Rodney, a cash-basis taxpayer, owes $40,000 in tax-deductible consulting fees for his business. Assume that it is December 28th and that Rodney can avoid any finance charges if he pays the accounting fees by January 10th. Rodney's tax rate this year is 32 percent and his after-tax rate of return is 10 percent. What tax rate next year will make Rodney indifferent between paying the $40,000 this year or next year? Use Exhibit 3.1. (Round discount factor(s) to three decimal places.)

Question

What will be an ideal response?

Answer 1

If Rodney pays the $40,000 in December, the $40,000 tax deduction will save him $12,800 (i.e., $40,000 × 0.32 = $12,800).
If Rodney pays the $40,000 in January, the tax savings in today's dollars is computed as:

Tax savings = $40,000 × tax rate × 0.909 (discount factor, one year, 10 percent).
For Rodney to be indifferent between paying the $40,000 in December or January, paying the $40,000 in January must generate $12,800 in tax savings. One can use this information to solve for next year's tax rate.
Tax savings = $40,000 × tax rate × 0.909 (discount factor, one year, 10 percent) = $12,800
Tax rate = ($12,800 / $40,000) × (1 / 0.909) = 35.20%
Alternatively, $40,000 × 0.909 = $36,360. $36,360 × tax rate = $12,800. $12,800 / $36,360 = 35.20%.