Question

One year​ ago, your company purchased a machine used in manufacturing for $ 110,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $ 170,000 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 $ 21,000 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 $ 10,000 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 11 %. Should your company replace its​ year-old machine? What is the NPV of replacing the​ year-old machine?

Answer 1

NPV = Present value of cash inflows - Present value of cash outflows

= Present value of savings - present value of costs

= -170,000 + 69750 + [(60,000-21000-17,000+10,000)(1-45%)+7000]*PVAF(11%, 10 years)

= -100,250 + 24600*5.8892

=$44,624.32

Should replace

Note: Purchase cost of old equipment is a sunk cost and hence irrelevant.

Note: Change in Depreciation = 17000 - 10,000 = $7000

Note: Written down value of old machine = 110,000 - 11000 = $100,000

selling price = $45000

Loss on sale = -$55000

Tax savings = 55000*45% = $24,750

After tax salvage value = 45000+24750 = $69,750