Question

One year​ ago, your company purchased a machine used in manufacturing for $ 115 comma 000. You have learned that a new machine is available that offers many advantages and you can purchase it for $ 145 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 $ 50 comma 000 per year for the next 10 years. The current machine is expected to produce a gross margin of $ 25 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 455 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 11 %. Should your company replace its​ year-old machine?

I have done this problem four times and can't get the answer correct. I think my math is wrong somewhere but I'm not finding it

Answer 1

Analysing the given problem from Incremental NPV standpoint. Hence we compute the after tax cashflow from sale of current machine and consider it as a part of Initial incremental cashflows.

Depreciation computation - Current machine

Purchase value	115,000.00
Useful life (in years)	11.00
Depreciation for year 1	10,454.55
Closing book value at the end of year 1	104,545.45

Depreciation computation - New machine

Purchase price	145,000.00
Useful life (in years)	10.00
Depreciation	14,500.00

Incremetal cashflow computation

Sale value of current machine	50,000.00
Less : Closing book value at the end of year 1	104,545.45
Profit / Sale from current machine	(54,545.45)
Less : Tax @ 45%	(24,545.45)
After tax profit / loss from sale of current macine	(30,000.00)
Add : Closing book value at the end of year 1	104,545.45
After tax cashflow from sale of current machine	74,545.45
Initial outlay to purchase new machine	(145,000.00)
Total Initial cashflows (After tax cashflow from sale of current machine + Initial outlay to purchase new machine	(70,454.55)

Incremental Intermediate cashflows

Details	Current machine	New machine
Gross margin	25,000.00	50,000.00
Less : Depreciation	10,454.55	14,500.00
Profit before tax	14,545.45	35,500.00
Less : Tax @ 45%	6,545.45	15,975.00
Profit after tax	8,000.00	19,525.00
Add : Depreciation	10,454.55	14,500.00
Cashflow after taxes	18,454.55	34,025.00
Net incremental cashflow after taxes (Net of cashflows from current and new machines)	15,570.45

Computation of Incremental NPV

Year	0	1-10
Incremental Initial cashflows	(70,454.55)
Incremental Intermediate cashflows		15,570.45
Net cashflows	(70,454.55)	15,570.45
PV factor @ 11% ---> Year 0 ---> 1/(1+11%)^year0 Year 1-10 (annuity formula) ---> (1-(1+11%)^-10)/11%	1	5.889232
PV of cashflows (Net cashflows x PV factor)	(70,454.55)	91,698.02
Net Present Value	21,243.47

Since Incremental cashflow of purchasing a new machine is positive it is beneficial to Purchase the new machine.

I hope this solves your question.

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