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Answer:
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a. B-C ratio = Equivalent annual worth of Benefits / Equivalent annual worth of costs
<u>Alternative A</u>
B-C ratio = Equivalent annual worth of Benefits for alternative A / Equivalent annual worth of costs for alternative A
B-C ratio = (Power Sales + Annual benefits from new industry) / ((Capital cost * Annuity factor(5%,50 years)) + Operating and maintenance costs costs)
B-C ratio = ($1,000,000 + $500,000) / (($20,000,000*(0.05 / (1 - 1.05^(-50))) + $200,000)
B-C ratio = ($1,500,000 / ($1,095,534.71 + $200,000))
B-C ratio = $1,500,000 / $1,295,534.71
B-C ratio = 1.1578
B-C ratio = 1.16
<u>Alternative B</u>
B-C ratio = Equivalent annual worth of Benefits for alternative B / Equivalent annual worth of costs for alternative B
B-C ratio = (Power Sales + Sum of all Annual benefits) / ((Capital cost*Annuity factor (5%,50 years)) + Operating and maintenance costs costs)
B-C ratio = ($800,000 + $600,000 + $400,000 + $200,000 + $100,000) / ($30000000 *(0.05/(1-1.05^(-50))) + $100,000)
B-C ratio = $2,100,000 / ($1,643,302 + $100,000)
B-C ratio = 1.2046
B-C ratio = 1.20
Conclusion: Alternative B should be selected because it has higher B/C ratio.
b Incremental B-C ratio for final pair = (Equivalent Annual Benefits of B - Equivalent Annual Benefits of A) / (Equivalent annual costs of B - Equivalent annual costs of A)
Incremental B-C ratio for final pair = ($2,100,000 - $1,500,000) / ($1,743,302 - $1,295,534.71)
Incremental B-C ratio for final pair = $600,000 / $447,767.29
Incremental B-C ratio for final pair = 1.339982
Incremental B-C ratio for final pair = 1.34
