Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,210,000; the new one will cost $1,470,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $210,000 after five years.

The old computer is being depreciated at a rate of $242,000 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 $330,000; in two years, it will probably be worth $111,000. The new machine will save us $281,000 per year in operating costs. The tax rate is 40 percent, and the discount rate is 11 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.)

	EAC
New computer	$
Old computer	$

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

a.	EAC for old and New computer
	New computer:
	Cash inflow
	Savings in operating cost after tax=281000*(1-0.40)=168600
	Depreciation tax shield=(1470000/5)*0.40=117600
	Salvage value after tax=210000*(1-0.38)=130200
	Cashoutflow
	Initial cost=1470000
	NPV=-1470000+(168600+117600)*PV factor @11% for 5 years+130200*PV factor @11% for 5th year
	NPV=-1470000+(286200*3.6959)+(130200*0.5935)=-334960
	EAC=NPV/PV factor @11% for 5 years=-334960/3.6959=-90630
	Old Computer:
	Cash inflow
	Depreciation tax shield=242000*0.40=96800
	After tax salvage value in 2 years=Salvage value+(Book value-Salvage value)*Tax
	After tax salvage value in 2 years=111000+(242000-110000)*0.40=163800
	Initial cost will be the opportunity cost of selling the old computer today
	Book value now will be the remaining depreciation=242000*3=726000
	Initial cost=330000+(726000-330000)*0.40=488400
	NPV=-488400+96800*PV factor @11% for 2 years+163800*PV factor @11% for 2nd year
	NPV=-488400+(96800*1.7125)+(163800*0.8116)=-189690
	EAC=NPV/PV factor @11% for 2 years=-189690/1.7125=-110768
	Decision: Replace the old computer with new one today.
b.	Year	New computer	Old Computer	Diference	PV @11%	Present Value
	0	-1470000	-488400	-981600	1	-981600
	1	286200	49400	236800	0.900901	213333.3
	2	286200	49400	73000	0.811622	59248.44
			163800
	3	286200	0	286200	0.731191	209267
	4	286200	0	286200	0.658731	188528.8
	5	286200	0	416400	0.593451	247113.1
		130200
				Net present value		-64109.3
	You should not replace the old computer since NPV is negative.