Final answer:
To find the equivalent pre-tax yield on a taxable bond, the yield to maturity (YTM) of the tax-exempt municipal bond is divided by (1 - the marginal tax rate). Using the given YTM of 5.35% and a marginal tax rate of 39%, the equivalent pre-tax yield for a taxable bond is approximately 8.77%.
Step-by-step explanation:
To find the equivalent pre-tax yield on a taxable bond, we need to adjust the after-tax yield we get from the municipal bond so it reflects what the yield would be before tax. The after-tax yield is the yield to maturity (YTM) of the bond, which is not taxed for municipal bonds. Therefore, we need to calculate what taxable yield would result in the same after-tax yield, given the investor's marginal tax rate.
We start by using the formula for the after-tax yield of a taxable bond, which is the yield multiplied by (1 - tax rate). For the municipal bond, the yield is equal to the after-tax yield since it is tax-exempt. So we need to solve for the yield on a taxable bond that would equal the municipal bond's YTM after being reduced by the tax rate:
The after-tax yield of a taxable bond = Taxable bond yield x (1 - tax rate)
Given the YTM of the municipal bond is 5.35%, and the tax rate is 39%, we use these values:
5.35% = Taxable bond yield x (1 - 0.39)
To find the taxable bond yield, we divide both sides by (1 - 0.39):
Taxable bond yield = 5.35% / (1 - 0.39)
Now we calculate the actual percentage:
Taxable bond yield = 5.35% / 0.61
Taxable bond yield = 8.7705%
Therefore, the equivalent pre-tax yield on a taxable bond for an investor in the 39% tax bracket who is considering a municipal bond with a YTM of 5.35% is approximately 8.77%.