A taxable corporate bond is yielding 8% while a similar risk municipal bond is yielding 5.5%. At what marginal tax rate would you be indifferent between the two bonds?

Question

Quizplus · Accepted Answer

To determine the marginal tax rate that would make an investor indifferent between the two bonds, we need to calculate the after-tax yield of the corporate bond and compare it with the yield of the municipal bond.

Let's assume a marginal tax rate of x%.

After-tax yield of the corporate bond = 8% * (1-x%) = 0.08(1-x)
After-tax yield of the municipal bond = 5.5%

The investor would be indifferent between the two bonds if the after-tax yield of the corporate bond is equal to the yield of the municipal bond.

0.08(1-x) = 0.055
0.08 - 0.08x = 0.055
0.025 = 0.08x
x = 0.025/0.08 = 0.3125 = 31.25%

Therefore, at a marginal tax rate of 31.25%, the after-tax yield of the corporate bond would be equal to the yield of the municipal bond, making the investor indifferent between the two bonds. To find the marginal tax rate at which an investor would be indifferent between the two bonds, we need to calculate the after-tax yield on the corporate bond and compare it to the yield on the municipal bond. 
After-tax yield on corporate bond = 8% x (1 - marginal tax rate)
After-tax yield on municipal bond = 5.5%
We need to find the marginal tax rate at which these two yields are equal: 
8% x (1 - marginal tax rate) = 5.5%
Solving for marginal tax rate, we get 31.25%. Therefore, at a marginal tax rate of 31.25%, an investor would be indifferent between the two bonds. Choosing the corporate bond will result in a higher yield if the marginal tax rate is above 31.25%, and choosing the municipal bond will result in a higher yield if the marginal tax rate is below 31.25%.

A Taxable Corporate Bond Is Yielding 8% While a Similar