258 INCREMENTALANALYSIS
alternatives.In an exam, this step probably should be skipped,but in less pressing situations,
these are logical computations.- Arrange the remaining alternatives in ascending order of investment. The goal
is to organizethe alternativesso that the incrementalanalysis will be of separableincrements
of investment when we analyze the higher-cost alternativeminusthe lower-cost alternative.
In textbook problems, this is usually easy-but there are lots of potential difficulties in
following this simple rule.
The ordering of alternatives is not a critical element in incremental analysis; in fact,
the differences between any two alternatives, like X andY,can be examined either as an
X-Y increment or aY-X increment. If this is done in a random fashion, however, we
will be looking sometimes at an increment of borrowing and sometimes at an increment of
investment.It can get a little difficultto keep all this straight; the basic goal is to restrict the
incremental analysis, where possible, to increments of investment. - Make a two-alternative analysis of the first two alternatives. If the increment
examined isY- X, which represents an increment of investment.
[Higher-cost
Alt.Y ]_
[LOWer-cost
] [Differences between
Alt. X + them(Y- X) ]Compute the ~IRR on the increment of investment. The criterion is:
·If ~IRR ~ MARR, retain the higher-cost Alt.Y.
·If ~IRR < MARR, retain the lower-cost Alt. X.
·Reject the other alternative used in the analysis.Sometimes the two alternatives being examined cannot be described as "higher cost" and
"lower cost." In Example 7-8, we encounteredtwo alternatives,AandB,with equal invest-
ments. There we selected theA-B increment because it was an increment of investment.
On the other hand, when we are examihing an increment of borrowing, the criteria are
as follows:· If ~IRR ::::MARR, the increment is acceptable.
·If ~IRR > MARR, the increment is not acceptable.- Take the preferred alternative from Step 4, and the next alternative from the
list created in Step 3. Proceed with another two-alternativecomparison. - Continue until all alternatives have been examined and the best of the multiple
alternatives has been identified.
Incremental Analysis with Unlimited Alternatives
At times the possible alternatives are a more or less continuous function. For example, in
an analysis to determine the economical height of a dam, the number of alternatives could
be infinite. If the alternatives were limited, however, to heights in even feet, the number
of alternatives would still be large and would have many of the qualities of a continuous
function, as in the following example.