Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,380,000; the new one will cost, $1,640,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $380,000 after five years.

The old computer is being depreciated at a rate of $276,000 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 $500,000; in two years, it will probably be worth $128,000. The new machine will save us $298,000 per year in operating costs. The tax rate is 35 percent, and the discount rate is 10 percent.

a.1	Calculate the EAC for the old computer and the new computer. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

	EAC
New computer	$
Old computer	$

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

NPV

$

References

Answer 1

Part a.1

Step 1: Calculate Operating Cash Flow for Both New and Old Computer

The operating cash flow for both new and old computer is calculated as below:

Operating Cash Flow (New Computer) = Cost Savings*(1-Tax Rate) + Depreciation*Tax Rate = 298,000*(1-35%) + 1,640,000/5*35% = $308,500

Operating Cash Flow (Old Computer) = Depreciation*Tax Rate = 276,000*35% = $96,600

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Step 2: Calculate After-Tax Salvage Value for Both New and Old Computer

The after-tax salvage value for new and old computer is arrived as below:

After-Tax Salvage Value (New Computer) = Market Value after 5 Years*(1-Tax Rate) = 380,000*(1-35%) = $247,000

After-Tax Salvage Value Today (Old Computer) = Sales Value of Old Computer Today + (Depreciation Amount*Remaining Life of Computer -  Sales Value of Old Computer Today)*Tax Rate = 500,000 + (276,000*3 - 500,000)*35% = $614,800

After-Tax Salvage Value After 2 Years (Old Computer) = Sales Value of Old Computer After 2 Years + (Depreciation Amount*Remaining Life of Computer After 2 Years - Sales Value of Old Computer After 2 Years)*Tax Rate = 128,000 + (276,000*1 - 128,000)*35% = $179,800  

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Step 3: Calculate NPV of Both New and Old Computer

The NPV can be calculated with the use of formula given below:

NPV (New Computer) = -Initial Investment + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5

NPV (Old Computer) = -After-Tax Salvage Value Today + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2

Substituting values in the above formula, we get,

NPV (New Computer) = -1,640,000 + 308,500/(1+10%)^1 + 308,500/(1+10%)^2 + 308,500/(1+10%)^3 + 308,500/(1+10%)^4 + (308,500+247,000)/(1+10%)^5 = -$317,174.71

NPV (Old Computer) = -614,800 + 96,600/(1+10%)^1 + (96,600+179,800)/(1+10%)^2 = -$298,552.07

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Step 4: Calculate EAC of Both New and Old Computer

The EAC of both new and old computer is calculated as below:

EAC (New Computer) = NPV/PVIFA(Discount Rate, Years) = -317,174.71/PVIFA(10%,5) = -317,174.71/3.7908 = -$83,669.89

EAC (Old Computer) = NPV/PVIFA(Discount Rate, Years) = -298,552.07/PVIFA(10%,2) = -298,552.07/1.7355 = -$172,022.86

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Notes:

1) There can be a slight difference in final answer on account of rounding off values.

2) The final answers have been calculated using the actual figures and not with the use of rounded off values.

3) PVIFA is present value Interest factor for an annuity.

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Part a.2)

To calculate NPV of the decision to replace the computer, we need to calculate the incremental cash flows as below:

	Cash Flows
Year	New Computer (A)	Old Computer (B)	Difference (A-B)
0	-1,640,000	-614,800	-1,025,200
1	308,500	96,600	211,900
2	308,500	276,400	32,100
3	308,500	0	308,500
4	308,500	0	308,500
5	555,500	0	555,500

Now, we can calculate the NPV as below:

NPV = -1,025,200 + 211,900/(1+10%)^1 + 32,100/(1+10%)^2 + 308,500/(1+10%)^3 + 308,500/(1+10%)^4 + 555,500/(1+10%)^5 = -$18,622.65