Question

One year​ ago, your company purchased a machine used in manufacturing for $ 90 comma 000. You have learned that a new machine is available that offers many​ advantages; you can purchase it for $ 140 comma 000 today. It will be depreciated on a​ straight-line basis over ten​ years, after which it has no salvage value. You expect that the new machine will contribute EBITDA​ (earnings before​ interest, taxes,​ depreciation, and​ amortization) of $ 35 comma 000 per year for the next ten years. The current machine is expected to produce EBITDA of $ 20 comma 000 per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, after which it will have no salvage​ value, so depreciation expense for the current machine is $ 8 comma 182 per year. All other expenses of the two machines are identical. The market value today of the current machine is $ 50 comma 000. Your​ company's tax rate is 35 %​, and the opportunity cost of capital for this type of equipment is 11 %. Is it profitable to replace the​ year-old machine?

Answer 1

So, difference in EBITDA between old and new machine = 35,000 - 20,000 = 15,000 for 10 years. So after tax amount = 15,000*(1-0.35) = 9,750 for 10 years

The tax benefit due to higher depreciation of new machine = 14,000 ( depreciation of new machine) - 8182(depreciation of old machine) = 5,818 *0.35 = 2,026.3

So, net benefit per year = 2,206.30 + 9,750 = 11,956.30

So, net present value of this for 10 years is calculated in excel as =PV(rate,nper,pmt) =PV(0.11,10,11956.30) = 70,413.42

Net present value of profits from purchase new machine = $ 70,413.42

Since the sale value of the old machine is less than book value, there is no tax on the sale of the old machine.

So, net cost of purchase of new machine = 140,000 - 50,000 = 90,000

So, cost of replacement = $90,000

Since the cost of replacement is higher than the net present value of the old machine, it is not profitable to replace the old machine