\"Machine A has an immediate cost of $12,000, and it will earn a net income of $

Question

"Machine A has an immediate cost of $12,000, and it will earn a net income of $5100 per year for a total of 5 years. Machine B has an immediate cost of $19,000, and it will earn a net income of $4000 per year for a total of 20 years. Assume that Machine A can continually be replaced at the end of its useful life with an identical replacement. Neither machine has any salvage value. Enter the annual equivalent worth of the machine that is the best alternative if the interest rate is 8.8%. If neither machine is acceptable, enter 0."

Explanation / Answer

Annual Worth (AW) of both machines is computed as follows.

AW, Machine A ($) = - 12,000 x A/P(8.8%, 5) + 5,100 = - 12,000 x 0.2558** + 5,100 = - 3,069.6 + 5,100 = 2,030.4

AW, Machine B ($) = - 19,000 x A/P(8.8%, 20) + 4,000 = - 19,000 x 0.108** + 4,000 = - 2,052 + 4,000 = 1,948

Since Machine A has a higher AW of net revenue, Machine A is selected with AW = $2,030.4.

**A/P(r%, N) = 1 / [P/A(r%, N)] = 1 / {[1 - (1 + r)-N] / r} = r / [1 - (1 + r)-N]

A/P(8.8%, 5) = 0.088 / [1 - (1.088)-5] = 0.088 / (1 - 0.6559) = 0.088 / 0.3441 = 0.2558

A/P(8.8%, 20) = 0.088 / [1 - (1.088)-20] = 0.088 / (1 - 0.1851) = 0.088 / 0.8149 = 0.1080

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