Question

One year​ ago, your company purchased a machine used in manufacturing for $ 120, 000. You have learned that a new machine is available that offers many advantages and you can purchase it for $ 140, 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 $ 60,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $ 23,000 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 $ 10,909 per year. The market value today of the current machine is $ 45,000. Your​ company's tax rate is 45 %​, and the opportunity cost of capital for this type of equipment is 10 %. Should your company replace its​ year-old machine?

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The NPV of replacing the​ year-old machine is (...) ​(Round to the nearest​ dollar.)

Answer 1

Calculation of NPV of replacing the old machine:

Net Initial Investment = Cost of new machine- sale proceeds of old machine +/- tax on sale proceeds

Cost of new machine = $140000

Sale proceeds of old machine = $45000

Book value of machine = $109091

Tax proceedings on sale proceedings= (45000-109091)*45%= $(28841)

Net Investment = $140000-$45000-$28841 = $66159

Incremental cash flows from year 1 to 10 :

Incremental revenue = $60000-$23000 = $37000

Incremental depreciation =$14000-$10909 =$3091

Net Incremental cash flows = (Incremental revenue- Incremental depreciation)*(1- tax rate) + incremental depreciation

= ($37000 - $3091)*(1-0.45) + $3091

= $ 21741

Net cash inflow for year 1 to 10 = Annual inflow * PV of annuity factor of 10% for 10 years

= $ 21741*6.1446

= $ 133590

NPV of replacing the old machine = PV of net cash inflows - net outflows

= $133590 - $66159

= $67431

Hence it is advisable to replace the old machine since the NPV is positive.

NPV of replacing the old machine = $67431