Question

5. Suppose the interest rate on a taxable corporate bond is 4 percent while a municipal, tax exempt bond has an interest rate of 3 percent, and they are similar in every other way.

a. Assuming the income tax rate is 30 percent, calculate the after tax interest rate on the corporate bond. Is it higher or lower than the after tax return on the municipal bond?

b. What is the income tax rate that equalizes the after tax return between the corporate bond and the municipal bond.

Answer 1

Question 5

(a)

Interest rate on corporate bonds = 4%

Tax rate = 30% or 0.30

Calculate the after tax interest rate on corporate bonds -

After-tax interest rate = Interest rate on corporate bonds * [1 - tax rate]

After-tax interest rate = 4 (1 - 0.30) = 4 * 0.70 = 2.80

Thus,

The after tax interest rate on the corporate bonds is 2.8%

The interest rate on municipal bonds is 3%.

The municipal bonds are tax exempt.

So, the after tax interest rate on municipal bonds would also be 3%.

Thus,

The after tax interest rate on corporate bonds is lower than the after tax return on the municipal bond.

(b)

Let income tax rate that will equalize the after tax return between the corporate bond and the municipal bond be t

Interest rate on municipal bond = Interest rate on corporate bonds(1 - tax rate)

3 = 4(1 - t)

3 = 4 - 4t

3 - 4 = -4t

4t = 1

t = 1/4

t = 0.25 or 25%

Thus,

The income tax rate that would equalize the after tax return between the corporate bond and the municipal bond is 25 percent.