Transcript Investment Criteria

Relevant Cash Flows and Other
Topics in Capital Budgeting
Timothy R. Mayes, Ph.D.
FIN 3300: Chapter 10
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Project Cash Flows
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When deciding whether or not to make an
investment, we must first estimate the cash flows that
the investment will provide
Generally, these cash flows can be categorized as
follows:
• The initial outlay (IO)
• The annual after-tax cash flows (ATCF)
• The terminal cash flow (TCF)
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Relevant Cash Flows
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Determining the relevant cash flows can sometimes
be difficult, here are some guidelines
Cash flows must be:
• Incremental (i.e., in addition to what you already have)
• After-tax

Ignore those cash flows that are:
• Sunk costs (monies already spent, and not recoverable)
• Additional financing costs (e.g., extra interest expense)
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The Initial Outlay
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The initial outlay is the total up-front cost of the
investment
The initial outlay can consist of many components,
among these are:
•
•
•
•

The cost of the investment
Shipping and setup costs
Training costs
Any increase in net working capital
When we are making a replacement decision, we also
need to subtract the after-tax salvage value of the old
machine (or land, building, etc.)
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The Annual After-tax Cash Flows
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The annual after-tax cash flows (ATCF) are the
incremental after-tax cash flows that the investment
will provide
Generally, these cash flows fall into four categories:
• Incremental savings (positive cash flow) or expenses
(negative cash flow)
• Incremental income (positive cash flow)
• The tax savings due to depreciation
• Lost cash flows (negative cash flow) from the existing
project. This is an opportunity cost.
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The Terminal Cash Flow
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
The terminal cash flow consists of those cash flows
that are unique to the last year of the life of the
project
There may be a number of components of the TCF,
but three common categories are:
• Estimated salvage value
• Shut-down costs
• Recovery of the increase in net working capital
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Problems in Capital Budgeting

Thus far we have been analyzing relatively simple
capital budgeting problems. The methodolgy that
we have used is fairly robust, but there are some
difficulties. In particular we will now look at
problems with:
• Unequal lives
• Inflation
• Differential risk
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The Unequal Lives Problem
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
Any time that mutually exclusive projects are being
examined, it is vital that we make “apples to apples”
comparisons. A perfect example is two projects with
unequal lives.
Suppose, for example, that we are trying to decide
between projects A and B and that they are mutually
exclusive. They have the following cash flows, and
the cost of capital is 10%:
Project A
Project B
-10,000 6000
-10,000 3000
0
1
6000
3000
3500
4000
2
3
4
5
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The Unequal Lives Problem (cont.)
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If we calculate the NPVs of both projects, we find:
• NPVA= $413.22
• NPVB = $568.27
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From these calculations it appears that project B is the
better project. However, we are making a potentially
serious mistake.
Obviously, because we are willing to invest in B we
have a 5-year investment horizon. So, we must ask if
we accepted project A, what would we do with our
money for the remaining 3 years? Only then can a
valid comparison be made.
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The Unequal Lives Problem (cont.)

There are two ways to correctly deal with the
unequal lives problem:
• The replacement chain approach
• The equivalent annual annuity approach
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The Replacement Chain Approach

The replacement chain approach assumes that a
project will be repeated as many times as necessary
to fit into the investment horizon. In this example,
we need to repeat project A just once so that it has a
4-year life (the same a B). After replication, the cash
flows for A are:
Project A
-10,000 6000
0
1
-10,000
6000
6000
6000
2
3
4
5
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The Rep. Chain Approach (Cont.)
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Note that the net cash flow in year 2 is now -$4,000
because we must pay for project A a second time.
Now, recalculating the NPV for project A reveals that
the correct NPV for the entire 4-year horizon is
actually $754.73 which exceeds the NPV of project B.
Therefore, when the problem is correctly analyzed,
we find that it is actually project A which should be
accepted, not B.
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The EAA Approach
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The equivalent annual annuity approach is identical
to the replacement chain approach in its results, but it
is much simpler to perform
First, we calculate the NPVs for both projects
assuming that they are NOT replicated. Then, we
convert these NPVs into equivalent annuity
payments that they could provide over the life of the
project.
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The EAA Approach (Cont.)
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Using the formula for the present value of an
ordinary annuity, we simply solve for the annuity
payment:
1

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
413.22  PMT 




1
(110
. )2 

.10

Solving for the payment for project A, we find that its
EAA is $238.09.
Using the same methodology for project B we find
that its EAA is $179.27.
Since the EAA for A is higher than the EAA for B, we
should accept project A.
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Dealing with Inflation
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Inflation must be accounted for in capital budgeting
if we are to make correct decisions.
Generally, we should inflate the cash flow estimates
by the expected rate of inflation since the discount
rate that we are using already incorporates expected
inflation. If we do not do this, then the estimated
NPV will be lower than the correct NPV. This could
cause us to reject a project that (because it appears to
have a negative NPV) when, in fact, we should accept
it.
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Incorporating Risk Estimates
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Recall from our discussions in Chapters 1 and 5 that
we assume that investors are risk averse. This means
that they will require higher rates of return on higher
risk investments.
This means that the WACC is not the appropriate
discount rate for projects that are riskier or less risky
than the average for the firm. Instead, we need to
increase the discount rate for riskier projects and
decrease it for less risky projects. This is known as
the risk-adjusted discount rate (RADR).
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Incorporating Risk Estimates
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There are, of course, several other techniques for
incorporating risk into our decision making.
However, they are beyond the scope of this course.
Just for completeness, here are a few:
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•
•
•
Certainty equivalents
Scenario analysis
Sensitivity analysis
Monte-Carlo Simulation
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