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

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

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(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_{k} −0.12 BV_{k-1} [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.

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

EVA = NOPAT − i · BV_{k-1} NOPAT EOY_{k}
$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.

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