Question

One year ago, your company purchased a machine used in manufacturing for $90,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $140,000 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 $40,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $20,000 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 $8,182 per year. The market value today of the current machine is $45,000. Your company's tax rate is 35%, and the opportunity cost of capital for this type of equipment is 10%Should your company replace its year-old machine?

The NPV of replacing the year-old machine is

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Answer 1

Book value = (purchase price)*remaining life/total life
= (90000)*10/11
= 81818.18

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	29250
Tax shield on existing asset book value	=Book value * tax rate	28636.363
Cost of new machine		-140000
=Initial Investment outlay		-82113.637
													100.00%
Profits			20000	20000	20000	20000	20000	20000	20000	20000	20000	20000
-Depreciation	Cost of equipment/no. of years		-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	0	=Salvage Value
=Pretax cash flows			6000	6000	6000	6000	6000	6000	6000	6000	6000	6000
-taxes	=(Pretax cash flows)*(1-tax)		3900	3900	3900	3900	3900	3900	3900	3900	3900	3900
+Depreciation			14000	14000	14000	14000	14000	14000	14000	14000	14000	14000
=after tax operating cash flow			17900.00	17900.00	17900	17900	17900	17900	17900	17900	17900	17900
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-82113.637	17900	17900	17900	17900	17900	17900	17900	17900	17900	17900
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051	1.771561	1.9487171	2.1435888	2.357948	2.593742
Discounted CF=	Cashflow/discount factor	-82113.637	16272.727	14793.388	13448.535	12225.941	11114.492	10104.083	9185.530316	8350.4821	7591.347	6901.225
NPV=	Sum of discounted CF=	27874.11