Chapter 7: Some Alternative Investment Rules

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Chapter 7 Some Alternative Investment Rules

• 1. Why use Net Present Value (NPV)
• 2. The Payback period rule
• 3. The discounted Payback period rule
• 4. Average accounting return (AAR)
• 5. Internal rate of return (IRR)
• 6. Problems with the IRR
• 7. The Profitability index (PI)
• 8. The practice of capital budgeting
• 9. Summary

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• 1. Why Use Net present value (NPV)
• NPV PV (cash inflow) PV (cash outflow)
• Example ABC Inc. is considering a riskless
  project. Initial cash outflow is 100, and ABC
  Inc. receive 110 one year later. The interest
  rate is 6 p.a.
• Solution NPV -100 110/1.06 3.77.
• NPV Rule Accept the project, if NPV gt 0
• Reject the project, if NPV lt
  0
• Estimating the cash flows and an appropriate
  discount rate is by no means an easy task.

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• Why NPV rule leads to good decisions?
• Consider two strategies for ABC
• Accept the project, and pay 110 as a dividend
  next year.
• Forgo the project, and pay the 100 as a dividend
  today. Then shareholder can earn 106 with a 6
  interest rate. The shareholder would prefer
  strategy (1).
• Accepting positive NPV projects benefits the
  shareholder.
• Interpretation of the NPV of 3.77 in ABC example
• Suppose ABCs current value is V, and ABC has
  obtained 100 cash. Consider two cases
• (1) ABC does nothing value today V 100.
• (2) ABC invests 100 in the project value today
  V 110/1.06
• The difference between (1) and (2) is 3.77. The
  value of the firm rises by the NPV of the project.

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• Three key attributes of the NPV
• It uses cash flows.
• It uses all the cash flows of the project.
• It discounts the cash flows properly.
• 2. The Payback period rule
• Definition The number of years it takes before
  forecasted cash flows recover the initial
  investment.
• The payback rule the initial outlay on any
  project should be recoverable within some
  specified cutoff period.

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• Example

With Payback period rule Accept A if the
cutoff period is 1 year, Accept A and B if the
cutoff period is 2 years. With NPV, we reject
A and accept B. Payback period rule can lead
to incorrect decisions.
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• Pros Easy to understand and calculate
• Cons
• Ignores the time value of money
• Ignores cash flows beyond the cut off date
• Depends on an arbitrary cut off point
• Biases against long-term projects
• Practice Companies often use the payback method
  for minor investment decisions.

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• Discounted payback period rule
• Use discounted cash flows to find out the payback
  period.
• Example Interest rate of 10. Consider the
  cash flows
• (-100, 50, 50, 20) ? (-100, 45.45, 41.32,
  15.03)
• Lacks the simplicity and conceptual rigor.

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• Average accounting return (ARR)
• Definition AAR Average net income/Average book
  value 
• Rule Accept if ARR is greater than a target
• Example Next slide.
• Pros Simple Availability of information
• Cons Time value of money is ignored.
• Based on accounting (book) values, not cash
  flows.
• Arbitrary yardstick

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• Example You want to invest in a new machine
  costing 90,000. The machine has a life of 3
  years.

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• Average net income (61848)/3 24
• Average book value of the investment
• (9060300)/445
• Average accounting return
• AAR 24/45 53.3
• Conclusion
• If target AAR lt 53.3 ? Accept,
• If target AAR gt 53.3 ? Reject.

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• 5. Internal Rate of Return (IRR)
• Definition A discount rate such that the
  PV(cash inflow) is equal to the PV(cash outflow),
  i.e., NPV equal to zero.
• Basic rule if IRR gt discount rate, accept the
  project.
• if IRR lt discount rate, reject the project.
• Problems with the IRR
• Borrowing or lending?
• Multiple IRRs
• For mutually exclusive projects
• Scale problem
• Timing problem

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• Borrowing or Lending?
• Consider Project A (-100, 110) and
• Project B (100, -110).
• For both project, IRR is 10. Can we use the
  basic IRR rule?

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• Multiples IRRs There are two IRRs for this
  project

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• Mutually Exclusive Projects
• Mutually exclusive projects you can only do one
  project, you can't do all of them.
• An example Replacing a copy machine. You can
  use either Zerox or Cannon machine.
• Let us try to use the IRR rule
• Choose the project with IRR above a cut off.

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Example scale problem (Mutually exclusive
project)

• r 18.18, i.e., at this discount rate NPV of
  both projects is identical. As an exercise,
  verify this.

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• Intuitively, what is going on here is a question
  of relative versus absolute returns.
• A has a high relative return but a low absolute
  return
• B has a low relative return but a high absolute
  return.
• Given they're mutually exclusive, you can't do
  both.
• What's important is which project gives you the
  highest absolute return since that's the amount
  of additional value created from the project.

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• IRR on incremental cash flows
• You first consider the smaller project, A, in our
  example. With a 10 IRR, A is acceptable.
• You now consider whether it is worth making the
  additional investment of 990 in B.
• To do this you consider an imaginary project C
  where C B - A. C is called the incremental
  project. 
• The IRR on project C is 18.18, so it is worth
  doing C.
• Hence you should do C B - A as well as A. But
  if you do both A and C what are you doing? Since
  A C A (B - A) B this means you should do
  B out of the two mutually exclusive projects A
  and B.

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• 7. Profitability Index (PI)
• Definition
• PI PV of project after initial
  investment/Initial investment
• Rule Accept project if PI gt 1. 
• Example PI
• Consider the example we used with IRR and
  mutually exclusive projects again.

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• NPV rule choose B
• A naive profitability index rule incorrectly
  choose A
• We can adapt the PI method by looking at the PI
  of the incremental investment. We should accept
  this incremental project, and therefore we should
  do B.
• Easy and simple to use.

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8. The practice of capital budgeting
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• 8. Summary
• 1. Discounted cash flow criteria
• A. Net present value (NPV). The NPV of an
  investment is the difference between its market
  value and its cost. The NPV rule is to take a
  project if its NPV is positive. NPV has no
  serious flaws it is the preferred decision
  criterion.
• B. Internal rate of return (IRR). The IRR is the
  discount rate that makes the estimated NPV of an
  investment equal to zero. The IRR rule is to take
  a project when its IRR exceeds the required
  return. When project cash flows are not
  conventional, there may be no IRR or there may be
  more than one.

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• C. Profitability index (PI). The PI, also called
  the benefit-cost ratio, is the ratio of present
  value to cost. The profitability index rule is to
  take an investment if the index exceeds 1.0. The
  PI measures the present value per dollar
  invested.

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• 2. Payback criteria
• A. Payback period. The payback period is the
  length of time until the sum of an investments
  cash flows equals its cost. The payback period
  rule is to take a project if its payback period
  is less than some prespecified cutoff.
• B. Discounted payback period. The discounted
  payback period is the length of time until the
  sum of an investments discounted cash flows
  equals its cost. The discounted payback period
  rule is to take an investment if the discounted
  payback is less than some prespecified cutoff.

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• 3. Accounting criterion
• A. Average accounting return (AAR). The AAR is
  a measure of accounting profit relative to book
  value. The AAR rule is to take an investment if
  its AAR exceeds a benchmark.