Question

One year​ ago, your company purchased a machine used in manufacturing for $95,000.You have learned that a new machine is available that offers many advantages and you can purchase it for $170,000 today. It will be depreciated on a​ straight-line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin​ (revenues minus operating expenses other than​ depreciation) of $50,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $22,000 per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, and has no salvage​ value, so depreciation expense for the current machine is $8,636 per year. The market value today of the current machine is $60,000. Your​ company's tax rate is 38 %​, and the opportunity cost of capital for this type of equipment is 12 %.Should your company replace its​ year-old machine?

The NPV of replacing the​ year-old machine is ​? (round to nearest dollar)

Answer 1

Book value old machine = (purchase price)*remaining life/total life
= (95000)*10/11
= 86363.64

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	37200
Tax shield on existing asset book value	=Book value * tax rate	32818.1832
Cost of new machine		-170000
=Initial Investment outlay		-99981.8168
													100.00%
Profits=EBIDTA machine2-EBIDTA machine 1	=50000-22000=		28000	28000	28000	28000	28000	28000	28000	28000	28000	28000
-Depreciation	Cost of equipment/no. of years		-17000	-17000	-17000	-17000	-17000	-17000	-17000	-17000	-17000	-17000	0	=Salvage Value
=Pretax cash flows			11000	11000	11000	11000	11000	11000	11000	11000	11000	11000
-taxes	=(Pretax cash flows)*(1-tax)		6820	6820	6820	6820	6820	6820	6820	6820	6820	6820
+Depreciation			17000	17000	17000	17000	17000	17000	17000	17000	17000	17000
=after tax operating cash flow			23820.00	23820.00	23820	23820	23820	23820	23820	23820	23820	23820
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-99981.8168	23820.00	23820.00	23820.000	23820	23820	23820	23820	23820	23820	23820
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	-99981.8168	21267.85714	18989.15816	16954.6055	15138.041	13516.108	12067.953	10774.95831	9620.4985	8589.731	7669.402
NPV=	Sum of discounted CF=	34607