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One year ago: your company purchased a machine used in manufacturing for dollar 95:000. You have learned that a new machine is available that offers many advantages and you can purchase it for dollar 150,000 today. It will be depreciated on a straight-line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin (revenues minus operating expenses other than depreciation) of dollar 35:000 per year for the next 10 years. The current machine is expected to produce a gross margin of dollar 24:000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, and has no salvage value, so depreciation expense for the current machine is dollar 8,636 per year. The market value today of the current machine is dollar 45,000. Your company's tax rate is 40 percent, and the opportunity cost of capital for this type of equipment is 10percent. Should your company replace its year-old machine? The NPV of replacing the year-old machine is $. (Round to the nearest dollar.)

Explanation / Answer

We'll do an incremental analysis for replacing old machine with new one.

Incremental initial cost = New machine purchase cost - Old machine market value

= $150,000 - $45,000 = $105,000

Incremental depreciation = [$150,000 / 10] - $8,636 = $(15,000 - 8,636) = $6,364

Incremental Net income = (Incremental gross margin - Incremenal depreciation) x (1 - Tax rate)

= $[(35,000 - 24,000) - 6,364] x (1 - 0.4)

= $4,636 x 0.6

= $2,782

Incremental cash flow = Incremental net income + Incremental depreciation

[Since depreciation is non-cash expense, it's added to net income to arrive at cash flow after taxes (CFAT)]

= $2,782 + $6,364 = $9,146

Therefore:

Incremental NPV ($) = - 105,000 + 9,146 x Present value interest factor of annuity, PVIFA (10%, 10 years)

= - 105,000 + 9,146 x 6.1446 (From PVIFA table)

= - 105,000 + 56,199

Incremental NPV ($) = - 48,801

Since NPV < 0, old machine should not be replaced.

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