One year ago, your company purchased a machine used in manufacturing for $120, 0
ID: 2738136 • Letter: O
Question
One year ago, your company purchased a machine used in manufacturing for $120, 000. You have learned that a new machine is available that offers many advantages; you can purchase it for $160, 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, 000 per year for the next ten years. The current machine is expected to produce EBITDA of $21,000 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 $ 10,909 per year. The current machine can be sold today for a market value of $50, 000. Your company's tax rate is 42%, and the opportunity cost of capital for this type of equipment is 12%. Is it profitable to replace the year-old machine? The NPV of the replacement is. (Round to the nearest dollar.) Should your company replace its year-old machine? (Select the best choice below.) Yes, there is a profit from replacing the machine. No, there is a loss from replacing the machine.Explanation / Answer
Replacing the machine increases EBITDA by $60,000 – $21,000 = $39,000.
Annual depreciation for new machine = $160,000/10 years = $16,000
Depreciation expenses rises by = $16,000 – $10,909 = $5,091.
Incremental annual free cash flows for 10 years = Incremental EBITDA * (1-tax rate) + Incremental depreciation * tax rate = ($39,000*0.58) + ($5,091*0.42) = $24,758.22
Present value of annuity of $1 = {1-(1+r)-n}/r = (1-1.12-10)/0.12 = 2.6831
Present value of free cash flows = $24,758.22 * 2.6831 = $66,429.04
In year 0, the initial cost of the machine is $160,000. Because the current machine has a book value of
$120,000 – $10,909 (one year of depreciation) = $109,091, selling it for $50,000 generates a capital gain of $50,000 – $109,091 = –$59,091. This loss produces tax savings of 0.42 × $59,091 = $24,818.22, so that the after-tax proceeds from the sales including this tax savings is $50,000 + $24,818.22 = $74,818.22. Thus, the FCF in year 0 from replacement is –$160,000 + $74,818.22 = –$85,181.78
NPV of replacement = -$85,181.78 + $66,429.04 = -$18,752.74 from replacing the machine.
B.
There is loss from replacing the machine. Hence, Machine should not be replaced.
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