Question

One year ago, your company purchased a machine used in manufacturing for $100,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $155,000 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 $55,000 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 $9,091 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 12%. Should your company replace its year-old machine?

a. The NPV of replacing the year-old machine is (Round to the nearest dollar.)

b. Should your company replace its year-old machine?  

Answer 1

Cost of current machine	100,000.00
Cost of new machine	155,000.00
Life of current machine (in years)	11.00
Life of new machine (in years)	10.00
Gross margin of new machine	55,000.00
Gros margin of current machine	22,000.00
Market value of current machine	45,000.00
Tax rate	35%
Cost of capital	12%

Book value of current machine

Cost of current machine	100,000.00
Less : Depreciation of 1st year ---> Cost / useful file ---> 100000/11	9,091.00
Book value of current machine	90,909.00

Cashflows from sale of current machine

Market value of current machine	45,000.00
Less : Book value of current machine	90,909.00
Loss on sale of current machine	(45,909.00)
Less : Tax @ 35%	(16,068.15)
After tax loss on sale of current machine	(29,840.85)
Add : Book value of current machine	90,909.00
After tax cashflows on sale of current machine	61,068.15

Depreciation of new machine

Cost of new machine	155,000.00
Useful life	10.00
Depreciation of new machine ---> Cost/ useful life	15,500.00

Incremental Initial cashflows

Cost of new machine	(155,000.00)
Cashflows from sale of current machine	61,068.15
Total incremental initial cashflows	(93,931.85)

Incremental Operating cashflows

	Current machine	New machine	Incremental cashflows
Gross margin	22,000.00	55,000.00	33,000.00
Less : Depreciation	9,091.00	15,500.00	6,409.00
Profit before taxes	12,909.00	39,500.00	26,591.00
Less : Tax @ 35%	4,518.15	13,825.00	9,306.85
Profit after taxes	8,390.85	25,675.00	17,284.15
Add : Depreciation	9,091.00	15,500.00	6,409.00
Cashflows after tax	17,481.85	41,175.00	23,693.15

NPV computation

Year	0	1-10
Incremental Initial cashflows	(93,931.85)
Incremental operating cashflows		23,693.15
Net cashflows	(93,931.85)	23,693.15
PV factor @ 12% --> Year 0 --> 1/(1+12%)^nth year; Year 1-10 ---> (1-(1+12%)^-10)/12%	1.00	5.65
PV of cashflows	(93,931.85)	133,871.58
NPV	39,939.73

Since NPV of replacing year old machine is positive, company can consider replacing the year old machine.

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