302 Planning and Forecasting
MORE NPV EXAMPLES
Consider two alternative projects, A and B. They both cost $1,000,000 to set
up. Project A returns $800,000 per year for two years starting one year after
setup. Project B also returns $800,000 per year for two years, but the cash
f lows begin two years after setup. The firm uses a discount rate of 20%. Which
is the better project, A or B?
Like project A, project C also costs $1,000,000 to set up, and it will pay
back $1,600,000. For both A and C, the firm will earn $800,000 per year for
two years starting one year after setup. However, C costs $500,000 initially and
the other $500,000 need only be paid at the termination of the project (it may
be a cleanup cost, for example). Project A requires the initial outlay all at once
at the outset. Which is the better project, A or C? Of projects A, B, and C,
which project(s) should be undertaken?
We should make the project decision only after analyzing each project’s
NPV. Exhibit 10.5 tabulates each project’s cash f lows, discounted cash f lows,
and NPVs. The NPVs of Projects A, B, and C, are, respectively, $222,222,
−$151,235, and $375,000. Project C has the highest NPV. Therefore, if only
one project can be selected, it should be project C. If more than one project
can be undertaken, then both A and C should be selected since they both have
positive NPVs. Project B should be rejected since it has a negative NPV and
would therefore destroy wealth.
It makes sense that project C should have the highest NPV, since its cash
outf lows are deferred relative to the other projects, and its cash inf lows are
early. Project B, alternatively has all costs up front, but its cash inf lows are
deferred.
Suppose a project has positive NPV, but the NPV is small, say, only a few
hundred dollars. The firm should nevertheless undertake that project if there
are no alternative projects with higher NPV. The reason is that a firm’s value
is increased every time it undertakes a positive-NPV project. The firm’s value
increases by the amount of the project NPV. A small NPV, as long as it is posi-
tive, is net of all input costs and financing costs. So, even if the NPV is low,
EXHIBIT 10.5 Cash f lows and discounted cash f lows for three
alternative projects (thousands).
Project A Project B Project C
Project A Discounted Project B Discounted Project C Discounted
Year Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow
0 $(1,000,000) $(1,000,000) $(1,000,000) $(1,000,000) $(500,000) $(500,000)
1 800,000 666,667 0 0 800,000 666,667
2 800,000 555,556 0 0 300,000 208,333
3 0 0 800,000 462,963 0 0
4 0 0 800,000 385,802 0 0
NPV= $0,(222,222 $0,(151,235) $ 375,000