A company is trying to decide between two machines for its manufacturing line. T

Question

A company is trying to decide between two machines for its manufacturing line. The Process1000 has an initial cost of $54758 and operating costs of $13 per hour. It will allow the company to produce a higher quality product, providing an annual benefit of $85246. The company will use the Process1000 11859 hours per year. The Process1000 has a useful life 3 years and an estimated salvage value of $18731 at the end of its useful life The Super X has an initial cost of $74773. It is a bigger machine and can process more at a time so the company will ony need to use it for 7574 hours per year. The Super X has an estimated benefit of $89277 per year. The Super X will have a useful life of 8 years and a salvage value of $29611 at the end of its useful life. Using a MARR of 2%, what is the maximum operating cost per hour at which the Super X could run to make it equally desirable to the Process1000? Enter your answer as follows: 12.34 Round your answer to 2 decimal places. Do not use a dollar sign ("$") or any commas

Explanation / Answer

Both the machines are having different lives, so we need to compute the Equivalent Annual Costs (EAC). For Super X to be indifferent, its EAC needs to be equal to the EAC of Process1000.

Process1000 - EAC

Annual Operating Costs = 11,859 Hours per year @ 13 per hour = 154167

Annual benefit = 85246

Net Operating Costs = 154167 - 85,246 = 69921

EAC = PV of Cash Outflows / Cumulative PVF (2%, 3years)

Or, EAC = 238751.362656 / 2.88388327262 = 82788.1505894

Super X

Let the operating cost per hour be 'p'.

Annual operating Costs = 7574 hours x p = 7574p

Net operating costs = 7574p - 89277

For the machines to be indifferent -

EAC of Process1000 = EAC of Super X

Or, 82788.1505894 = PV of Cash Outflows / Cumulative PVF (2%, 8years)

Or, 82788.1505894 = (55483.1964286p - 604496.709923) / 7.32548144028

Or, 55483.1964286p - 604496.709923 = 606463.060617

Or, 55483.1964286p = 1210959.77054

Or, p = 21.8257030684 or 21.83

I am not sure how much you needed the intermediate answers to be rounded off, so I did not round off the intermediate calculations. Hope this helps!

Present Value of Cash Outflows Particulars Year PVF@2% Amount Present Value Initial Cost 0 1 54758 54758 Add: Annual net operating Costs 1-3 2.88388327262 69921 201644.002304 Less: Salvage Value 3 0.94232233453 18731 17650.639648 PV of Cash Outflows 238751.362656

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