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

Since the two computers have unequal lives, the correct method to analyze the decision is the EAC. We will begin with the EAC of the new computer.
Using the depreciation tax shield approach, the OCF for the new computer system is:
OCF = ($281,000)(1 – .40) + ($1,470,000/5)(.40) = $286,200

After Tax Salvage Value = 210,000(1-0.4) = 126,000

NPV = -1,470,000 + 286,200 (PVIFA_11%,5) + 126,000/1.11⁵ = -$337,459.41

EAC = -$337,459.41/(PVIFA_11%,5) = 337,459.41/3.6959 = -$91,306.42

Analyzing the old computer, the only OCF is the depreciation tax shield, so:
OCF = $242,000(.40) = $96,800

The initial cost of the old computer is a little trickier. You might assume that since we already own the old computer there is no initial cost, but we can sell the old computer, so there is an opportunity cost. We need to account for this opportunity cost. To do so, we will calculate the aftertax salvage value of the old computer today. We need the book value of the old computer to do so. The book value is not given directly, but we are told that the old computer has depreciation of $242,000 per year for the next three years, so we can assume the book value is the total amount of depreciation over the remaining life of the system, or $726,000. So, the aftertax salvage value of the old computer is:

Aftertax salvage value = $330,000 + ($726,000 – 330,000)(.40) = $488,400

This is the initial cost of the old computer system today because we are forgoing the opportunity to sell it today. We next need to calculate the aftertax salvage value of the computer system in two years since we are “buying” it today. The aftertax salvage value in two years is:

Aftertax salvage value = $111,000 + ($242,000 – 111,000)(.40) = $163,400

Now we can calculate the NPV of the old computer as:
NPV = -$488,400 + 96,800(PVIFA_11%,2) + 163,400/1.11² = -$190,008.64
And the EAC of the old computer is:
EAC = -$190,008.64 /(PVIFA_11%,2) = 337,459.41/1.7125 = -$110,953.95

b. If we are only concerned with whether or not to replace the machine now, and are not worrying about what will happen in two years, the correct analysis is NPV. To calculate the NPV of the decision on the computer system now, we need the difference in the total cash flows of the old computer system and the new computer system. From our previous calculations, we can say the cash flows for each computer system are:

t	New computer	Old computer	Difference
0	($1,470,000)	$488,400	($981,600)
1	$286,200	($96,800)	$189,400
2	$286,200	($260,200)	$26,000
3	$286,200	$0	$286,200
4	$286,200	$0	$286,200
5	$412,200	$0	$412,200

Since we are only concerned with marginal cash flows, the cash flows of the decision to replace the old computer system with the new computer system are the differential cash flows. The NPV of the decision to replace, ignoring what will happen in two years is:

NPV = -$147,450.77