A nonprofit government corporation is considering two alternatives for generatin

Question

A nonprofit government corporation is considering two alternatives for generating power: Alternative A. Build a coal-powered generating facility at a cost of $20000000. Annual power sales are expected to be $1000000 per year. Annual operating and maintenance costs are $200000 per year. A benefit of this alternative is that it is expected to attract new industry, worth $500000 per year, to the region. Alternative B. Build a hydroelectric generating facility. The capital investment, power sales, and operating costs are $30000000, $800000, and $100000 per year, respectively. Annual benefits of this alternative are as follows. Flood-control savings Irrigation Recreation Ability to attract new industry $600,000 $200,000 $100,000 400,000 The useful life of both alternatives is 50 years. Using an interest rate of 5%, determine which alternative (if either should be selected according to the conventional B-C ratio method. a) Which alternative should be analyzed first, comparing to the do-nothing baseline? b) Which alternative should be selected because the incremental B-C ratio for the final pair is (please keep two decimal place)

Explanation / Answer

B-C ratio = Equivalent annual worth of Benefits / Equivalent annual worth of costs

Annuity factor (i,n) = i/ (1- (1+i)^-n) where i = interest rate and n = number of years

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For Alternative A,

B-C ratio = Equivalent annual worth of Benefits for alternative A / Equivalent annual worth of costs for alternative A

= (Power Sales + Annual benefits from new industry)/ ((Capital cost * annuity factor(5%,50 years))+ O&M costs)

= ($1000000 + $500000)/ (($20000000 * (0.05/(1- 1.05-50)) + $200000)

= ($1500000/ ($1095534.71 + $200000)) = 1.1578 ~ = 1.16

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For Alternative B,

B-C ratio = Equivalent annual worth of Benefits for alternative B / Equivalent annual worth of costs for alternative B

= (Power Sales + Sum of all Annual benefits)/ ((Capital cost * annuity factor (5%,50 years)) + O&M costs)

= ($800000 + $600000 + $400000 + $200000 + $100000)/ ($30000000 * (0.05/(1-1.05-50)) + $100000)

= $2100000 / ($1643302 + $100000) = 1.2046 ~ = 1.20

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Alternative B should be selected as it has higher B-C ratio. Only B-C ratio less than 1 is unfavorable therefore both projects when not comparing can be accepted.

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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

= $2100000 - $1500000/ $1743302 - $1295534.71

= 1.34

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