Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,260,000; the new one will cost $1,520,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $260,000 after five years.

The old computer is being depreciated at a rate of $252,000 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 $380,000; in two years, it will probably be worth $116,000. The new machine will save us $286,000 per year in operating costs. The tax rate is 35 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.)

	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.)

NPV

$

Answer 1

a)	OLD MACHINE:
	Initial cost (the after tax sale value now, being the opportunity cost of using the old machine) =-((380000-(380000-252000*3)*35%)) =	$     -5,11,600.00
	PV of depreciation tax shield for 2 years = 252000*35%*(1.1^2-1)/(0.1*1.1^2) =	$       1,53,074.38
	PV of after tax salvage at EOY 2 = [116000-(116000-252000)*35%]/1.1^2 =	$       1,55,338.84
	NPV of old machine	$     -2,03,186.78
	EAC = -203187*0.1*1.1^2/(1.1^2-1) =	$     -1,17,074.29
b)	Initial cost	$   -15,20,000.00
	PV of after tax savings in operating costs = 304000*(1-35%)*(1.1^5-1)/(0.1*1.1^5) =	$       7,49,059.47
	PV of depreciation tax shield = (1520000/5)*35%*(1.1^5-1)/(0.1*1.1^5) =	$       4,03,339.71
	PV of after tax salvage value = 260000*(1-35%)/1.1^5 =	$       1,04,935.70
	PV of new machine	$     -2,62,665.12
	EAC = -262665*0.1*1.1^5/(1.1^5-1) =	$         -69,290.40
c)	NPV of replacement:
	NPV of new computer	$     -2,62,665.12
	NPV of old computer	$     -2,03,186.78
	NPV of replacement	$         -59,478.34