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Unformatted text preview: ead to incorrect decisions in comparisons of
mutually exclusive investments
941 IRR and Nonconventional Cash
Flows
• Consider the following nonconventional cash flow:
•
•
•
• Year 0: 90,000
Year 1: 132,000
Year 2: 100,000
Year 3: 150,000 • When the cash flows change sign more than once, then
mathematically there is more than one IRR
• When you solve for the IRR, you are solving for the root
of an equation. When you cross the xaxis more than
once, there will be more than one return that solves the
equation.
• Your calculator should give you a result of 10.11%, which
is one of the correct IRRs. The other is 42.66%.
942 NPV Profile
IRR = 10.11% and 42.66% $4,000.00
$2,000.00 NPV $0.00
($2,000.00) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ($4,000.00)
($6,000.00)
($8,000.00)
($10,000.00)
Discount Rate
943 So what’s the IRR?
• Is the IRR 10.11% or 42.66%?
• There really isn’t an answer to this
question, since both are IRRs.
• The best way to resolve the question of
whether to approve the project or not is to
use NPV to sort it out.
• Note: you must recognize that the
problem is not straightforward if there are
unconventional cash flows. Don’t rely on
your calculator.
944 Using NPV to sort it out
• •
• Calculate the NPV of this project using three
different discount rates: 10.11%, 15% and
42.66%.
• Year 0: 90,000
• Year 1: 132,000
• Year 2: 100,000
• Year 3: 150,000
Answer: The NPV is zero when the discount rate is
10.11% and 42.66%. The NPV is $1,769 when using
15%.
So if the NPV rule is being used and the required rate
of return is 15%, then the project should be approved.
945 IRR and Mutually Exclusive
Projects
• This is the second disadvantage to IRR relative
to NPV
• Mutually exclusive projects
• If you choose one, you can’t choose the other
• Example: You can choose to attend graduate school
next year at either Harvard or Stanford, but not both • Intuitively you would use the following decision
rules:
• NPV – choose the project with the higher NPV
• IRR – choose the project with the higher IRR
946 Example With Mutually Exclusive
Projects
Period Project A Project B
0 500 400 1 325 325 2 325 200 IRR 19.43% 22.17% NPV 64.05 60.74 The required return
for both projects is
10%.
Which project
should you accept
and why? Project A, hi...
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 Fall '14

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