Question

In: Finance

"Machine A has an immediate cost of $13,000, and it will earn a net income of...

"Machine A has an immediate cost of $13,000, and it will earn a net income of $6600 per year for a total of 7 years. Machine B has an immediate cost of $24,000, and it will earn a net income of $4600 per year for a total of 28 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 14.8%. If neither machine is acceptable, enter 0."

Expert Solution

Machine A

Yearly net income = Equivalent Annual Benefit, EAB = $6,600

Cost of Machine = $13,000

number of years for which income is earned = 7

Equivalent Annual Cost of the machine can be calculated by dividing the initial cost by an annuity factor calculated using PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = interest rate = 14.8%

number of periods = 7

payment amount = 1

future value = 0

when-due = when is the income received each year = end = 0

PV = PV(14.8%, 7, 1, 0, 0) = 4.1855

Equivalent Annual Cost = 13000/4.1855 = $3,105.96

Equivalent Annual Worth = EAB - EAC = $6,600 - $3,105.96 = $3,494.04

Machine B

Yearly net income = Equivalent Annual Benefit, EAB = $4,600

Cost of Machine = $24,000

number of years for which income is earned = 28

Equivalent Annual Cost of the machine can be calculated by dividing the initial cost by an annuity factor calculated using PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = interest rate = 14.8%

number of periods = 28

payment amount = 1

future value = 0

when-due = when is the income received each year = end = 0

PV = PV(14.8%, 28, 1, 0, 0) = 6.6151

Equivalent Annual Cost = 24000/6.6151 = $3,628.09

Equivalent Annual Worth = EAB - EAC = $4,600 - $3,628.09 = $971.91

Machine A is a better alternative and the equivalent annual worth of the machine is $3,494.04

jeff jeffy answered 1 year ago

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