Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,290,000; the new one will cost $1,550,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $290,000 after five years. The old computer is being depreciated at a rate of $258,000 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 $410,000; in two years, it will probably be worth $119,000. The new machine will save us $289,000 per year in operating costs. The tax rate is 21 percent and the discount rate is 10 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

a)	OLD MACHINE:
	Initial cost (the after tax sale value now, being the opportunity cost of using the old machine) = 410000-(410000-258000*3)*21% =	$      -4,86,440
	PV of depreciation tax shield for 2 years = 258000*21%*(1.1^2-1)/(0.1*1.1^2) =	$           94,031
	PV of after tax salvage at EOY 2 = [119000-(119000-258000)*21%]/1.1^2 =	$        1,22,471
	NPV of old machine	$      -2,69,938
	EAC = -269938*0.1*1.1^2/(1.1^2-1) =	$      -1,55,536
b)	Initial cost	$    -15,50,000
	PV of after tax savings in operating costs = 289000*(1-21%)*(1.1^5-1)/(0.1*1.1^5) =	$        8,65,475
	PV of depreciation tax shield = (1550000/5)*21%*(1.1^5-1)/(0.1*1.1^5) =	$        2,46,780
	PV of after tax salvage value = 290000*(1-21%)/1.1^5 =	$        1,42,253
	PV of new machine	$      -2,95,492
	EAC = -295492*0.1*1.1^5/(1.1^5-1) =	$          -77,950
c)	NPV of replacement:
	NPV of new computer	$      -2,95,492
	NPV of old computer	$      -2,69,938
	NPV of replacement	$          -25,555