Question

One year​ ago, your company purchased a machine used in manufacturing for $ 110 comma 000$110,000. You have learned that a new machine is available that offers many​ advantages; you can purchase it for $ 150 comma 000$150,000 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 $ 60 comma 000$60,000 per year for the next ten years. The current machine is expected to produce EBITDA of $ 22 comma 000$22,000 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 $ 10 comma 000$10,000 per year. All other expenses of the two machines are identical. The market value today of the current machine is $ 50 comma 000$50,000. Your​ company's tax rate is 35 %35%​, and the opportunity cost of capital for this type of equipment is 10 %10%. Is it profitable to replace the​ year-old machine?

Answer 1

Yes, it would be profitable to replace the year old machine because the new machine will provide an NPV of $171916 against the NPV of $5611 of old machine as displayed hereunder:

Formula : NPV = { [ (Yearly inflow - dep.) * (1- tax) + dep. ] * PVIFA(Discount rate , n) } - Initial cash outflow

NPV (OLD) = [ (22000-10000)*(1-0.35) + 10000 ] * pvifa(10%, 11) - 110000 =
NPV (OLD) = [17800] * 6.495 - 110000 =
NPV (OLD) = [17800] * 6.495 - 110000 = 5611
NPV = [ (60000-15000)*(1-0.35) + 15000 ] * pvifa(10%, 10) - (150000-50000) =
NPV = [44250] * 6.145 - (150000-50000) =
NPV = 271916 - (150000-50000) = 171916