Corporate bonds issued by Johnson Corporation currently yield 9.5%. Municipal bonds of equal risk currently yield 5%. At what tax rate would an investor be indifferent between these two bonds? Round your answer to two decimal places.
To find the tax rate at which an investor would be indifferent between the two bonds, we need to determine the after-tax yield of the municipal bonds.
The formula to calculate the after-tax yield is:
After-tax yield = Municipal bond yield * (1 - Tax rate)
Setting the after-tax yield of the municipal bonds equal to the yield of the corporate bonds, we can now solve for the tax rate:
9.5% (yield of corporate bonds) = 5% (municipal bond yield) * (1 - Tax rate)
Rearranging the equation, we get:
1 - Tax rate = 9.5% / 5%
Tax rate = 1 - (9.5% / 5%)
Tax rate = 1 - 1.9
Tax rate = 0.1
Therefore, an investor would be indifferent between the two bonds at a tax rate of 10%.
To determine the tax rate at which an investor would be indifferent between the two bonds, we need to compare the after-tax yield on the corporate bond with the yield on the municipal bond.
Let's assume that the investor's marginal tax rate is "T". The after-tax yield on the corporate bond can be calculated by subtracting the tax liability from the yield, while the yield on the municipal bond remains unchanged.
After-tax yield on the corporate bond = Corporate Bond Yield × (1 - T)
Yield on the municipal bond = Municipal Bond Yield
Based on the question, we have:
Corporate Bond Yield = 9.5%
Municipal Bond Yield = 5%
Let's substitute these values into the formulas:
After-tax yield on the corporate bond = 9.5% × (1 - T)
Yield on the municipal bond = 5%
The investor would be indifferent between the two bonds when their yields are the same. Therefore, we can set the after-tax yield on the corporate bond equal to the yield on the municipal bond:
9.5% × (1 - T) = 5%
Now, let's solve for the tax rate "T":
9.5% × (1 - T) = 5%
0.095 × (1 - T) = 0.05
0.095 - 0.095T = 0.05
-0.095T = 0.05 - 0.095
-0.095T = -0.045
T = -0.045 / -0.095
Calculating this expression gives us:
T ≈ 0.47368
Rounding this to two decimal places, the investor would be indifferent between the two bonds when his or her tax rate is approximately 47.37%.