Question

A newly issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 6%.

a) Find the price of the bond.

b) After one year, the bond is selling at a yield to maturity of 5.5%. Find the holding period return if you sell the bond after one year.

c) If you sell the bond after one year, what taxes will you owe? Assume that the tax rate on interest income is 40% and the tax rate on capital gains income is 30%.

d) What is the after-tax holding period return on the bond?

Answer 1

a

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =20

Bond Price =∑ [(5*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^20

k=1

Bond Price = 885.3

b

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =20

Bond Price =∑ [(5*1000/100)/(1 + 5.5/100)^k]     +   1000/(1 + 5.5/100)^20

k=1

Bond Price = 940.25

HPR = ((price in 1 year + coupon)/price today-1)*100 = ((940.25+50)/885.35-1)*100=11.85%

c

Tax on capital gain = tax rate*(selling price-purchase price) = 0.3*(940.35-885.35)=16.5

Tax on coupon=tax rate*coupon = 0.4*50=20

d

New HPR = ((price in 1 year + coupon-tax on capital gain -tax on coupon)/price today-1)*100 = ((940.25+50-16.5-20)/885.35-1)*100=7.73%