Question

A tax-exempt municipal bond with a coupon rate of 6.00% has a market price of 99.18% of par. The bond matures in 13.00 years and pays semi-annually. Assume an investor has a 35.00% marginal tax rate. The investor would prefer otherwise identical taxable bond if it's yield to maturity was more than _____% (round to 2 decimal places).

Answer 1

The Annual Coupon payment of the municipal bond is 6% of Face value. Considering the Face Value to be 100. So the coupon is 6% of 100, that is 6.

Now there is no tax charged on this interest earned of municipal bond. So if tax is charged 35% and still the coupon ends up to be 6, so the coupon should be:

(New Coupon) * (1 - Tax Rate) = 6 ---- (New Coupon Rate after tax should be 6)

(New Coupon) * (1 - 35%) = 6

New Coupon = 6 / 0.65

New Coupon = 9.2307

So the Annual Coupon Should be 9.2307

Calculate the new YTM using the new coupon rate.

You need to use Financial calculator to solve this problem. You can download it.

N => 13* 2 = 26 (As semiannual payment for 13 years, so 26 payments)

PV = -99.18 (Present value of bond)

PMT => 9.2307 / 2 = 4.61535 (As coupon is yearly, so convert is semiannual)

FV = 100 (The face value of the bond is 100)

CPT + I/Y = 4.6742 (Half Yearly YTM)

So yearly YTM will be 4.6742 * 2= 9.3484

So the YTM should be more than 9.3484% for a taxable bond to get net coupon of $6.