Given the net cash flow for two machines as shown below, what is the benefit cos

Question

Given the net cash flow for two machines as shown below, what is the benefit cost ratio for the difference in the benefits and costs for the higher initial cost machine and the lower initial cost machine if the MARR is 12%?

0.92

1.05

1.12

1.26

Machine B Machine C Years CF Costs CF Benefits CF Costs CF Benefits 0 ($121,000) $0 ($193,000) $0 1 ($15,200) $48,600 ($28,400) $116,500 2 ($15,656) $48,600 ($29,252) $116,500 3 ($16,126) $48,600 ($221,726) $116,500 4 ($16,609) $48,600 ($31,033) $116,500 5 ($17,108) $48,600 ($31,964) $116,500 6 $4,159 $48,600 ($11,834) $116,500

Explanation / Answer

Calculation of benefit cost ratio for the difference in the benefits and costs for the higher initial cost machine and the lower initial cost machine Years Machine B Machine C Costs Benefits Costs Benefits Cost Differences Benefit Differences Discount Factor @ 12% Present Value of cost differences Present Value of benefit differences A B C D E F = B-D G = C-E H F*H G*H 0 -$121,000 $0 -$193,000 $0 -$72,000 $0 1 -$72,000.00 $0.00 1 -$15,200 $48,600 -$28,400 $116,500 -$13,200 $67,900 0.892857 -$11,785.71 $60,625.00 2 -$15,656 $48,600 -$29,252 $116,500 -$13,596 $67,900 0.797194 -$10,838.65 $54,129.46 3 -$16,126 $48,600 -$221,726 $116,500 -$205,600 $67,900 0.71178 -$146,342.02 $48,329.88 4 -$16,609 $48,600 -$31,033 $116,500 -$14,424 $67,900 0.635518 -$9,166.71 $43,151.68 5 -$17,108 $48,600 -$31,964 $116,500 -$14,856 $67,900 0.567427 -$8,429.69 $38,528.28 6 $4,159 $48,600 -$11,834 $116,500 -$15,993 $67,900 0.506631 -$8,102.55 $34,400.25 -$266,665.34 $279,164.56 Benefit Cost ratio = Sum of present value of benefit differences / Sum of present value of cost differences Benefit Cost ratio = $279164.56 / $266665.34 = 1.05

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