# solution

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

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