Question

c. [7.5 marks] The city council is considering the purchase of a new fire truck. The capital investment is $50,000 and the maintenance expenses per year are $6,000. The fire truck has a life of six years and by using this truck there will be an annual reduction in fire damage of $20,000. If the MARR is 12% per year, what is the modified B-C ratio for this truck using the annual worth method? i. 1.15 ii. 0.87 iii. 1.64 iv. 1.41

Answer 1

The correct answer is option i

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Annual worth of benefits - Annual worth of costs Modified B-C ratio = Capitalized cost

Annual worth of benefits = Present worth of benefits $\times$ capital recovery factor

Annual worth of benefits = $ 20,000 $\times$ ( P/A, 12% , 6 years ) $\times$ ( A/P, 12%, 6 years)

( P/A, 12% , 6 years ) = Uniform series present worth factor

( A/P, 12%, 6 years) = Capital recovery factor

Annual worth of benefits = $ 20,000 $\times$ 4.111 $\times$ 0.2432 =  19995.904

Annual worth of costs = $ 6000 $\times$ 4.111 $\times$ 0.2432 =  5998.7712

Capitalized cost = $ 50,000 $\times$ ( A/P, 12%, 6 years)

Capitalized cost = $ 50,000 $\times$ 0.2432 =  12160

Modified B-C ratio = 19995.904 5998.7712 12160

Modified B-C ratio = 1.15