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Homework 24 Solution

Homework 24 Solution - Homework 24 Solution 7.22 The...

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Homework 24 Solution 7.22 The problem statement says “select one” so we have to assume that “do nothing” is not an option even though these look like the equivalent of “revenue” projects because they have direct benefits. If we use the modified B/C definition, the only cost in the denominator is the initial cost (there is no salvage value) so we need to determine if the additional $49,000 it would cost to use the new sensors is justified by the additional benefits. Since all of the remaining costs are annual values, we’ll amortize the $49,000 cost difference over the 10-year study period: 0.14238 C $49,000 A | P,7%,10 $6977 per year Counting the O&M costs as disbenefits, the annual benefits of the two options are B EC = $110,000 – $26,000 – $49,000 = $35,000 B NS = $160,000 – $64,000 = $96,000 B = $96,000 – $35,000 = $61,000 per year So the incremental B/C ratio is $61,000 B C 1 $6977  Therefore, select the more-expensive NS option. We could have also used the conventional B/C definition. In that case, we’d have to include the O&M costs in the denominator. Now the costs of the two options are C EC = $38,000 (0.14238) + $49,000 = $54,410 C NS = $87,000 (0.14238) + $64,000 = $76,387 C = $76,387 – $54,410 = $21,977 Omitting the O&M costs, the annual benefits of the two options are B EC = $110,000 – $26,000 = $84,000 B NS = $160,000
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