Question

What explicit tax rate would keep Jason indifferent between purchasing a municipal bond with a 3.0 percent return and a taxable bond with a 4.5 percent before-tax return? (Round your answer to the nearest percent)

A. 25%
B. 30%
C. 33%
D. 36%
E. None of these

Answer 1

The explicit tax rate that would keep Jason indifferent between purchasing a municipal bond with a 3.0 percent return and a taxable bond with a 4.5 percent before-tax return is C. 33%.

Step-by-step explanation:

Taxable bond returns are subject to income tax, whereas municipal bond returns are typically exempt from federal income tax. To determine the explicit tax rate, we need to compare the after-tax returns of both bonds. The formula is:

`\[ \text{Taxable Bond Return} * (1 - \text{Tax Rate}) = \text{Municipal Bond Return} \]`

In this case, the taxable bond return is 4.5 percent, the municipal bond return is 3.0 percent, and the tax rate is what we're trying to find. Rearranging the formula to solve for the tax rate:

`\[ \text{Tax Rate} = 1 - \left( \frac{\text{Municipal Bond Return}}{\text{Taxable Bond Return}} \right) \]`

Substitute the given values:

`\[ \text{Tax Rate} = 1 - \left( (3.0)/(4.5) \right) \]`

`\[ \text{Tax Rate} = 1 - 0.6667 \]`

`\[ \text{Tax Rate} = 0.3333 \]`

To convert this to a percentage, multiply by 100:

`\[ \text{Tax Rate} = 33.33\% \]`

Rounding to the nearest percent, the explicit tax rate is 33%, so the correct answer is C. 33%.