Question

Answer the following multiple-choice question. You have to select the correct option and provide a complete correct solution.

c. 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

Investment = $ 50,000

Annual maintenance expense = $ 6,000

Useful life = 6 years

Annual saving = $ 20,000

MARR = 12%

The modified BCR can be calculated using the following formula

$\large BCR = \frac{AW_B - D - AW_{MC}}{AW_C}$

Calculating the annual worth of capital investment

$\large AW_C = 50,000(A/P,12\%,6) = 50,000\times \frac{0.12}{1-1.12^{-6}}\approx\$ \ 12,161.29$

Annual worth of benefit = $ 20,000

Annual maintenance cost = $ 6,000

Plug in these values in the BCR equation we get

$\large BCR = \frac{20,000 - 6,000}{12,161.29} \approx 1.15$

Modified Benefit Cost Ratio = 1.15

First option is correct.

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