Alternative Investment Criterion

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Alternative Investment Criterion
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Previously

• In Chapters 4 and 5 we looked at how to use NPV
  to evaluate any investment opportunity.
• I.e., accept a project if NPVgt0.
• Advantages of the NPV rule
• Explicitly incorporates the time value of money.
• Uses forecasted project cash flows and a
  risk-adjusted discount rate.
• NPVs are additive.

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Alternative Investment Criteria

• Payback and Discounted Payback
• Profitability Index
• Internal Rate of Return

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The Payback Period Method

• Payback Period The time it takes to recover the
  initial investment.
• Payback Period Rule A particular cutoff date,
  say, 2 years, is selected. All investment
  projects that have payback periods of 2 years or
  less are accepted. The rest are rejected.

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Example of Payback Period

• Which one to choose?
• All three have the same payback period.
• Any problems with Payback Period?

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The Problems with Payback Periods

• Problem 1 Payback Period Method ignores all cash
  flows occurring after the project has paid for
  itself. ( NPV rule considers all cash flows .)
• Problem 2 Treats cash flows that occur before
  the payback period equally. In other words, it
  ignores the time value of money, since the cash
  flows are not discounted!
• ( NPV rule discounts cash flows properly.)

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Discounted Payback period

• We first discount all cash flows.
• Then, we ask how long it takes for the discounted
  cash flows to equal the initial investment.

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Problems still remain

• Unfortunately, a few problems still remain
• Problem 1 We still ignore all (discounted) cash
  flows occurring after the project has paid for
  itself.
• Problem 2 Again, how do we decide what the
  required payback period should be?

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Example (recurring)

• Note This will be a recurring example.
• What is the NPV of the two projects?
• What is the payback period for projects A and B?
  What is the discounted payback period?

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Profitability Index (PI) or Benefit/Cost Ratio

• PI Rule Accept all projects with PI gt 1
• Popular in Non-Profit Management

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Internal Rate Of Return (IRR)

• The IRR is the discount rate that equates a
  projects NPV to Zero.
• The IRR is defined exclusively in terms of an
  assets cost and its cash flows. It is
  independent of market rates.
• IRR RULE
• Accept an investment/project if the opportunity
  cost of capital (discount rate) is less than the
  IRR.

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Example

• A project with an Initial Investment of 4,000
  and Cash flows at time 1,2 of 2,000 and 4,000
  respectively.

IRR 28.
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Graphically,

• When the discount rate is less than IRR, NPV is
  positive, so we accept the project.
• This graph assumes we have an initial cash
  outflow followed by cash inflows in the future.

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Example II

• An investment costs 125 and produces cash
  inflows of 15 per year in perpetuity.
• What is the IRR of this investment?

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Problems with IRR

• Hard to calculate
• Since it may involve solving a polynomial, the
  best way is often trial and error.
• Investing vs. financing
• Investing C0lt0 and C1, C2, gt0.
• Accept the project if r lt IRR.
• Financing C0gt0 and C1, C2, lt0.
• Accept the project if r gt IRR.

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Financing graph
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Problems (continued)

• Can have multiple IRRs.
• If cash flows change signs more than once (for
  example, C0 100, C150, C260, C3 30, C445,
  ), then we will have more than one IRR!
• In general, of IRRs equals of times the sign
  changes.

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Example

• Calculate the IRR for an investment with the
  following cash flows

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Problems III

• The Scale Problem.
• Small project with high IRR is preferred to large
  project with lower IRR but the latter may have
  higher PV!
• So the IRR rule may not work correctly when
  comparing two mutually exclusive projects of
  different scales.

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Example of IRR (text, page 160)

• Incremental Cash flows from choosing large
  instead of small budget

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Incremental IRR

• Incremental IRR66.67
• NPV of Incremental cash flow
• 66.67 gt25 (discount rate) and NPV is positive,
  so we accept the large budget.

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Incremental Cash Flow Example

• Dioxal Oil Company is in the process of cleaning
  up a minor oil spill. The firm could do the work
  with one cleanup team or two. One team would
  cost 25 per month for five months. Two teams
  would cost 40 per month for three months. If
  two teams are used, the firm can start refining
  earlier and collect 10 in earnings in months 4
  and 5. Should Dioxal use one or two teams to
  clean up the oil spill? Base your decision on
  IRR.