Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,250,000; the new one will cost $1,510,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $250,000 after five years.

The old computer is being depreciated at a rate of $250,000 per year. It will be completely written off in three years. If we don’t replace it now, we will have to replace it in two years. We can sell it now for $370,000; in two years, it will probably be worth $115,000. The new machine will save us $285,000 per year in operating costs. The tax rate is 25 percent and the discount rate is 12 percent.

a.	Calculate the EAC for the old computer and the new computer. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

    

b.	What is the NPV of the decision to replace the computer now? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

    

Answer 1

		OLD MACHINE
		Current Book value of old machine	$750,000	(250000*3)
		Book value of old machine after2 years	$250,000
		Current Salvage value	$370,000
		Salvage value after 2 years	$115,000
		Loss on salvage now	$380,000	(750000-370000)
		Tax saving on salvage	$95,000	(380000*0.25)
		Total expected cash flowCash on salvage now	$465,000	(370000+95000)
		Loss on salvage after 2 years	$135,000	(250000-115000)
		Tax saving on salvage	$33,750	(135000*0.25)
		Total expected cash flowCash on salvage in 2 years	$148,750	(115000+33750)
		annual Depreciation	$250,000
		Depreciation tax shield	$62,500	(250000*0.25)
		CASH FLOW
	N	Year	0	1	2
	A	Opportunity cost of not selling	($465,000)
	B	Salvage value after 2 years			$148,750
	C	Depreciation tax shield		$62,500	$62,500
	D=A+B+C	Net cash Flow	($465,000)	$62,500	$211,250	SUM
	E=D/(1.12^N)	Present Value of cash flow(discount rate 12%)	($465,000)	$55,804	$168,407	($240,789)
		Net Present Value of cash flow	($240,789)
		Equivalent Annual Cost (EAC)	($142,475)	(Using PMT function of excelwith Rate =12%, Nper=2, Pv=240789)
		NEW MACHINE
		Salvage value after 5 years	$250,000
		Gain on salvage	$250,000
		Tax saving on salvage	$62,500	(250000*0.25)
		After tax salvage value	$187,500
		annual Depreciation	$302,000	(1510000/5)
		Depreciation tax shield	$75,500	(302000*0.25)
		CASH FLOW
	N	Year	0	1	2	3	4	5
	A	Cost of machine	($1,510,000)
	B	Salvage value after 5 years						$187,500
	C	Depreciation tax shield		$75,500	$75,500	$75,500	$75,500	$75,500
	D	After tax savings(285000*(1-0.25))		$213,750	$213,750	$213,750	$213,750	$213,750
	E=A+B+C+D	Net cash Flow	($1,510,000)	$289,250	$289,250	$289,250	$289,250	$476,750	SUM
	F=E/(1.12^N)	Present Value of cash flow(discount rate 12%)	($1,510,000)	$258,259	$230,588	$205,882	$183,824	$270,521	($360,926)
		Net Present Value of cash flow	($360,926)
		Equivalent Annual Cost (EAC)	($100,124)	(Using PMT function of excelwith Rate =12%, Nper=5, Pv=213559)
	b	CLCULATION OF NPV of NEW MACHINE
	N	Year	0	1	2	3	4	5
	A	Cost of machine	($1,510,000)
	B	After tax salvage value of old machine	$465,000
	C	Salvage Value after5 years						$187,500
	D	Depreciation tax shield		$75,500	$75,500	$75,500	$75,500	$75,500
	E	After tax savings		$213,750	$213,750	$213,750	$213,750	$213,750
	F=A+B+C+D+E	Net Cash Flow	($1,045,000)	$289,250	$289,250	$289,250	$289,250	$476,750	SUM
	G=F/(1.12^N)	Present Value of Cash Flow	($1,045,000)	$258,259	$230,588	$205,882	$183,824	$270,521	$104,074
		Net Present Value	$104,074