Rarke Company must choose between two alternate transactions. Transaction 1 requires a $20,000 nondeductible cash outlay, while transaction 2 requires a $25,000 deductible cash outlay. Determine the marginal tax rate at which the after-tax costs of the two transactions are equal.

Question

Quizplus · Accepted Answer

To determine the marginal tax rate at which the after-tax costs of the two transactions are equal, we can set up the following equation:

($25,000 - $25,000 x Marginal Tax Rate) = ($20,000 - $20,000 x Marginal Tax Rate x (1-Marginal Tax Rate))

Simplifying and solving for the marginal tax rate:

$25,000 - $25,000 x Marginal Tax Rate = $20,000 - $20,000 x Marginal Tax Rate + $20,000 x Marginal Tax Rate - $20,000 x Marginal Tax Rate^2

$5,000 = $0 + $20,000 x Marginal Tax Rate - $20,000 x Marginal Tax Rate^2

$20,000 x Marginal Tax Rate^2 - $20,000 x Marginal Tax Rate + $5,000 = 0

Solving for Marginal Tax Rate using the quadratic formula:

Marginal Tax Rate = (-(-$20,000) ± sqrt((-20,000)^2 - 4 x $20,000 x $5,000)) / (2 x $20,000)

Marginal Tax Rate = (0.25 ± 0.15)

Marginal Tax Rate = 0.10 or 0.40

Since we are looking for the marginal tax rate where the after-tax costs of the two transactions are equal, we want to choose the marginal tax rate that falls within the range of current tax rates. According to the IRS, the current marginal tax rates range from 10% to 37%, so we can eliminate the choice of 0.10.

Therefore, the best choice is B) 20%. At a marginal tax rate of 20%, the after-tax cost of Transaction 1 would be $16,000 and the after-tax cost of Transaction 2 would be $20,000, making Transaction 1 the better option.

Rarke Company Must Choose Between Two Alternate Transactions