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j. As a separate project (Project P), you are considering sponsoring a pavilion at
the upcoming World’s Fair. The pavilion would cost $800,000, and it is expected
to result in $5 million of incremental cash inflows during its 1 year of operation.
However, it would then take another year, and $5 million of costs, to demolish
the site and return it to its original condition. Thus, Project P’s expected net
cash flows look like this (in millions of dollars):
Year Net Cash Flows
0 ($0.8)
1 5.0
2 (5.0)
The project is estimated to be of average risk, so its cost of capital is 10%.
j. 1. What are normal and nonnormal cash flows?
Answer: Normal cash flows begin with a negative cash flow (or a series of negative cash
flows), switch to positive cash flows, and then remain positive. They have only one
Projects with normal cash flows have outflows, or costs, in the first year (or years)
Inflow (+) Or Outflow (–) In Year
0 1 2 3 4 5
j. 2. What is Project P’s NPV? What is its IRR? Its MIRR?
Answer: Here is the time line for the cash flows, and the NPV:
012
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10%
We can find the NPV by entering the cash flows into the cash flow register, entering
I/YR = 10, and then pressing the NPV button. However, calculating the IRR presents
j. 3. Draw Project P’s NPV profile. Does Project P have normal or nonnormal cash
flows? Should this project be accepted?
Answer: You could put the cash flows in your calculator and then enter a series of r values, get
an NPV for each, and then plot the points to construct the NPV profile. We used a
Project P has nonnormal cash flows; that is, it has more than one change of signs
Since Project P’s NPV is negative, the project should be rejected, even though
1 Looking at the figure below, if you guess an IRR to the left of the peak NPV rate, the lower IRR will
appear. If you guess IRR > peak NPV rate, the higher IRR will appear.
k. In an unrelated analysis, you have the opportunity to choose between the
following two mutually exclusive projects, Project T (which lasts for two years)
and Project F (which lasts for four years):
Expected Net Cash Flows
Year Project T Project F
0 ($100,000) ($100,000)
1 60,000 33,500
2 60,000 33,500
3 — 33,500
4 — 33,500
The projects provide a necessary service, so whichever one is selected is expected
to be repeated into the foreseeable future. Both projects have a 10% cost of
capital.
k. 1. What is each project’s initial NPV without replication?
Answer: The NPVs, found with a financial calculator, are calculated as follows:
However, if we make our decision based on the initial NPVs, we would be biasing
k. 2. What is each project’s equivalent annual annuity?
Answer: We begin with the NPVs found in the previous step. We then find the annuity
payment stream that has the same present value as follows:
k. 3. Now apply the replacement chain approach to determine the projects’ extended
NPVs. Which project should be chosen?
Answer: The simple replacement chain approach assumes that the projects will be replicated
Project F’s common-life NPV is its initial NPV:
However, Project T would be replicated in Year 2, and if we assume that the
01234
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Thus, when compared over a 4-year common life, Project T has the higher NPV,
10%
k. 4. Now assume that the cost to replicate Project T in 2 years will increase to
$105,000 because of inflationary pressures. How should the analysis be handled
now, and which project should be chosen?
Answer: If the cost of Project T is expected to increase, the replication project is not identical
to the original, and the EAA approach cannot be used. In this situation, we would put
the cash flows on a time line as follows:
With this change, the common-life NPV of Project T is less than that for Project F,
and hence Project F should be chosen.
l. You are also considering another project which has a physical life of 3 years; that
is, the machinery will be totally worn out after 3 years. However, if the project
were terminated prior to the end of 3 years, the machinery would have a positive
salvage value. Here are the project’s estimated cash flows:
Initial Investment End-of-Year
And Operating Net Salvage
Year Cash Flows Value
0 ($5,000) $5,000
1 2,100 3,100
2 2,000 2,000
3 1,750 0
Using the 10% cost of capital, what is the project’s NPV if it is operated for the
full 3 years? Would the NPV change if the company planned to terminate the
project at the end of Year 2? At the end of Year 1? What is the project’s optimal
(economic) life?
Answer: Here are the time lines for the 3 alternative lives:
No termination:
Terminate after 2 years:
Terminate after 1 year:
