BUSINESS Financial
Management
RUTGERS SCHOOL
Lecture 22 NPV, IRR, and
Other Investment Criteria
Lecture Sources
Lectures are compiled using the slides provided
by McGraw-Hill for courses based on:
Ross, Westerfield, Jordan. Fundamentals of Corporate Finance
Chapter 9
Additional material, compilation, and
presentation layout is provided by the lecturer.
Outline
Net
Present Value
The Payback Rule
The Discounted Payback
The Average Accounting Return
The Internal Rate of Return
The Profitability Index
The
Practice of Capital Budgeting
Good Decision Criteria
We need to ask ourselves the following
questions when evaluating capital
budgeting decision rules:
Does the decision rule adjust for the time
value of money?
Does the decision rule adjust for risk?
Does the decision rule provide information on
whether we are creating value for the firm?
Internal Rate of Return
This
NPV
is the most important alternative to
It
is often used in practice and is intuitively
appealing
It
is based entirely on the estimated cash
flows and is independent of interest rates
found elsewhere
IRR Definition and Decision Rule
Definition:
IRR is the return that makes the NPV = 0
[one period example]
Decision Rule:
Accept the project if the IRR is greater than
the required return
Appeal of IRR
Management, and individuals in general, often have a
much better feel for percentage returns, and the value
that is created, than they do for dollar increases.
A dollar increase doesnt appear to provide as much
information if we dont know what the initial expenditure
was.
Whether or not the additional information is relevant is
another issue.
Project Example Information
You are reviewing a new project and have
estimated the following cash flows:
Year 0:
CF = -165,000
Year 1:
CF = 63,120;
NI = 13,620
Year 2:
CF = 70,800;
NI = 3,300
Year 3:
CF = 91,080;
NI = 29,100
Average Book Value = 72,000 (needed for AAR)
Your required return for assets of this risk level is
12%.
Computing IRR for the Project
Calculator
Enter the cash flows as you did with NPV
Press IRR and then CPT
IRR = 16.13% > 12% required return
Do we accept or reject the project?
NPV Profile for the Project
with Initial Costs Only
70,000
Monotone decreasing graph
Year 0: CF = -165,000
Year 1: CF = 63,120
Year 2: CF = 70,800
Year 3: CF = 91,080
60,000
50,000
NPV
40,000
30,000
20,000
10,000
0
-10,000
-20,000
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Discount Rate
NPV profile is also a form of sensitivity
analysis
0.16
0.18
0.2
0.22
Decision Criteria Test - IRR
Does the IRR rule account for the time value of money?
The IRR rule accounts for time value because it is finding the rate of return that
equates to 0 the sum of all of the cash flows on a time value basis.
Does the IRR rule account for the risk of the cash flows?
The IRR rule accounts for the risk of the cash flows because you
compare it to the required return, which is determined by the risk of
the project.
Does the IRR rule provide an indication about the increase in
value?
The IRR rule provides an indication of value because we will always
increase value if we can earn a return greater than our required
return.
Should we consider the IRR rule for our primary decision criteria?
We should consider the IRR rule as our primary decision criteria, but
as we will see, it has some problems that the NPV does not have.
That is why we end up choosing the NPV as our ultimate decision
rule.
Advantages of IRR
Knowing a return is intuitively appealing
It is a simple way to communicate the value of a
project to someone who doesnt know all the
estimation details
If the IRR is high enough, you may not need to
estimate a required return, which is often a difficult
task
Note: extremely high IRRs should be rare. Also, since the
IRR calculation assumes that you can reinvest future
cash flows at the IRR, a high IRR may be unrealistic
Calculating IRRs With A
Spreadsheet
You
start with the cash flows the same as
you did for the NPV
You
use the IRR function
You first enter your range of cash flows,
beginning with the initial cash flow
You can enter a guess, but it is not necessary
The default format is a whole percent you will
normally want to increase the decimal places
to at least two
Summary of Decisions for the
Project
Summary
Net Present Value
Payback Period
Discounted Payback Period
Accept
Reject
Reject
Average Accounting Return
Reject
Internal Rate of Return
Accept
NPV vs. IRR
NPV and IRR will generally give us the same
decision
Exceptions:
Nonconventional cash flows cash flow signs
change more than once
Mutually exclusive projects
Initial investments are substantially different
(issue of scale)
Timing of cash flows is substantially different
IRR and Nonconventional
Cash Flows
When the cash flows change sign more than
once, there is more than one IRR
When
you solve for IRR you are solving for the
root of an equation, and when you cross the
x-axis more than once, there will be more
than one return that solves the equation
If
you have more than one IRR, which one do
you use to make your decision?
Nonconventional Cash Flows
Nonconventional cash flows and multiple IRRs occur when
there is a net cost to shutting down a project. The most
common examples deal with collecting natural resources.
After the resource has been harvested, there is generally a
cost associated with restoring the environment.
Another type of nonconventional cash flow involves a
financing project, where there is a positive cash flow
followed by a series of negative cash flows. This is the
opposite of an investing project: our decision rule
reverses, and we accept a project if the IRR is less than the
cost of capital, since we are borrowing at a lower rate.
Another Example
Nonconventional Cash Flows
Suppose an investment will cost $90,000
initially and will generate the following
cash flows:
Year 1: 132,000
Year 2: 100,000
Year 3: -150,000
The required return is 15%.
Should we accept or reject the project?
Solution
NPV = 90,000 + 132,000 / 1.15 + 100,000 / (1.15)2
150,000 / (1.15)3 = 1,769.54
Calculator: CF0 = -90,000; C01 = 132,000; F01 = 1;
C02 = 100,000; F02 = 1; C03 = -150,000; F03 = 1; I =
15; CPT NPV = 1769.54
If you compute the IRR on the calculator, you get
10.11% because it is the first one that you come to.
So, if you just use the calculator without
recognizing the uneven cash flows, NPV would say
to accept and IRR would say to reject.
NPV Profile
$4,000.00
$2,000.00
Reject
$0.00
NPV
0
0.05
Reject
Accept
0.1
0.15
0.2
0.25
0.3
($2,000.00)
($4,000.00)
($6,000.00)
($8,000.00)
($10,000.00)
Discount Rate
0.35
0.4
0.45
0.5
0.55
Summary
The NPV is positive at a required return of 15%, so
you should Accept
If you use the financial calculator, you would get
an IRR of 10.11% which would tell you to Reject
You need to recognize that there are nonconventional cash flows and look at the NPV
profile
IRR and
Mutually Exclusive Projects
Mutually exclusive projects
If you choose one, you cant choose the other
Example: You can choose to attend graduate
school at either Harvard or Stanford, but not
both
Intuitively, you would use the following
decision rules:
NPV choose the project the with higher NPV
IRR choose the project with the higher IRR
Example With
Mutually Exclusive Projects
Period
Project A Project B
0
1
2
IRR
-500
325
325
19.43%
-400
325
200
22.17%
NPV
64.05
60.74
The required
return for both
projects is 10%.
Which project
should you accept
and why?
Mutually Exclusive Projects
As long as we do not have limited capital, we should
choose project A. What if we choose B and invest the
additional $100 in another good project, say C? The point
is that if we do NOT have limited capital, we can invest in A
and C and still be better off.
If we have limited capital, then we will need to examine
what combinations of projects with A provide the highest
NPV and what combinations of projects with B provide the
highest NPV. You then go with the set that will create the
most value. If you have limited capital and a large number
of mutually exclusive projects, then you will want to set up a
computer program to determine the best combination of
projects within the budget constraints.
DO NOT use IRR to choose between projects regardless of
whether or not we have limited capital.
NPV-based:
If the required return is
less than the crossover
point of 11.8%, then
you should choose A
NPV Profiles
IRR for A = 19.43%
$160.00
IRR for B = 22.17%
$140.00
$120.00
Crossover Point = 11.8%
NPV
$100.00
If the required return is
greater than the
crossover point of
11.8%, then you should
choose B
$80.00
A
B
$60.00
$40.00
$20.00
$0.00
($20.00) 0
0.05
0.1
0.15
0.2
0.25
0.3
($40.00)
Discount Rate
Embedded in the analysis, we may want to calculate the NPV of the incremental project, i.e.,
the additional CF represented by project A above project B. The IRR of this CF stream is the
crossover point and provides the return on the incremental investment.
Conflicts Between NPV and IRR
NPV
directly measures the increase in
value to the firm
Whenever there is a conflict between
NPV and another decision rule, you
should ALWAYS use NPV
IRR
is unreliable in the following situations:
Nonconventional cash flows
Mutually exclusive projects
Modified IRR
Treat inflows and outflows separately:
I.
Calculate the PRESENT value of all cash outflows
using the borrowing rate.
II.
Calculate the FUTURE value of all cash inflows
using the investing rate.
III.
Find the rate of return that equates these values.
Benefit: single answer and specific rates for
borrowing and reinvestment
Profitability Index
PV(inflows) / ini_cost
Measures the benefit per unit cost, based on the time
value of money
A profitability index of 1.1 implies that for every $1 of
investment, we create an additional $0.10 in value
This measure can be very useful in situations in which
we have limited capital. Otherwise, it can me
misleading think of projects of vastly different scales.
Advantages and Disadvantages
of Profitability Index
Advantages
Closely related to
NPV, generally
leading to identical
decisions
Easy to understand
and communicate
May be useful when
available investment
funds are limited
Disadvantages
May lead to
incorrect decisions in
comparisons of
mutually exclusive
investments
Capital Budgeting In Practice
We should consider several investment criteria when
making decisions
NPV and IRR are the most commonly used primary
investment criteria
Payback is a commonly used secondary investment
criteria.
Even though payback and AAR should not be used to
make the final decision, we should consider the project
very carefully if they suggest rejection. There may be more
risk than we have considered or we may want to pay
additional attention to our cash flow estimations.
Payback - Revisited
The fact that payback is commonly used as a secondary criterion
may be because short paybacks allow firms to have funds sooner
to invest in other projects without going to the capital markets.
Why are smaller firms more likely to use payback as a primary
decision criterion?
small firms dont have direct access to the capital markets and
therefore find it more difficult to estimate discount rates based on
funds cost;
other possibilities include:
the AAR is the project-level equivalent to the ROA measure used
for analyzing firm profitability;
some small firm decision-makers may be less aware of DCF
approaches than their large firm counterparts.
Corporate Governance
When managers are judged and rewarded primarily
on the basis of periodic accounting figures, there is
an incentive to evaluate projects with methods such
as payback or average accounting return.
On the other hand, when compensation is tied to
firm value, it makes more sense to use NPV as the
primary decision tool.
Summary DCF Criteria
Net present value
Internal rate of return
Difference between market value and cost
Take the project if the NPV is positive
Has no serious problems
Preferred decision criterion
Discount rate that makes NPV = 0
Take the project if the IRR is greater than the required return
Same decision as NPV with conventional cash flows
IRR is unreliable with nonconventional cash flows or mutually
exclusive projects
Profitability Index
Benefit-cost ratio
Take investment if PI > 1
Cannot be used to rank mutually exclusive projects
May be used to rank projects in the presence of capital rationing
Summary Payback Criteria
Payback period
Length of time until initial investment is recovered
Take the project if it pays back within some specified
period
Doesnt account for time value of money, and there is
an arbitrary cutoff period
Discounted payback period
Length of time until initial investment is recovered on a
discounted basis
Take the project if it pays back in some specified period
There is an arbitrary cutoff period
Summary
Accounting Criterion
Average
Accounting Return
Measure of accounting profit relative to book
value
Similar to return on assets measure
Take the investment if the AAR exceeds some
specified return level
Serious problems and should not be used
Quiz
Consider an investment that costs $100,000 and has a cash inflow of
$25,000 every year for 5 years. The required return is 9%, and required
payback is 4 years.
What is the payback period?
What is the discounted payback period?
What is the NPV?
What is the IRR?
Should we accept the project?
What decision rule should be the primary decision method?
When is the IRR rule unreliable?
Comprehensive Problem
An investment project has the following cash
flows: CF0 = -1,000,000; C01 C08 = 200,000 each
If the required rate of return is 12%, what decision
should be made using NPV?
How would the IRR decision rule be used for this
project, and what decision would be reached?
How are the above two decisions related?
Solution
NPV = -$6,472; reject the project since it would lower the
value of the firm.
IRR = 11.81%, so reject the project since it would tie up
investable funds in a project that will provide insufficient
return.
The NPV and IRR decision rules will provide the same
decision
for
all
independent
projects
with
conventional/normal cash flow patterns. If a project adds
value to the firm (i.e., has a positive NPV), then it must be
expected to provide a return above that which is required.
Both of those justifications are good for shareholders.