Question

One year​ ago, your company purchased a machine used in manufacturing for $115,000. You have learned that a new machine is available that offers many​ advantages; you can purchase it for $140,000 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 $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 $10,455 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 45%​, and the opportunity cost of capital for this type of equipment is 10%. Is it profitable to replace the​ year-old machine?

The NPV of the replacement is ​$____. ​(Round to the nearest​ dollar.)

Answer 1

current book value of old machine = purchase price-1 year depreciation = 115000-10455=104545

incremental EBIDTA = EBIDTA new machine-EBIDTA old machine = 60000-22000=38000

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	27500
Tax shield on existing asset book value	=Book value * tax rate	47045.25
Cost of new machine		140000
=Initial Investment outlay		214545.25
Incremental EBIDTA			38000	38000	38000	38000	38000	38000	38000	38000	38000	38000
-Depreciation	Cost of equipment/no. of years		14000	14000	14000	14000	14000	14000	14000	14000	14000	14000
=Pretax cash flows			52000	52000	52000	52000	52000	52000	52000	52000	52000	52000
-taxes	=(Pretax cash flows)*(1-tax)		28600	28600	28600	28600	28600	28600	28600	28600	28600	28600
+Depreciation			-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000
=after tax operating cash flow			14600	14600	14600	14600	14600	14600	14600	14600	14600	14600
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		214545.25	14600	14600	14600	14600	14600	14600	14600	14600	14600	14600
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051	1.771561	1.948717	2.14359	2.357948	2.593742
Discounted CF=	Cashflow/discount factor	214545.25	13272.72727	12066.1157	10969.196	9971.9964	9065.4513	8241.3194	7492.109	6811.01	6191.825	5628.932
NPV=	Sum of discounted CF=	304255.93

NPV is positive hence it is profitable