Engineering Economic Analysis

Elements in Incremental Rate of Return Analysis 259

A careful analysis has been made of the consequences of constructing a dam in the Blue Canyon.

It would be feasible to construct a dam at this site with a height anywhere from 200 to 500 feet.

Using a 4% MARR and a 75-year life, the various data have been used to construct Figure 8-9.

Note particularly that the dam heights are plotted on thexaxis along with the associated PWof

cost. What height of dam should be constructed?

FIGURE 8-9 Benefit-cost graph for

Example 8-9.

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1 2 3 4 5 6 7 8 9 10 11

PresentWorth of Cost (millionsof dollars)

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200 250300 400 500

PaIn Height (ft)

Five points have been labeled on Figure 8-9 to aid in the discussion. Damheignts below PointA
have a PW of cost> PW of benefit; hence, the rate of return is le.ssthanMARR.. and we woulq
not build a dam of these heights..In the region of PointB,an increment of additional PW of
cost-.6.C-produces a larger increment of PW ofbenefit-AB. These are,tI1erefore,desirable
increments of additional investment and, hence, dam height. At poiritDand also atPointE,tI1e
reverse is true. An increment of additionalJnvestment-.6.C-p],"oduces."a smalle.rincreIIientof
PW of benefit-.6.B; this is undesirable. We do not want these increments, so.tI1e~aIIlshould not
be bUiltto these heights.
At Point C, we see thatfJ.B=.6.C.LoWer dam heights have desirable increments of.in.-

vestmeIlt and higher dam heights have unfavorable increments of investri;lent.1;'heoptimal dam

height, th.erefore, is where.6.B =.6.C.In Figure 8..9, this corresponds to a heighto£app],"oximately

250 feet. Another way of definingthe poin.tat whichfJ.B= AC is to describe it as tI1epointwnere
the slope of the curve equals the slope of the NPW 0 line,

The techniques for solving discrete alternativesor continuousfunction alternativesare really

the same. We proceed by adding increments whenever .6.IRR2:MARR and discarding

increments when, fJ.IRR < MARR.

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