One year ago, your company purchased a machine used in manufacturing for 130,000.00. You have learned that a new machine is available that offers many advantages; you can purchase it for 123,000.00 today. It will be depreciated on a straight-line basis over 10 years, after which it has a salvage value of 10,000.00. You expect that the new machine will produce EBITDA (earnings before interest, taxes, depreciation, and amortization) of 33,000.00 per year for the next 10 years. The current machine is expected to produce EBITDA of 13,000.00 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 11,818.18 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 34%, and the opportunity cost of capital for this type of equipment is 16%.
What is the NPV of replacing the year-old machine?
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SOLUTION:
You need to find three things:
- The initial outlay
- The operating cash flows
- The terminal cash flow
Initial Outlay
In year 0, the initial cost of the new machine is 123,000.00.
Because the current machine has a book value of 130,000.00 - 11,818.18 (total years of depreciation) = 118,181.82, selling it for 33,000.00 generates a capital gain of 33,000.00 - 118,181.82 = -85,181.82. This produces tax savings of 0.34 * 85,182 = 28,961.82, so that the after-tax proceeds from the sales including this tax savings is 61,961.82.
Thus, the FCF in year 0 from replacement is -123,000 + 61,961.82 = -61,038.18. This is the initial outlay.
Operating Cash Flows
Replacing the machine increases EBITDA by 33,000.00 - 13,000.00 = 20,000.00 per year.
Depreciation expenses rises by 12,300.00 - 11,818.18 = 481.82 per year.
FCF = (chg in Rev - chg in Costs)*(1-tax rate)+(tax rate)*(chg in Depreciation)
Therefore, FCF will increase by (20,000.00) * (1-0.34) + (0.34)(481.82) = 13,363.82 in years 1 through 10.
Terminal Cash Flow
The terminal cash flow includes anything involved with terminating the project, as well as a recovery of any remaining investment in working capital. Remember, when you sell the machine in the last year, you must consider the taxes on the transaction.
Terminal CF = After tax salvage value = 10,000.00* (1-0.34) = 6,600.00
NPV of replacement = PV of Cash Inflows - Initial Outlay
NPV of replacement = - Cost + PV of the annuity payments + PV of after-tax Salvage value
Since the annual cash flows are the same, you can treat the operating cash flows as an annuity, with a lump sum for the after-tax salvage value in the last year.
This means that you can use the TVM functions on your calculator like this:
(N=10,I=16,PV=??,PMT=13,363.82,FV=6,600.00) = 5,048.30.
You can use the annuity formulas like this:
NPV of replacement = - Cost + PV of the annuity payments + PV of after-tax Salvage value
NPV of replacement = -61,038.18 + 13,363.82 * (1 / 0.16)(1 - 1 / (1+0.16)^10) + 6,600.00 / (1+0.16)^10 = 5,048.30.
Since the NPV is positive, you WOULD replace the project.