Capital Budgeting
For 9.220, Term 1, 2002/03
02_Lecture9.ppt
Outline
Introduction
Problems with IRR
Special Considerations for DCF Techniques
Mutually Exclusive Projects
Capital Rationing
Non-Discounted Cash Flow Methods
Payback
Average Accounting Return (AAR)
Summary and Conclusions
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Introduction
Discounted Cash Flow (DCF) Techniques are
widely accepted as being among the better
methods used for capital budgeting analysis.
The three techniques discussed so far include
NPV, IRR, and PI
There are situations when one method is
better to use than another or when
adjustments should be made to use a
method correctly.
IRR Problem Cases: Borrowing vs. Lending
Consider the
Project A Project B
following two
Year
Cash
Cash
Flows
Flows
projects.
Evaluate with
IRR given a
0
-$10,000 +$10,000
hurdle rate of
20%
1
+$15,000 -$15,000
2
The non-existent or multiple IRR problem
Example:
Cash flows Cash flows
Year of
Project A of Project B
Do the
evaluation using
IRR and a
0
-$312,000 +$350,000
hurdle rate of
15%
1
+$800,000
-$800,000
2
-$500,000
+$500,000
NPV Profile – where are the IRRs?
$80,000
$60,000
NPV
$40,000
Project A
Project B
$20,000
$0
0%
20%
40%
60%
80%
100%
-$20,000
-$40,000
Discount Rate
-$60,000
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No or Multiple IRR Problem – What to do?
IRR cannot be used in this circumstance,
the only solution is to revert to another
method of analysis. NPV can handle these
problems.
How to recognize when this IRR problem
can occur
When changes in the signs of cash flows happen
more than once the problem may occur
(depending on the relative sizes of the individual
cash flows).
Examples: +-+ ; -+- ; -+++-; +---+
Special situations for DCF analysis
When projects are independent and the firm has few
constraints on capital, then we check to ensure that
projects at least meet a minimum criteria – if they do,
they are accepted.
NPV≥0; IRR≥hurdle rate; PI≥1
If the firm has capital rationing, then its funds are
limited and not all independent projects may be
accepted. In this case, we seek to choose those projects
that best use the firm’s available funds. PI is especially
useful here.
Sometimes a firm will have plenty of funds to invest, but
it must choose between projects that are mutually
exclusive. This means that the acceptance of one
project precludes the acceptance of any others. In this
case, we seek to choose the one highest ranked of the
acceptable projects.
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Using IRR and PI correctly when projects are
exclusive
and are of
differing scales
Consider the
following two
mutually exclusive
projects. Assume
the opportunity
cost of capital is
12%
Year
mutually
Cash flows Cash flows
of Project of Project
A
B
0
-$100,000
-$50
1
+$150,000
+$100
Incremental Cash Flows: Solving
the Problem with IRR and PI
As you can see, individual IRRs and PIs are not good
for comparing between two mutually exclusive
projects.
However, we know IRR and PI are good for evaluating
whether one project is acceptable.
Therefore, consider “one project” that involves
switching from the smaller project to the larger
project. If IRR or PI indicate that this is worthwhile,
then we will know which of the two projects is better.
Incremental cash flow analysis looks at how the cash
flows change by taking a particular project instead of
another project.
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Using IRR and PI correctly when projects are
mutually exclusive and are of differing scales
Incremental
Cash
flows
Cash
flows
Cash
flows of
Year of Project A of Project B A instead
of B
(i.e., A-B)
0
-$100,000
-$50
-$99,950
1
+$150,000
+$100
+$149,900
Using IRR and PI correctly when projects are
mutually exclusive and are of differing scales
IRR and PI analysis of incremental cash
flows tells us which of two projects are
better.
Beware, before accepting the better
project, you should always check to see
that the better project is good on its own
(i.e., is it better than “do nothing”).
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Incremental Analysis – Self Study
For self-study,
consider the
flows
following two
Year ofCash
Project A
investments and
do the
incremental IRR
and PI analysis. 0 -$100,000
The opportunity
cost of capital is
10%. Should
either project be 1 +$101,000
accepted? No,
prove it to
yourself!
Incremental
Cash flows
Cash
flows of of A instead
of B
Project B
(i.e., A-B)
-$50,000
+$50,001
Mutually Exclusive Projects of Different
Length or with Different Risks
IRR gives us one rate of return for all the cash flows
relevant to a project.
If necessary, NPV and PI allow for different discount rates
to be used on different cash flows.
This is useful when cash flows are of differing risk levels or
when different discount rates apply due to the different timing
of cash flows (recall the term structure of interest rates allows
for different interest rates for different cash flows through
time).
If different rates should be used for different cash flows
over a project’s life, then IRR cannot be used.
If we choose between two mutually exclusive projects of
different length, based on IRR, then, by comparing IRR’s,
we must be assuming that the project’s cash flows can be
reinvested at their IRR rates. NPV and PI make a more
conservative assumption that all reinvested cash flows earn
the opportunity cost of capital.
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Mutually Exclusive Projects of
Different Lengths – Example
Check the IRR’s. If B’s
cash flows can be
reinvested at B’s IRR,
then B may indeed be
the better investment.
Otherwise, it depends
on what are the
appropriate discount
rates for cash flows 1
year in the future,
versus cash flows 10
years in the future.
Cash
Cash flows flows
Year of
Project A ProjectofB
0
-$10,000
-$10,000
1
0
$11,500
10 $31,058.48
0
Capital Rationing
Recall: If the firm has capital rationing, then its
funds are limited and not all independent projects
may be accepted. In this case, we seek to choose
those projects that best use the firm’s available funds.
PI is especially useful here.
Note: capital rationing is a different problem than
mutually exclusive investments because if the capital
constraint is removed, then all projects can be
accepted together.
Analyze the projects on the next page with NPV, IRR,
and PI assuming the opportunity cost of capital is
10% and the firm is constrained to only invest
$50,000 now (and no constraint is expected in future
years).
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Capital
Rationing – Example
(All $ numbers are in thousands)
Year
Proj. A
Proj. B
Proj. C
Proj. D
Proj. E
0
-$50
-$20
-$20
-$20
-$10
1
$60
$24.2
-$10
$25
$12.6
2
$0
$0
$37.862
$0
$0
NPV
$4.545
$2.0
$2.2
IRR
20%
21%
14.84%
25%
26%
PI
1.0909
1.1
1.11
1.136
1.145
$2.727 $1.4545
Capital Rationing Example:
Comparison of Rankings
NPV rankings (best to worst)
A, D, C, B, E
A uses up the available capital
Overall NPV = $4,545.45
IRR rankings (best to worst)
E, D, B, A, C
E, D, B use up the available capital
Overall NPV = NPVE+D+B=$6,181.82
PI rankings (best to worst)
E, D, C, B, A
E, D, C use up the available capital
Overall NPV = NPVE+D+C=$6,381.82
The PI rankings produce the best set of investments
to accept given the capital rationing constraint.
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Capital Rationing Conclusions
PI is best for initial ranking of
independent projects under capital
rationing.
Comparing NPV’s of feasible
combinations of projects would also
work.
IRR may be useful if the capital
rationing constraint extends over
multiple periods (see project C).
Other methods to analyze
investment projects – self study
Payback – the simplest capital budgeting
method of analysis
Know this method thoroughly.
Discounted Payback
Know thoroughly.
Average Accounting Return (AAR)
You will not be asked to calculate it, but you
should know what it is and why it is the most
flawed of the methods we have examined.
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Summary and Conclusions
DCF techniques are the best of the methods
we have presented.
In some cases, the DCF techniques need to
be modified in order to obtain a correct
decision. It is important to completely
understand these cases and have an
appreciation of which technique is best
given the situation.
Other techniques you should know include
payback (which is nice because of its
simplicity), discounted payback, and AAR.
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