness of the project, no i.
Requires an arbitrary cutoff point.
Ignores cash flows beyond the cutoff.
Biased against long-term projects, such as R&Ds.
3rd method: discounted payback period

Discounted payback period: the length of
time required for an investment’s discounted
cash flows to equal its initial cost.
Decision rule


An investment is accepted (rejected), if
discounted payback period < (>) some
specified number of time period.
Again, the cutoff is arbitrarily chosen.
Project discounted payback period
Year
0
1
2
3
CF
30000
50000
60000
Discount rate
0.1
C(0)
100000
PV
Accu. PV
27272.7 27272.727
41322.3 68595.041
45078.9 113673.93
To be recovered
Dis. Payback
72727.27273
31404.95868
-13673.92938
>2
<3
2+ (31404/45079)
2.70 years
The decision



The discounted payback period is longer
than 2 years and shorter than 3 years.
If the cutoff is 2 years, we’d reject the project.
If the cutoff is 3 years, we’d accept the
project.
Judging discounted payback period



Does the payback period rule take the time
value of money into consideration?
Does the payback period rule adjust for risk?
Does the payback period rule tell us whether
and by how much the project add value to
the firm?

–
–

Still fairly easy to understand and communicate.
Take TVM into consideration.
–
–
–
Requires an arbitrary cutoff point.
Ignores cash flows beyond the cutoff.
Biased against long-term projects, such as R&Ds.
4th method: IRR

IRR: the discounted rate that makes the NPV
of an investment zero.
Decision rule

An investment is accepted (rejected), if the
IRR > (<) the required rate.
Project IRR
Year
0
1
2
3
CF
C(0)
IRR-CF
100000 -100000
30000
30000
50000
50000
60000
60000
IRR
17%
PV
25686
36654
37660
100000
The decision

The computed IRR is 17%, which is higher
than the 10% required rate. Thus, we accept
the project.
Judging the IRR



Does the IRR rule take the time value of
money into consideration?
Does the IRR rule adjust for risk?
Does the IRR rule tell us whether and by how
much the project add value to the firm?
NPV vs. IRR



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For most projects, NPV and IRR lead to the same
conclusion.
Practitioners really like to use IRR because this
measure gives practitioners a good idea about at
what rate they are able to earn. Knowing a return is
intuitively appealing.
IRR provides a measure about the value of a project
to someone who doesn’t know all the estimation
details.
If the IRR is high enough, one may not need to
estimate the required return at all.
A warning


Typical IRR calculations build in
reinvestment assumptions.
This makes projects look better than they
actually are.
But, non-unique IRR solutions
Year Costs
0
100
1
2
132
CF
230
IRR-CF
-100
230
-132
IRR
10%
20%
NPV
-100
191.67
-91.67
0
Lesson


Before you use your IRR estimate, always
verify the result with the NPV result.
In real life, NPV and IRR are the 2 most
popular decision rules used by modern (big)
U.S. corporations. And, they tend to be used
together.
5th method: the profitability index

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Profitability index (PI) = PV / C0.
Often used for government or other non-forprofit investments.
Measures the benefit per unit cost, based on
the time value of money.
A profitability index of 1.2 suggests that for
every \$1 of initial investment, we create an
Decision rule



For a project, we accept the project only if PI
> 1.
For mutually exclusive projects, practitioners
sometimes choose the project with the
highest PI. However, this approach is
problematic.
If there is no capital constraint, one should
choose the project with the highest NPV from
the mutually exclusive pool.
Project PI
Year
0
1
2
3
CF
30000
50000
60000
Discount rate
0.1
C(0)
100000
PV
PI
1.1367
27272.73
>1
41322.31 Accept!
45078.89
113673.9

–
–
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Related to NPV, generally leading to identical
decisions.
Easy to understand and communicate.
–
Should not be used for making mutually exclusive
decisions.
Real options


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So far, you know that NPV is the best
criterion; IRR is another almost equally good
and important one.
independent projects whose acceptance or
rejection has no implications on the
acceptance or rejection of other projects.
When projects have (real) options, NPV and
IRR may perform poorly.
An example: timing option


Suppose that the NPV for a developer to built a
building on a vacant land now is positive. The
simple version of the NPV rule would lead to the
conclusion that the developer should build the
building now.
In real life, the developer may choose to wait. For
instance, the developer may believe that this is not
the best timing (although the NPV is positive). The
developer may want to wait for another few years
when the real estate market is stronger to realize a
much larger NPV at that time.
More real options

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
In real life, there are several more types of
real options that will make capital budgeting
Chapter 7, pp. 221-224 has an introduction
to another two types of real options: (1) the
option to expand, and (2) the option to
abandon.
I bet these will be treated in your
intermediate corporate finance course.
Assignment



The ABC Co. is considering expanding its production capacity
by 30%. The expansion will require \$20 million initially. The
net cash flow from this expansion is \$4 million for the first year.
The net cash flows are expected to grow at a rate of 5% each
year for 4 years, but then slow to a 3% growth thereafter. The
ABC Co. estimates that the cost of capital (i.e., required return)
for this expansion is 8%.