Comparisons
with Rate of Return
Executives prefer the
rate of return
method because it expresses
the worth of an investment as the annual percentage
return. This is
a familiar measure to most investors. For situations involving
the selection of the best of alternative solutions, we must be
careful when using his method. The most intuitive application
of the rate of return method will lead to decision errors. For
example, consider the following scenario.
Suppose that you are offered three alternatives
and must choose one of them. The first alternative has a
1000% rate of return, the second alternative has a 100% rate
of return and the third has a 20% rate of return. Which do you
select?
You probably chose the first alternative since
it earns 10 times the return of second and 50 times the third,
but that isn't the whole story. For
the first alternative, an investment of one cent today will
receive 11 cents in one year. For the second alternative, an
investment of $10 today will receive $20 in one year. For the
third alternative, an investment of $100 today will
receive $120
in one year. Assuming you have the capital, which
do you select now?
The first earns
10 cents, the second $10 and the third $20, so given
this additional information, you say the choice is obvious: Select
the third
because it makes the most profit.
Both the rate of return and the profit
are unreliable
measures when selecting among alternatives because they both
neglect part of the information. The rate of return
is a relative
measure; that is, the ratio of profit to investment. The amount
invested is lost in the ratio. The profit subtracts
the investment
from the income, again losing the amount of the
investment.
In fact, all three answers are correct
under different
situations. You should be able to find the answer by the end
of this lesson, which considers two decision problems
that involve sets of projects. The first is
project selection.
Here we desire to choose a subset of projects from a
set of proposed
projects. The second is how to select the best
alternative project from a set of two or more proposals.
Although the IRR is the measure used throughout this
lesson we use rate
of return as the more general term.


Goals 



Given a set of projects and an
investment budget, use the ROR method
for selecting
the best subset of projects.

Use the ROR method to compare
two or more alternatives and select
the best.

Select and use a study period
when alternative lives are different

Do incremental analysis for
comparing two or more alternatives.

Use the Economics
addin for
ROR comparisons.




Text




3.4.5
Internal Rate of Return Method





Project
Selection 


An
organization has a set of proposed projects
from which
some subset must be chosen. The IRR
provides a measure
for project selection. 


A primary purpose of most corporations is
to invest capital to make profit. The capital comes
from investors,
debt, recovery of depreciation, and profits retained
in the business.
An annual exercise for some organizations is to seek proposals
for investment projects and then select from the proposals a
subset of projects to pursue. Using finance analysis we compute
the IRR of each project. These measures are used for
project selection.
This lesson considers a very simple version of this problem.
The text has an entire chapter that addresses many other
factors including multiple criteria and risk.


5
Project Screening and Selection
Read 5.1 for background. The remainder of the
chapter is not required. 


Click the QuickTime symbol to see how select projects
given the MARR and how to select projects with a
fixed investment
budget.
Summary of Example
Each year several departments in a
corporation propose projects with different
investment amounts,
annual net incomes and lives. The corporation must choose
from the proposals. The corporation's MARR is 25%. The list
is below.


With
a given MARR and no budget restriction, select the
projects that have IRR ≥ MARR.


To apply this rule, first compute the
IRR for each project. The MARR of 25% leads
to the selection
of projects 2, 3, 4, 6, 7, 9 and 10. The
total investment
in the projects is $10,450.

A related problem arises when a budget limit
is imposed. This is the usual case.

When the budget is restricted,
rank the projects by IRR and in
order of the ranking choose the largest subset that
does not exceed the budget.


To apply this rule it is convenient to
sort the alternatives by IRR and compute the cumulative
investment as below. When the budget is
$5,000 we select
the subset of projects 7, 6 and 2 with the
total investment
of $3750. Since adding project 10 exceeds the budget
by only $150, we select that one too. Perhaps
the budget
is flexible.

This solution is only approximate because of
the discrete nature of the projects. We can either accept a
project or not. Selecting the very best subset is
an optimization
problem that requires some highpowered methods for solution.
The problem is addressed by the Portfolio
addin. The tables above were also obtained via
this addin. For this
course we are satisfied with this simple approximation, so
you are not required to use the Portfolio addin.
The link is provided for reference.


Portfolio
Addin
For Reference  Not
Required



The sorted list is sometimes
suggested as a method
for determining the MARR. The MARR depends on the
capital available.
To find the MARR we move down the ranking as far as possible
until the budget is violated by the next project. The MARR
is the IRR of the last project selected. For a $5,000 budget
the MARR would be 45%. For a $10,000 budget the MARR is 33%.
This leads to the conclusion that the greater the
capital available,
the smaller the MARR. Companies with little capital will have
a high MARR, while companies with plentiful capital will have
a low MARR.


Mutually
Exclusive Alternatives



To
choose among mutually exclusive alternatives, you must
use incremental analysis. The IRR of each increment
of investment must satisfy the MARR
requirement.



The presentation
describes how the incremental analysis is
used when the rate of return is the criterion. Click the icon
to see the presentation.
A distinction can be drawn between problems where
some alternative must be chosen or where it is
allowable to choose
none. We handle this for problems of the latter
variety by including
the null alternative
in the incremental analysis.
Summary of the
CostOnly Example in
the ROR:Mutually Exclusive Lecture
With only costs, the IRR values for the individual
alternatives are undefined. Incremental analysis selects
the best alternative.

The result of each analysis depends on
the MARR. After the first analysis the
alternatives compared
may be different when a different MARR is specified.



Different
Lives 


When
the alternatives have different lives, they must be
compared over a common study period. We
choose the least common multiple of the
lives. 


Click the QuickTime symbol to see how
to use the present worth method when the alternatives have the
different lives.
Summary of the Example in the
Different Lives movie
This example involves incomes, but the individual
rates of returns are irrelevant because we must choose one
of the mutually exclusive alternatives. Again incremental
analysis is required. The problem is more complex because
one of the incremental analyses involves alternatives
with different lives.



The
Economics Addin 


You
should be able to perform NPW or NAW analyses by hand
with equivalency expressions, but for problem solving
the Economics addin can handle problems of
arbitrary complexity. 

The Economics addin is easy
to use and it should be handy for
homework and computerbased exams.


Economics
Addin: Compare Projects



The figure below shows projects defined for the
machine example introduced in the ROR: Mutually
Exclusive movie.
To perform an incremental analysis, we
choose Compare
Projects from the menu. We select the
First alternative,
with the smaller investment, as the defender and
the Second alternative,
with the greater investment, as the challenger. The
results for the example are below. When two projects
are compared
the addin automatically prepares an incremental analysis. The
IRR value of 21.41% reported in the table is the
IRR of the increment of investment. Because this
value is greater
than the MARR, the increment of the Second
alternative
over the First is justified. Economically
speaking, we should
choose the Second alternative.
To compare more than two alternatives with the rate
of return method, more than one of these 2way
comparisons is required.
Follow the incremental method. Starting with the alternative with
the smallest investment as the initial defender and incumbent,
we must test each increment of investment to see if the IRR
of the increment exceeds the MARR. An alternative whose
incremental
investment is justified becomes the incumbent.
The process continues in order of increasing investment until all
alternatives have been considered. The final incumbent
is the selected
alternative. 

This discussion should have provided a method
to answer the original question.
"You are offered three
alternatives and you must choose one of them. The
first alternative has a 1000% rate of return, the
second alternative has a 100% rate of return and
the third has a 20% rate of return. Which do you
select?"

You should know at this point in the course that
the answer depends on your MARR. From the material
presented here, you should have learned
the additional lesson that the individual values of
the ROR don't tell the whole tale. You must use incremental
analysis.
The three alternatives are listed below in order
of increasing investment. We have added the
Null alternative
to make available the donothing option.
Alternative 
Investment 
Return
after one year 



A 
$0.01 
$0.11 
B 
$10 
$20 
C 
$100 
$120 
For example, let's say your MARR is 10%. The
incremental analysis
shows that C is the best decision.

Challenger 
Defender 


IRR
(chal  def) 









B 
A 


99.1% 


C 
B 


11.1% 


Let's say your MARR is 15%. The incremental analysis
shows that B is the best decision.

Challenger 
Defender 


IRR
(chal  def) 









B 
A 


99.1% 


C 
B 


11.1% 


Let's say your MARR is 100%. The incremental analysis shows
that A is the best decision.

Challenger 
Defender 


IRR
(chal  def) 









B 
A 


99.1% 


C 
A 


19.9% 


Let's say your MARR is 1000%. Boy you sure are
greedy! The analysis
shows that you should select none.

Challenger 
Defender 


IRR
(chal  def) 









B 
Null 


100% 


C 
Null 


20% 


So unless you know your MARR there is no correct
solution. You should answer:
"The answer could be anything.
It depends on my MARR."

The important lesson to learn is that the rate of return for
any alternative makes little difference when deciding between
mutually exclusive alternatives. Each increment of investment
must make the MARR.


Summary 



Problems 


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