Question

company p must choose between two alternate transactions. the cash generated by transaction 1 is taxable, and the cash generated by transaction 2 is nontaxable.
required:
a. determine the marginal tax rate at which the after - tax cash flows from the two transactions are equal assuming that transaction 1 generates $122,000 of income and transaction 2 generates $95,160 of income.
b. determine the marginal tax rate at which the after - tax cash flows from the two transactions are equal assuming that transaction 1 generates $215,000 of income and transaction 2 generates $154,800 of income.

Explanation:

Step1: Set up the equation

Let the marginal - tax rate be $t$. The after - tax cash flow from Transaction 1 is $(1 - t)\times$ income from Transaction 1, and the after - tax cash flow from Transaction 2 is the income from Transaction 2 (since it's non - taxable). For part a, we set up the equation $(1 - t)\times122000=95160$.

Step2: Solve for $t$

First, divide both sides of the equation by 122000: $1 - t=\frac{95160}{122000}$. Then, calculate $\frac{95160}{122000}=0.78$. So, $1 - t = 0.78$. Next, solve for $t$: $t=1 - 0.78=0.22$ or 22%.

Step3: For part b

Set up the equation $(1 - t)\times215000 = 154800$. Divide both sides by 215000: $1 - t=\frac{154800}{215000}$. Calculate $\frac{154800}{215000}=0.72$. Then, solve for $t$: $t = 1-0.72 = 0.28$ or 28%.

Answer:

a. 22%
b. 28%