CH8_100 - FIGURE 8—1 Graph of PW of benefits versus PW...

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Unformatted text preview: FIGURE 8—1 Graph of PW of benefits versus PW of cost. _______ alteestiy92_-_____-. Alternative 1 Present Worth of Benefits £6 en .— 0 UI 9999 930 I l I I t I I I I I I I I I I I I I t I I I I l I I I t I l‘ l I I I I I I I I I I I I I x I I I I I $3 $6 $9 $12 $15 $18 $21 $24 $27 $30 Present Worth of Cost Alternative 2 PW of cost = $20 PW ofbenefits = $28(P/F, 6%, l) = 28(0.9434) = $26.42 The alternatives are plotted in Figure 8-1. which looks very simple yet tells us a great deal about the situation. On a graph of PW of benefits versus PW of cost (for convenience, we will call it a benefit— cost graph), there will be a line where NPW = 0. Where the scales used on the two axes are identical, as in this case, the resulting line will be at a 45° angle. If unequal scales are used, the line will be at some other angle. . L For the chosen interest rate (6% in this example), this NPW = 0 line divides the graph into '- areas of desirable and undesirable alternatives. To the left (or above) the line is “desirable," while ', to the right (or below) the line is “undesirable.” We see that to the left of the line, PW of benefits :7 exceeds the PW of cost or, we could say, NPW is positive. To the right of the line, in the shaded area, PW of benefits is less than PW of cost; thus, NPW is negative. In this example, both alternatives are to the left of the NPW = 0 line. Therefore, both alternatives will have a rate of return greater than the 6% interest rate used in constructing the graph. In fact, other rate of return lines could also be computed and plotted on the graph for this special case of a one-year analysis period. We must emphasize at the outset that the additional rate of return lines shown in Figutefid can be plotted only for this special situation. For analysis periods greater than one year, fth NPW = 0 line is the only line that can be accurately drawn. ' L ' ' ’ agree with the calculations made in Example 7-6, where the _ ere 50% and 40%, respectively. _ Figure 8~2 shows that the s 1a line on the graph represents a particular rate of return for this special case of a one—year _. { period. Between the origin and Alt. 1, the slope represents f 50% rate of return, while rm 'gin to Alt. 2, the slope represents a 40% rate of return. ...
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