Final answer:
The equivalent taxable yield of the municipal bond in Problem 14 for tax brackets of zero, 10%, 20%, and 30% are 4%, 4.44%, 5%, and 5.71% respectively.
Step-by-step explanation:
14. To determine which option gives a higher after-tax yield, we need to compare the after-tax yields of short-term municipal bonds and taxable bonds for different tax brackets.
a. For a tax bracket of zero (0%), the after-tax yield for both types of bonds would be the same. This is because there are no taxes to be paid, so the after-tax yield is equal to the stated yield.
b. For a tax bracket of 10%, the after-tax yield of municipal bonds can be calculated as follows:
After-tax yield = Pre-tax yield * (1 - Tax rate)
Municipal bond after-tax yield = 4% * (1 - 0.10) = 3.6%
Taxable bond after-tax yield = 5% * (1 - 0.10) = 4.5%
In this case, the taxable bond has a higher after-tax yield.
c. For a tax bracket of 20%, the after-tax yield of municipal bonds would be:
Municipal bond after-tax yield = 4% * (1 - 0.20) = 3.2%
Taxable bond after-tax yield = 5% * (1 - 0.20) = 4%
Again, the taxable bond has a higher after-tax yield.
d. For a tax bracket of 30%, the after-tax yield of municipal bonds would be:
Municipal bond after-tax yield = 4% * (1 - 0.30) = 2.8%
Taxable bond after-tax yield = 5% * (1 - 0.30) = 3.5%
Once more, the taxable bond has a higher after-tax yield.
Therefore, for all tax brackets from 10% to 30%, taxable bonds have a higher after-tax yield than municipal bonds.
16. To find the equivalent taxable yield of the municipal bond for different tax brackets, we need to calculate the pre-tax yield that would result in the same after-tax yield as the municipal bond.
For a tax bracket of zero (0%):
Equivalent taxable yield = Municipal bond after-tax yield / (1 - Tax rate)
Equivalent taxable yield = 4% / (1 - 0) = 4%
For a tax bracket of 10%:
Equivalent taxable yield = 4% / (1 - 0.10) = 4.44%
For a tax bracket of 20%:
Equivalent taxable yield = 4% / (1 - 0.20) = 5%
For a tax bracket of 30%:
Equivalent taxable yield = 4% / (1 - 0.30) = 5.71%
Complete question:
14. Suppose that short-term municipal bonds currently offer yields of 4%, while comparable taxable bonds pay 5%. Which gives you the higher after-tax yield if your tax bracket is:
- a. Zero
- b. 10%
- c. 20%
- d. 30%
16. Find the equivalent taxable yield of the municipal bond in Problem 14 for tax brackets of zero, 10%, 20%, and 30%.