for an alternative with an initial cost of $350 and an annual benefit of $47.50 that...
for an alternative with an initial cost of $350 and an annual benefit of $47.50 that increases by $10 each years. use a 8-year useful life and an 6%MARR to calculate:
A. Future worth?
B. Standard Benefit-cost Ratio?
C. Simple Payback Period?
Homework Answers
A. Present worth = -350 + 47.50 * (P/A, 6%,8) + 10 * (P/G, 6%,8)
= -350 + 47.50 * 6.209794 + 10 * 19.841581
= 143.38
Future worth = 143.38 * (F/P, 6%,8) = 143.38 * 1.593848 = 228.53
B.
B/C ratio = [47.50 * (P/A, 6%,8) + 10 * (P/G, 6%,8) ] / 350
= [ 47.50 * 6.209794 + 10 * 19.841581 ] / 350
= 493.38 / 350
= 1.41
c.
Simple payback period
For Simple payback period, we do not discount future cash flows. we find Cumulative cash flow (CCF), we need to find the year in which CCF turns positive
Simple payback period = Year bef CCF turns positive + (Absolute value of CCF bef it turns positive/Value of cash flow in the year in which CCF turns positive)
| year | investment | Net Revenue | Net cash Flow | Cumulative Cash flow |
| 0 | -350 | -350 | -350 | |
| 1 | 47.5 | 47.5 | -302.5 | |
| 2 | 57.5 | 57.5 | -245 | |
| 3 | 67.5 | 67.5 | -177.5 | |
| 4 | 77.5 | 77.5 | -100 | |
| 5 | 87.5 | 87.5 | -12.5 | |
| 6 | 97.5 | 97.5 | 85 | |
| 7 | 107.5 | 107.5 | 192.5 | |
| 8 | 117.5 | 117.5 | 310 |
Simple payback period = 5 + 12.5 / 97.5 = 5.13 yrs
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for an alternative with an initial cost of $350 and an annual
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