252 INCREMENTALANALYSIS
Alt.A':PW of benefits =122(P/A,6%, 20)
= 122(11.470) = 1399
The revised plot of the three alternatives (Figure 8-7) shows that the revised Alt.A'is no longer
desirable. We see that it has a rate of return less than 6%.
FIGURE 8-7 Benefit-cost graph for
Example 8-4. $9000
$8000
'"$7000
f.,t:;-
g(\) $6000
~
'"0 $5000..Q
1::
~-$4000
=
~ $3000(\)
~
$2000
$1000
'"
o $1000 $3000 $5000 $7000
PresentWorthof Cost
$9000
Now we wish to examine Alt.B.Should we compare it with the do-nothing alternative (wIiich
is representedby the origin) or as aB-A' increment overA'?Graphically;should we examine line
O-B orB-A'? SinceA'is an undesirable alternative, it should be discarded and not considered
further. Thus ignoringA',we should compareBwith the do-nothing alternative, which is line
O-B.AlternativeB is preferred over the do-nothing alternative because it has a rate of return
greater than 6%. Then incrementC--Bis examined and, as we saw, it is an undesirable increment
of investment.The decision to selectBhas not changed, which shouldbe no surprise: if an inferior
Ahad become an even less attractiveA',we still would select the superior alternative,B.
The graphical solution of the four example problems has helped us visualize the mechanics
of incremental analysis. While problems could be solved this way, in practice they are
solved mathematically rather than graphically. We will now proceed to solve problems
mathematically by incremental rate of return analysis.
INCREMENTAL RATE OF RETURN ANALYSIS
To illustrate incremental rate of return analysis, we will solve three of the examples again
by mathematical, rather than graphical, methods.
