Question

One year​ ago, your company purchased a machine used in manufacturing for $ 110,000. You have learned that a new machine is available that offers many​ advantages; you can purchase it for $ 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 $ 45,000 per year for the next ten years. The current machine is expected to produce EBITDA of $ 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 $ 10,000 per year. All other expenses of the two machines are identical. The market value today of the current machine is $ 50,000. Your​ company's tax rate is 38 %​, and the opportunity cost of capital for this type of equipment is 12 %. Is it profitable to replace the​ year-old machine?

Answer 1

BV of old machine

Book value = (purchase price)*remaining life/total life
= (110000)*10/11
= 100000

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	31000
Tax shield on existing asset book value	=Book value * tax rate	38000
Cost of new machine		-150000
=Initial Investment outlay		-81000
													100.00%
Incremental ebidta =	45000-22000=		23000	23000	23000	23000	23000	23000	23000	23000	23000	23000
			23000	23000	23000	23000	23000	23000	23000	23000	23000	23000
-Depreciation	Cost of equipment/no. of years		-15000	-15000	-15000	-15000	-15000	-15000	-15000	-15000	-15000	-15000	0	=Salvage Value
=Pretax cash flows			8000	8000	8000	8000	8000	8000	8000	8000	8000	8000
-taxes	=(Pretax cash flows)*(1-tax)		4960	4960	4960	4960	4960	4960	4960	4960	4960	4960
+Depreciation			15000	15000	15000	15000	15000	15000	15000	15000	15000	15000
=after tax operating cash flow			19960	19960	19960	19960	19960	19960	19960	19960	19960	19960
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-81000	19960	19960	19960	19960	19960	19960	19960	19960	19960	19960
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544	1.404928	1.5735194	1.7623417	1.9738227	2.210681407	2.4759632	2.773079	3.105848
Discounted CF=	Cashflow/discount factor	-81000	17821.42857	15911.99	14207.134	12684.941	11325.84	10112.357	9028.890338	8061.5092	7197.776	6426.586
NPV=	Sum of discounted CF=	31778.45165

Replace old machine as NPV is positive