EUAC Analysis The replacement analysis of a welding robot purchased 3 years ago at an initial cost of $20,000 has determined its economic life to be 5 years and its current market value to be $5,000. The robot began straight-line depreciation over its then-estimated useful life of 5 years, with

Question

EUAC Analysis

The replacement analysis of a welding robot purchased 3 years ago at an initial cost of $20,000 has determined its economic life to be 5 years and its current market value to be $5,000. The robot began straight-line depreciation over its then-estimated useful life of 5 years, with zero salvage value. Its future maintenance cost is predicted to be $200 per year.

It (defender) is being considered for replacement by a more accurate deluxe model(challenger), whose analysis yields an economic life of 5 years. The challenger is priced at $25,000 and is estimated to cost $300 annually in maintenance. It will also be straight-line depreciated over its useful life, with zero salvage value. An analysis has determined the challenger’s useful life to be its economic life. In relation to the defender, the deluxe model is estimated to generate an annual income of $10,000 through savings. With tax obligation at the 50% rate, should the deluxe model replace the defender if [latex]i=15\%[/latex]?

Accepted Answer

Note that the defender’s 5-year economic life equals that of the challenger. The analysis period should therefore be 5 years. Also note that the defender has already been depreciated for 3 years.

Since no comparison criterion is specified, we can choose any of those discussed in the text. Let us opt for EUAC. Our task is to determine the defender’s EUACs and compare them with those of the challenger, taking depreciation and income tax into account. The one with the lower EUAC should be selected. For both, [latex]i=15\%[/latex], and n = 5 years .

Since the redundant data in the problem statement can be confusing, it is preferable to summarize the relevant data.

Defender (existing welding robot):

Initial Cost [latex]=\$20,000[/latex]

Then-estimated Life = 5 years

Then-estimate Salvage [latex]= \$0[/latex]

Annual Maintenance [latex]= \$200[/latex]

Current Market Value [latex]= \$5,000[/latex]

Annual Depreciation [latex]({\$20,000}/{5}) =\$4,000[/latex]

Since depreciation has already been charged for 3 years,

Book value = First cost - Cumulative depreciation

[latex]=\$20,000-3 imes \$4,000[/latex]

[latex]=\$8,000[/latex]

Since the defender’s market value of $5,000 is lower than its $8,000 book value, a capital loss occurs in replacing the defender now.

Capital loss = Book value - Current market value

[latex]=\$8,000-\$5,000[/latex]

[latex]=\$3,000[/latex]

We can summarize the results in a table as follows. An explanation of the entries is provided following the table. Note that the columns have been selected on the basis of what we learned in Chapters 10 and 11. The $3,000 capital loss can be used to reduce income tax now (year 0 in the table).

(1) Year	(2) Before-Tax Cashflow	(3) Depr. Loss	(4) Capital Loss	(5) Taxable Income	(6) Tax @ 50%	(7) After-Tax Cashflow
0	-$5,000		$3,000		-$1,500	$6,500
1	-$200	$4,000		$4,200	-$2,100	$1,900
2	-$200	$4,000		$4,200	-$2,100	$1,900
3	-$200	$0		-$200	-$100	-$100
4	-$200	$0		-$200	-$100	-$100
5	-$200	$0		-$200	-$100	-$100

Explanatory Notes:

1. In the first column, year 0 means now. The past 3 years of the defender are of no relevance. The $5,000 entry in the first row second column represents the defender’s current market value.

2. In the fourth column, the row for year 0, there is an entry[latex]^{21}[/latex] of $3,000. Since replacing the defender now would result in a capital loss of $3,000, saving the company $1,500 in income tax, by not doing so an opportunity to reduce tax is forfeited.

Thus, the defender represents an investment[latex]^{22}[/latex] of $5,000 + $1,500 = $6,500.

3. In the third column, the $4,000 SL-depreciation for the remaining 2 years has been charged. For year 1, the taxable income is equal to the before-tax cashflow of –$200 minus the depreciation charge of $4,000, yielding –$4,200. The income tax on this is –$2,100. The negative sign indicates a tax refund rather than a payment.

Negative numbers in other rows means negative cashflows and losses.

4. The data in the last column are the after-tax cashflows. For each row, the entry equals before-tax cashflow minus income tax. For example, for year 1, it is –$200 – (–$2,100) = $1,900; its positive sign indicates a cash inflow (due to the $2,100 tax refund).

We next determine the EUAC of the after-tax cashflows, as follows. Note that the –ve signs of these cashflows are being treated as +ve since EUAC represents cost. If you have difficulty comprehending the following equation[latex]^{23}[/latex], help yourself by sketching an appropriate cashflow diagram.

[latex]EUAC_{defender} =\left\{6,500-2,000({P}/{A},15\%,2) ight\} ({A}/{P},15\%,5)+100[/latex]

[latex]=(6,500-2,000 imes 1.626) imes 0.2983+100[/latex]

[latex]=(6,500-3,252) imes 0.2983+100[/latex]

[latex]=969+100[/latex]

[latex]=\$1,069[/latex]

Challenger (deluxe model):

Initial Cost [latex]=\$25,000[/latex]

Useful Life = 5 years

Estimated Salvage [latex]=\$0[/latex]

Annual Maintenance [latex]=\$300[/latex]

Annual Savings (Benefit) [latex]=\$10,000[/latex]

Annual Depreciation [latex](\$25,000-{0}/{5}) = \$5,000[/latex]

Net Annual Benefit [latex]=\$10,000-\$300[/latex]

Savings - Maintenance Cost $9,700

A table similar to that for the defender is prepared for the challenger, as follows. The explanation given earlier on the entries in the defender’s table should be helpful in comprehending the entries in this table too .

Year	Before-Tax Cashflow	Depr. Loss	Taxable Income	Tax @ 50%	After-Tax Cashflow
0	-$25,000				-$25,000
1	$9,700	$5,000	$4,700	$2,350	$7,350
2	$9,700	$5,000	$4,700	$2,350	$7,350
3	$9,700	$5,000	$4,700	$2,350	$7,350
4	$9,700	$5,000	$4,700	$2,350	$7,350
5	$9,700	$5,000	$4,700	$2,350	$7,350

The EUAC of the after-tax cashflows for the challenger is

[latex]EUAC_{challenger} =25,000({A}/{P},15\%,5)-7,350[/latex]

[latex]=25,000 imes 0.2983-7,350[/latex]

[latex]=\$108[/latex]

With the [latex]EUAC_{challenger}[/latex] being lower, the challenger is attractive, and hence the deluxe model should replace the existing welding robot.

[latex]^{21}[/latex]The posting of $3,000 capital loss in row 0 means that the associated tax saving is being realized at the time investment is made (year 0). If the saving is delayed due to accounting or tax cycle, then this entry should be made in the following year (year 1), and calculations modified accordingly.

[latex]^{22}[/latex]The capital loss would reduce income tax for the year. The forfeiture of this opportunity if the defender is not replaced is equivalent to an increase in taxable income by that amount. The equivalency is based on the fact that by not realizing the capital loss now the company is not reducing its taxable income by $3,000, and thus its tax by $1,500. In other words, not replacing the defender results in $1,500 more payable tax.

[latex]^{23}[/latex]To tailor the cashflow pattern, consider the $1,900 cashflow divided into two components: $2,000 and –$100. This makes the $100 cash outflow form a uniform series. In the absence of tailoring, evaluation would have been longer, as follows:

EUAC[latex]_{defender}[/latex] = {6,500 − 1,900(P/A, 15%, 2)}(P/A, 15%, 5)

+ 100(F/A, 15%, 3)(A/F, 15%, 5)

= (6,500 - 1,900 × 1.626) × 0.2983 + 100 × 3.472 × 0.1483

= 1,017 + 51

= $1,068

Question 12.6: EUAC Analysis The replacement analysis of a welding robot pu...

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