Planning Capital Expenditure 311accepted. When a project has two or more IRRs, the analyst would have no way
of knowing which was the correct one to use if he or she did not also compute
the NPV and apply the NPV rule. If the analyst only computed the IRR of
100%, then she or he would reject this valuable project.
It turns out that a project will have one IRR for every change in sign in its
cash f lows. If a project has an initial outlay and then subsequently all cash
f lows are positive inf lows, there will be one unique IRR. If a project has an
initial outlay, a string of positive inf lows, and then a cleanup cost at the end,
there will be two IRRs since the direction of cash f low changed twice. If there
were an initial outlay, a positive inf low, another net outf low during a retooling
year, followed by a positive inf low, the three sign changes would produce three
different IRRs. The IRR rule would provide little guidance in such a scenario
and could possibly lead to an incorrect judgment of the project’s worth.
In situations where its two fatal f laws are not an issue, the IRR rule gives
the same result as the NPV rule. If the project’s cash f lows change sign only
once, there is no problem of multiple IRRs. If all competing projects are of the
same magnitude or if there is only one project under consideration, the size
issue will not be a problem either. In such a situation, the firm would be justi-
fied in selecting the project on the basis of IRR.
One circumstance in which alternative projects are of equal size and cash
f lows only change direction once is in the analysis of alternative mortgage
plans. These days, a person financing a home may choose from a multitude of
mortgage plans. A variety of payment schedules are available and some plans
charge points in exchange for lower monthly payments. Since all mortgages
considered by the homebuyer finance the same house, the size issue is not a
concern. Also, the typical home mortgage involves a cash inf low at the begin-
ning and then only cash outf lows over the period when the borrower must pay
back the loan. Thus, there is only one sign change among the cash f lows. A bor-
rower can thus compare mortgages on the basis of their IRRs. The borrower
should calculate the cash f lows over the horizon during which he or she ex-
pects to pay back the mortgage, and should then choose the lowest IRR mort-
gage from among those whose monthly payments are affordable. The annual
percentage rate (APR) quoted by mortgage companies is the IRR of the mort-
gage calculated after factoring in points and origination fees and assuming the
mortgage will not be prepaid.
RECENT INNOVATIONS IN CAPITAL BUDGETING
Recent years have seen the introduction of two new capital budgeting para-
digms. The fact that new approaches are still being invented tells us that NPV
is not the last word in capital budgeting. Analysts and investors are constantly
looking for better tools for making long-range capital decisions. One new ap-
proach, known as economic value added (EVA), was introduced by the consult-
ing firm Stern Stewart & Company, which owns the term as a registered