One year ago, your company purchased a machine used in manufacturing for 110,000.00. You have learned that a new machine is available that offers many advantages; you can purchase it for 116,000.00 today. It will be depreciated on a straight-line basis over 10 years, after which it has a salvage value of 16,000.00. You expect that the new machine will produce additional EBITDA (earnings before interest, taxes, depreciation, and amortization) of 31,000.00 per year for the next 10 years. The current machine is expected to produce EBITDA of 19,000.00 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 a salvage value of 0.00, so depreciation for the current machine is 10,000.00 per year. All other expenses for the two machines are identical. The market value today of the current machine is 33,000.00. Your company's tax rate is 31%, and the opportunity cost of capital for this type of equipment is 14%.

What is the NPV of replacing the year-old machine?

 

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SOLUTION:

Replacing the machine increases EBITDA by 31,000.00 - 19,000.00 = 12,000.00. Depreciation expenses rises by 11,600.00 - 10,000.00 = 1,600.00.
Therefore, FCF will increase by (12,000.00) * (1-0.31) + (0.31)(1,600.00) = 8,776.00 in years 1 through 10.

In year 0, the initial cost of the new machine is 116,000.00. Because the current machine has a book value of 110,000.00 - 0.00 (total years of depreciation) = 100,000.00, selling it for 33,000.00 generates a capital gain of 33,000.00 - 100,000.00 = -67,000.00. This produces tax savings of 0.31 * 67,000 = 0.00, so that the after-tax proceeds from the sales including this tax savings is 33,000.00. Thus, the FCF in year 0 from replacement is -116,000 + 33,000.00 = -83,000.00.

NPV of replacement = PV of Cash Inflows - Initial Outlay
Since the annual cash flows are the same, you can treat this as an annuity. This means that you can use the TVM functions on your calculator (N=10,I=14,PV=??,PMT=8,776.00,FV=0) or you can use the annuity formula.

NPV of replacement = -83,000.00 + 8,776.00 * (1 / 0.14)(1 - 1 / (1+0.14)^10) = -37,223.37.

Since the NPV is negative, you WOULD NOT replace the project.