Question

Derrick is deciding between investing in a municipal bond with an interest rate of 3.95% and a corporate bond. Derrick's marginal tax rate is 22%. For what interest rate on the corporate bond will Derrick be indifferent between investing in the municipal bond and the corporate bond?

Answer 1

To be indifferent between the municipal bond and the corporate bond, Derrick needs the interest rate on the corporate bond to be 3.95%.

Step-by-step explanation:

To find the interest rate on the corporate bond for which Derrick would be indifferent, we need to compare the after-tax return on the municipal bond with the after-tax return on the corporate bond. Let's assume the interest rate on the corporate bond is x%. To calculate the after-tax return on the municipal bond, we multiply the interest rate (3.95%) by (1 - marginal tax rate (22%)), which gives us 3.95% * (1 - 0.22) = 3.08%. For Derrick to be indifferent between the two bonds, the after-tax return on the corporate bond should also be 3.08%. So, we set up the equation:

Corporate Bond Interest Rate * (1 - Marginal Tax Rate) = After-Tax Return on Municipal Bond

x% * (1 - 0.22) = 3.08%

Solving for x:

x% = 3.08% / (1 - 0.22)

x% = 3.08% / 0.78

x% = 3.95%

Therefore, for Derrick to be indifferent between investing in the municipal bond and the corporate bond, the interest rate on the corporate bond should also be 3.95%.