An agricultural corporation that paid 53% in income tax wanted to build a grain elevator...

To calculate the 25-year after-tax present worth of this project, we need to consider the income, expenses, depreciation, and taxes.

First, calculate the annual depreciation:

Depreciation=Initial CostLife=80,00025=3,200\text{Depreciation} = \frac{\text{Initial Cost}}{\text{Life}} = \frac{80,000}{25} = 3,200Depreciation=LifeInitial Cost​=2580,000​=3,200

Now, calculate the taxable income each year:

Taxable Income=Revenue−Expenses−Depreciation=22,500−12,000−3,200=7,300\text{Taxable Income} = \text{Revenue} - \text{Expenses} - \text{Depreciation} = 22,500 - 12,000 - 3,200 = 7,300Taxable Income=Revenue−Expenses−Depreciation=22,500−12,000−3,200=7,300

Calculate the tax:

Tax=Taxable Income×Tax Rate=7,300×0.53=3,869\text{Tax} = \text{Taxable Income} \times \text{Tax Rate} = 7,300 \times 0.53 = 3,869Tax=Taxable Income×Tax Rate=7,300×0.53=3,869

Net income after tax:

Net Income=Taxable Income−Tax=7,300−3,869=3,431\text{Net Income} = \text{Taxable Income} - \text{Tax} = 7,300 - 3,869 = 3,431Net Income=Taxable Income−Tax=7,300−3,869=3,431

Add back depreciation (since it’s a non-cash expense):

Cash Flow=3,431+3,200=6,631\text{Cash Flow} = 3,431 + 3,200 = 6,631Cash Flow=3,431+3,200=6,631

Finally, calculate the present worth using the formula for the present worth of an annuity:

Present Worth=6,631×(1−(1+0.10)−250.10)≈137,466\text{Present Worth} = 6,631 \times \left(\frac{1-(1+0.10)^{-25}}{0.10}\right) \approx 137,466Present Worth=6,631×(0.101−(1+0.10)−25​)≈137,466

So, the correct answer isB. $137,466.