EVA Consider the following proposed capital investment in an engineering project and determine its (a) year-by-year ATCF, (b) after-tax AW, (c) annual equivalent EVA. Proposed capital investment = $84,000 Salvage value (end of year four) = $0 Annual expenses per year = $30,000 Gross revenues per

Question

EVA
Consider the following proposed capital investment in an engineering project and determine its
(a) year-by-year ATCF,
(b) after-tax AW,
(c) annual equivalent EVA.

Proposed capital investment = $84,000
Salvage value (end of year four) = $0
Annual expenses per year = $30,000
Gross revenues per year = $70,000
Depreciation method = Straight line
Useful life = four years
Effective income tax rate (t) = 50%
After-tax MARR (i) = 12% per year

Accepted Answer

(a) Year-by-year ATCF amounts are shown in the following table:

ATCF	Income Taxes	Taxable Income	Depreciation	BTCF	EOY
−$84,000	—	—	—	− $84,000	0
30,500	−$9,500	$19,000	$21,000	70,000 − 30,000	1
30,500	−9,500	19,000	21,000	70,000 − 30,000	2
30,500	−9,500	19,000	21,000	70,000 − 30,000	3
30,500	−9,500	19,000	21,000	70,000 − 30,000	4

(b) The annual equivalent worth of the ATCFs equals − $ 8 4 , 0 0 0(A/P, 12%, 4) + $30,500 = $2,844.

(c) The EVA in year k equals NOPAT[latex]_{k}[/latex] −0.12 BV[latex]_{k-1}[/latex] [Equation (7-22)]. The yearby-year EVA amounts and the annual equivalent worth of EVA ($2,844) are shown in the next table. Hence, the after-tax AW and the annual equivalent worth of EVA of the project are identical.

[latex]EVA_{k}= NOPAT_k -i\cdot BV_{k-1}[/latex] (7-22)

EVA = NOPAT − i · BV[latex]_{k-1}[/latex]	NOPAT	EOY[latex]_{k}[/latex]
$9,500 − 0.12($84,000) = −$580	$19,000 − $9,500 = $9,500	1
$9,500 − 0.12($63,000) = $1,940	= $9,500	2
$9,500 − 0.12($42,000) = $4,460	= $9,500	3
$9,500 − 0.12($21,000) = $6,980	= $9,500	4

Annual equivalent EVA = [−$580(P/F, 12%, 1) + $1,940(P/F, 12%, 2) + $4,460(P/F, 12%, 3) + $6,980(P/F, 12%, 4)](A/P, 12%, 4) = $2,844.

Question 7.21: EVA Consider the following proposed capital investment in an...

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