Question

A taxable bond with a coupon rate of 4.00% has a market price of 98.18% of par. The bond matures in 7.00 years ans pays semi-annually. Assume an investor has a 28.00% marginal tax rate. The investor would prefer otherwise identical tax-exempt bond if it's yield to maturity was more than _____%

Answer 1

Given about a bond,

Coupon rate = 4% paid semiannually,

Let face value of the bond be $100

So, semiannual coupon payment be (4%/2) of 100 = $2

price = 98.18% of face value

=> Price = 98.18% of 100 = $98.18

years to maturity = 7 years

YTM of the bond can be calculated on financial calculator using following values:

FV = 100

PV = -98.18

PMT = 2

N = 2*7 = 14

Compute for I/Y, we get I/Y = 2.15

So, semiannual yield on the bond = 2.15%

So, Semiannual YTM of the bond = 2*2.15 = 4.30%

Tax rate T = 28%

So, after tax yield = yield*(1-T) = 4.3*(1-0.28) = 3.10%

The investor would prefer otherwise identical tax-exempt bond if it's yield to maturity was more than 3.10%