Relevant Cash Flows and Other Topics in Capital Budgeting

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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

• 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

• 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

• 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

• 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

• 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

• 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

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The Unequal Lives Problem (cont.)

• If we calculate the NPVs of both projects, we
  find
• NPVA 413.22
• NPVB 568.27
• 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

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The Rep. Chain Approach (Cont.)

• 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

• 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.)

• Using the formula for the present value of an
  ordinary annuity, we simply solve for the annuity
  payment

• 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

• 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

• 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

• 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
• Certainty equivalents
• Scenario analysis
• Sensitivity analysis
• Monte-Carlo Simulation