Question

One year​ ago, your company purchased a machine used in manufacturing for $ 110 comma 000. You have learned that a new machine is available that offers many advantages and you can purchase it for $ 150 comma 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 comma 000 per year for the next 10 years. The current machine is expected to produce a gross margin of $ 20 comma 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 $ 10 comma 000 per year. The market value today of the current machine is $ 50 comma 000. Your​ company's tax rate is 45 %​, 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 ​$_

Answer 1

NPV is the difference between sum of present value of incremental cash flows and initial investment or net cash outflow at year 0.

sum of present value of incremental cash flows = year 1 incremental cash flow/(1+cost of capital) + year 2 incremental cash flow/(1+cost of capital)² + year 3 incremental cash flow/(1+cost of capital)³ ... + year 10 incremental cash flow/(1+cost of capital)¹⁰

Tax on salvage value of current machine = (salvage value - book value)*tax rate = ($50,000 - $100,000)*45% = -$50,000*45% = -$22,500

original cost of current machine was $110,000 and depreciation is $10,000. after one year book value is $110,000 - $10,000 = $100,000.

The NPV of replacing the​ year-old machine is ​$3,915.51. your company should replace its​ year-old machine because NPV of replacement is positive.

	Years	0	1	2	3	4	5	6	7	8	9	10
	Cost of New machine	-$150,000
	Gross Margin on new machine	$0	$40,000	$40,000	$40,000	$40,000	$40,000	$40,000	$40,000	$40,000	$40,000	$40,000
Less:	Gross Margin on current machine	$0	$20,000	$20,000	$20,000	$20,000	$20,000	$20,000	$20,000	$20,000	$20,000	$20,000
Less:	Depreciation on new machine	$0	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000
Plus:	Depreciation on current machine	$0	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000
	Margin before tax	$0	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000
Less:	Taxes @ 45%	$0	$6,750	$6,750	$6,750	$6,750	$6,750	$6,750	$6,750	$6,750	$6,750	$6,750
	Margin after tax	$0	$8,250	$8,250	$8,250	$8,250	$8,250	$8,250	$8,250	$8,250	$8,250	$8,250
Plus:	New Depreciation	$0	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000
Less:	Old Depreciation	$0	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000	$10,000
Plus:	Salvage value of current machine	$50,000	$0	$0	$0	$0	$0	$0	$0	$0	$0	$0
Less:	Tax on Salvage value	-$22,500	$0	$0	$0	$0	$0	$0	$0	$0	$0	$0
	Incremental cash flows	-$77,500	$13,250	$13,250	$13,250	$13,250	$13,250	$13,250	$13,250	$13,250	$13,250	$13,250
	NPV of replacement	$3,915.51

Calculations