Question 9.9: After-Tax Economic Life of an Asset Find the economic life o...
After-Tax Economic Life of an Asset
Find the economic life on an after-tax basis for the new forklift truck (challenger) described in Example 9-4. Assume that the new forklift is depreciated as a MACRS (GDS)∗ three-year property class asset, the effective income tax rate is 40%, and the after-tax MARR is 6% per year.
The calculations using Equation (9-4 : TC_{k}(i%) =(1−t)(MV_{k-1} − MV_{k}+ iMV_{k-1} + E_{k})+i(t)(BV_{k-1}). are shown in Table 9-5. The expected year by-year MVs and annual expenses are repeated from Example 9-4 in columns and 5, respectively. In column 6, the sum of the loss in MV during year k, cost of capital based on the MV at the beginning-of-year (BOY) k, and annual expenses in year k are multiplied by (1 − t) to determine an approximate after- tax total marginal cost in year k. The BV amounts at the end of each year, based on the new forklift truck being a MACRS (GDS) three-year property class asset, are shown in column 7. These amounts are then used in column 8 to determine an annual tax adjustment [last term in Equation (9-4)], based on the beginning of year (BOY) book values (BV_{k-1}). This annual tax adjustment is algebraically added to the entry in column 6 to obtain an adjusted after-tax total marginal cost in year k, TC _{k}. The total marginal cost amounts are used in column 10 to calculate, successively, the EUAC _{k} of retirement of the asset at the end of year k. In this case, the after-tax economic life (N^{\ast}_{AT}) is three years, the same result obtained on a before-tax basis in Example 9-4 .
TABLE 9-5 Determination of the After-Tax Economic Life for the Asset Described in Example 9-4
| (1)
End of Year, k |
(2)
MV, End of Year k |
(3)
Loss in Market Value (MV) during Year k |
(4)
Cost of |
(5)
Annual |
(6)
Approximate |
| 0 | $30,000 | 0 | 0 | 0 | 0 |
| 1 | 22,500 | $7,500 | $1,800 | $3,000 | $7,380 |
| 2 | 16,875 | 5,625 | 1,350 | 4,500 | 6,885 |
| 3 | 12,750 | 4,125 | 1,013 | 7,000 | 7,283 |
| 4 | 9,750 | 3,000 | 765 | 10,000 | 8,259 |
| 5 | 7,125 | 2,625 | 585 | 13,000 | 9,726 |
| (1)
End of Year, k |
(7)
MACRS BV at End of Year k |
(8)
interest on Tax Adjustment = 6% · t · BOY BV in Col. 7 |
(9)
Adjusted After-Tax Total ( Marginal) |
(10)
EUAC^{a} (After Tax) through Year k |
|
| 0 | $30,000 | 0 | 0 | 0 | |
| 1 | 20,001 | $720 | $8,100 | $8,100 | |
| 2 | 6,666 | 480 | 7,365 | 7,743 | |
| 3 | 2,223 | 160 | 7,442 | 7649 N^{\ast}_{AT}=3 | |
| 4 | 0 | 53 | 8,312 | 7,800 | |
| 5 | 0 | 0 | 9,726 | 8,142 |
^{a} EUAC_k =\left[\sum_{j=1}^{k} (Col.9)j(P/F,6\%,j)\right] (A/P,6\%,k)