Corporate bonds issued by Johnson Corporation currently yield 11.5%. Municipal bonds of equal risk currently yield 6.5%. At what tax rate would an investor be indifferent between these two bonds? Round your answer to two decimal places.
To determine the tax rate at which an investor would be indifferent between corporate and municipal bonds, we need to consider the after-tax yield of the corporate bond.
The after-tax yield of the corporate bond can be calculated by subtracting the tax savings from the corporate bond yield. The tax savings is equal to the corporate bond yield multiplied by the tax rate. Therefore, the after-tax yield of the corporate bond is:
After-Tax Yield = Corporate Bond Yield - (Corporate Bond Yield * Tax Rate)
Since the investor is indifferent between the two bonds, the after-tax yield of the corporate bond should equal the yield of the municipal bond.
Setting the after-tax yield of the corporate bond equal to the yield of the municipal bond, we can solve for the tax rate:
Municipal Bond Yield = Corporate Bond Yield - (Corporate Bond Yield * Tax Rate)
Simplifying the equation:
Municipal Bond Yield + (Corporate Bond Yield * Tax Rate) = Corporate Bond Yield
Now we can solve for the tax rate by isolating the tax rate term:
Corporate Bond Yield * Tax Rate = Corporate Bond Yield - Municipal Bond Yield
Tax Rate = (Corporate Bond Yield - Municipal Bond Yield) / Corporate Bond Yield
Plugging in the given values:
Tax Rate = (0.115 - 0.065) / 0.115
Calculating the tax rate:
Tax Rate = 0.05 / 0.115
Tax Rate ≈ 0.4348
Rounding the answer to two decimal places:
Tax Rate = 0.43
Therefore, an investor would be indifferent between the two bonds at a tax rate of 43%.
To determine the tax rate at which an investor would be indifferent between corporate and municipal bonds, we need to calculate the after-tax yield on the municipal bonds.
1. Calculate the after-tax yield on municipal bonds:
After-tax yield = Municipal yield * (1 - Tax rate)
Let's assume the tax rate is represented by 'X'.
After-tax yield = 6.5% * (1 - X)
2. Since the investor is indifferent between the two bonds, the after-tax yield on the municipal bonds should be equal to the yield on the corporate bonds.
6.5% * (1 - X) = 11.5%
3. To solve for 'X', we can rearrange the equation:
(1 - X) = 11.5% / 6.5%
1 - X = 1.7692
X = 1 - 1.7692
X = -0.7692
However, since a tax rate cannot be negative, this answer is not valid. It means that there is no tax rate at which an investor would be indifferent between these two bonds.