A company purchases an asset that costs $41,000. This asset qualifies as three-year property under MACRS. The company uses an after-tax discount rate of 14% and faces a 33% income tax rate. (Use Table 1, Table 2 and Exhibit 12.4.)
1. Demonstrate that the PV of the depreciation deductions, when the income tax rate is 33%, is $10,526.
– What are the present values for each year? Years (1-4)
2. Given an after-tax discount rate of 14%, what tax rate would be needed in order for the PV of the depreciation deductions to equal $13,530? Use the Goal Seek function of Excel.
– What is the marginal income tax rate?
Exhibit 12.4:
EXHIBIT 12.4
MACRS Depreciation Rates
| Year | 3-year | 5-year | 7-year | 10-year | 15-year | 20-year |
|---|---|---|---|---|---|---|
| 1 | 33.33 | 20.00 | 14.29 | 10.00 | 5.00 | 3.75 |
| 2 | 44.45 | 32.00 | 24.49 | 18.00 | 9.50 | 7.22 |
| 3 | 14.81 | 19.20 | 17.49 | 14.40 | 8.55 | 6.68 |
| 4 | 7.41 | 11.52* | 12.49 | 11.52 | 7.70 | 6.18 |
| 5 | 11.52 | 8.93* | 9.22 | 6.93 | 5.71 | |
| 6 | 5.76 | 8.92 | 7.37 | 6.23 | 5.28 | |
| 7 | 8.92 | 6.55* | 5.90* | 4.89 | ||
| 8 | 4.47 | 6.55 | 5.90 | 4.52 | ||
| 9 | 6.56 | 5.91 | 4.46* | |||
| 10 | 6.55 | 5.90 | 4.46 | |||
| 11 | 3.28 | etc. | etc. |
Table 1: Present Value of $1
| Periods | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 11% | 12% | 13% | 14% | 15% | 20% | 25% | 30% |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.962 | 0.952 | 0.943 | 0.935 | 0.926 | 0.917 | 0.909 | 0.901 | 0.893 | 0.885 | 0.877 | 0.870 | 0.833 | 0.800 | 0.769 |
| 2 | 0.925 | 0.907 | 0.890 | 0.873 | 0.857 | 0.842 | 0.826 | 0.812 | 0.797 | 0.783 | 0.769 | 0.756 | 0.694 | 0.640 | 0.592 |
| 3 | 0.889 | 0.864 | 0.840 | 0.816 | 0.794 | 0.772 | 0.751 | 0.731 | 0.712 | 0.693 | 0.675 | 0.658 | 0.579 | 0.512 | 0.455 |
| 4 | 0.855 | 0.823 | 0.792 | 0.763 | 0.735 | 0.708 | 0.683 | 0.659 | 0.636 | 0.613 | 0.592 | 0.572 | 0.482 | 0.410 | 0.350 |
| 5 | 0.822 | 0.784 | 0.747 | 0.713 | 0.681 | 0.650 | 0.621 | 0.593 | 0.567 | 0.543 | 0.519 | 0.497 | 0.402 | 0.328 | 0.269 |
