Question 9.12: After-Tax EUAC Analysis (Restatement of Example 9-3 with Tax...

The after-tax computations for keeping the defender (Pump A) and not purchasing the challenger (Pump B) are shown in Table 9-7. Year zero of the analysis period is at the end of the current (fifth) year of service of the defender. The year-zero entries of Table 9-7 are computed using the general format presented in Figure 9-5 and are further explained in the following:
1. BTCF (−$750): The same amount used in the before-tax analysis of Example 9-3. This amount is based on the outsider viewpoint and is the opportunity cost of keeping the defender instead of replacing it (and selling it for the estimated present MV of $750).
2. Taxable income ($7,750): This amount is the result of an increase in taxable income of $7,750 due to the tax consequences of keeping the defender instead of selling it. Specifically, if we sold the defender now, the loss on disposal would be as follows:
Gain or loss on disposal (if sold now) = MV_{0} − BV_{0},
BV_{0} = $17,000[1 − 0.0556 − 4(0.1111)] = $8,500,
Loss on disposal (if sold now) = $750 − $8,500 = −$7,750

But since we are keeping the defender (Pump A) in this alternative, we have the reverse effect on taxable income, an increase of $7,750 due to an opportunity forgone.
3. Cash flow for income taxes (−$3,100): The increase in taxable income because of the tax consequences of keeping the defender results in an increased tax liability (or tax credit forgone) of −0.4($7,750) = −$3,100.
4. ATCF (−$3,850): The total after-tax investment value of the defender is the result of two factors: the present MV ($750) and the tax credit ($3,100) forgone by keeping the existing Pump A. Therefore, the ATCF representing the investment in the defender (based on the outsider viewpoint) is −$750 − $3,100 = −$3,850.
The remainders of the ATCF computations over the nine year analysis period for the alternative of keeping the defender are shown in Table 9-7. The after tax computations for the alternative of purchasing the challenger (Pump B) are shown in Table 9-8. The next step in an after-tax replacement study involves equivalence calculations using an after-tax MARR. The following is the after-tax EUAC analysis for Example 9-12:

EUAC(6% ) of Pump A(defender) = $3,850(A/P, 6%, 9)
+ $2,448(P/A, 6%, 4)(A/P, 6%, 9)
+ [$2,826(F/P, 6%, 4)
+ $3,204(F/A, 6%, 4) − $120]
× (A/F, 6%, 9)
= $3,332;

EUAC(6% ) of Pump B (challenger) = $16,000(A/P, 6%, 9)
+ [$712(P/F, 6%, 1) − $56(P/F, 6%, 2)
+ $763(P/F, 6%, 3)
+···+ $1,992(P/F, 6%, 9)](A/P, 6%, 9)
− $1,920(A/F, 6%, 9)
= $3,375.
Because the EUACs of both pumps are very close, other considerations, such as the improved reliability of the new pump, could detract from the slight economic preference for Pump A. The after-tax annual costs of both alternatives are considerably less than their before-tax annual costs. The after-tax analysis does not reverse the results of the before-tax analysis for this problem (see Example 9-3). Due to income tax considerations, however, identical before-tax and after-tax recommendations should not necessarily be expected.

TABLE 9-7 ATCF Computations for the Defender (Existing Pump A) in Example 9-12

TABLE 9-8 ATCF Computations for the Challenger (Replacement Pump B) in Example 9-12