Engineering Economic Analysis

260 INCREMENTALANALYSIS

Present Worth Analysis with Benefit cost .Graphs

Any of the example problems presented so far in this chapter could be solved by the presel

worth method. The benefit-cost graphs we introduced earlier can be used to graphicall

Rationing Capital by Present Worth Methods

In present worth analysis,where neither input nor output is fixed,the economiccriterio

is to maximize NPW. In Example 8-1, we had two alternatives and the MARR equc

to 6%:

These points are plotted in Figure 8-10, which has the NPW=0 line at 450, since identical

scales were used on both axes. The point for Alt. 2 is plotted at the coordinates (PW of

cost, PW of benefits). We drop a vertical line from Alt. 2 to the diagonal NPW=0 line.

The coordinates of any point on the graph are (PW of cost, PW of benefits), but along,the

NPW = 0 line (450line), thexandycoordinates are equal. Thus, the coordinates of Point 4

are also (pW of cost, PW of cost). Since

NPW = PW of benefits - PW of cost

the vertical distance from Point 4 to Alt. 2 represents NPW. Similarly, the vertical distance

between Point 3 and Alt. 1presents NPW for Alt. 1. Since the criterion is to maximize NPW,

FIGURE 8-10 Benefit-cost graph for

PW analysis. $27

$24

'"$21

tE

~~ $18

r:Q

'C3 $15

'€

~$12

C

~ $9

£

2

$6

$3 $6 $9 $12 $15 $18 $21

PresentWorth of Cost

$3

.. --'--