How do I work this out?
Corporate bonds issued by Johnson Corporation currently yield 11%. Municipal bonds of equal risk currently yield 6.5%. At what tax rate would an investor be indifferent between these two bonds?
My answer is: 6.5%/1-11%=7.3
(7.3)(1- .11)=6.5
However, I keep getting this wrong and can not figure out the issue or how to solve this problem
To solve this problem, you need to find the tax rate at which an investor would be indifferent between investing in corporate bonds yielding 11% and municipal bonds yielding 6.5%. The key concept to apply here is that the after-tax yield of the corporate bond should be equal to the yield of the municipal bond.
To calculate the after-tax yield of the corporate bond, you need to subtract the tax paid on interest income from the yield. The formula to calculate the after-tax yield is:
After-tax Yield = Yield * (1 - Tax Rate)
Let's assume the tax rate is "x". The after-tax yield of the corporate bond would then be 11% * (1 - x). Since the investor is indifferent between the two bonds, the after-tax yield of the corporate bond should be equal to the yield of the municipal bond, which is 6.5%.
So, we can set up the equation:
11% * (1 - x) = 6.5%
Now, let's solve for "x":
11% * (1 - x) = 6.5%
Divide both sides by 11%:
(1 - x) = 6.5% / 11%
Simplify the right side:
(1 - x) = 0.065 / 0.11
Simplify further:
(1 - x) = 0.591
To isolate "x", subtract 1 from both sides:
-x = 0.591 - 1
-x = -0.409
Multiply both sides by -1 to make "x" positive:
x = 0.409
Therefore, the tax rate at which an investor would be indifferent between these two bonds is 0.409, or 40.9%.