Question

Consider a coupon bond with 15 years to maturity. The coupon rate is 8%, and the principal is 100. The marginal tax rate on interest income is 40%.

(a) If yield to maturity is 2%, with simple compounding, what is the bond price?

(b) At the 40% tax rate, would be the yield to maturity of an equivalent municipal bond?

(c) Which security under (a) and (b) above would be picked by a foreign investor who does not pay income tax in the United States?

Answer 1

a. YTM = [(C + F - P) / n] / [(F + P) / 2]

where C = coupon payment

F = face value

P = bond price

n = number of years to maturity

0.02 = [(8 + 100 - P) / 15] / [(100 + P) / 2]

0.01 (100 + P) = (108 - P) / 15

0.15 (100 + P) = (108 - P)

15 + 0.15 P = 108 - P

1.15 P = 93

P = 93 / 1.15 = $80.87

b. Coupon payment = $100 * 8% * (1 - 40%)

= $4.8

YTM = [(4.8 + 100 - 80.87) / 15] / [(100 + 80.87) / 2]

= (23.93 / 15) / 90.44

= 1.60 / 90.44

= 0.0177 or 1.77%

c. Foreign investor who does not pay income tax in the United States will pick up security under option (a) as it has more YTM and coupon payment as compared to under option (b)