Let’s walk through each part step-by-step, using tax concepts: --- ### **a. After-Tax Cost if Isabel Pays the $41,000 Bill in December** Since Isabel is on the **cash method**, if she pays in December, she gets a deduction this year. - **Deduction = $41,000** - **Marginal Tax Rate = 40%** **Tax Savings = Deduction × Tax Rate = $41,000 × 40% = $16,400** **After-tax cost = Amount paid – Tax savings** \[ \text{After-tax cost} = \$41,000 - \$16,400 = \$24,600 \] --- ### **b. After-Tax Cost if Isabel Pays the $41,000 Bill in January** If she pays in January, deduction occurs **next year** (not this year). The tax rate is the same (40%) in both years. But, **by delaying the deduction, she loses 1 year of tax savings**, but she can earn a 6% after-tax return on the money if she holds it for that year. Let’s calculate the **present value (PV) of the tax savings** she’ll get next year. - **Tax savings next year = $41,000 × 40% = $16,400** - **Discount back 1 year at 6% after-tax rate:** \[ \text{Present value of tax savings} = \frac{\$16,400}{1.06} = \$15,471.70 \] **After-tax cost = Amount paid – PV of tax savings** \[ \text{After-tax cost} = \$41,000 - \$15,471.70 = \$25,528.30 \] (Round to nearest dollar: **$25,528**) --- ### **c. Should Isabel pay in December or January?** - **Pay in December:** After-tax cost = **$24,600** - **Pay in January:** After-tax cost = **$25,528** **Conclusion:** Isabel should pay the bill in **December** to minimize the after-tax cost. --- ## **Summary Table** | Timing | After-tax Cost | |-----------|----------------| | December | $24,600 | | January | $25,528 | **Isabel should pay in December.** --- **Final Answers:** a. $24,600 b. $25,528 c. **Isabel should pay in December.**