Question

A newly issued bond pays its coupons once annually. Its coupon rate is 8%, its maturity is 20 years, and its yield to maturity is 10%. a. Find the holding-period return for a 1-year investment period if the bond is selling at a yield to maturity of 9% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. If you sell the bond after one year, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%

Answer 1

a) total HPR = 19.38%

b) tax liability = $56.23

Step-by-step explanation:

price paid for the bond:

PV of face value = $1,000 / (1 + 10%)²⁰ = $148.64

PV of coupon payments = $80 x 8.5136 (PVIFA, 10%, 20 periods) = $681.09

market price = $829.73

coupon received during the year = $80

market price when bond is sold:

PV of face value = $1,000 / (1 + 9%)¹⁹ = $194.49

PV of coupon payments = $80 x 8.9501 (PVIFA, 9%, 19 periods) = $716.01

market price = $910.50

total HPR = ($910.50 + $80 - $829.73) / $829.73 = 19.38%

tax liability = ($80 x 40%) + ($80.77 x 30%) = $56.23