Question

Jason has just bought a bond that pays 2% annual coupons with $1,000 face value and 30 years to maturity.

(a) If the yield of the bond bought today was 3%, what was its purchase price?

(b) One year later, the bond's YTM has dropped to 2.5%. If you sell the bond immediately after receiving the coupon, i) what is the bond’s current yield? ii) what is the bond’s capital gains yield (CGY)? iii) what is the bond’s total (holding period/1-year total) yield? (1 mark)

(c) Now suppose another year has passed and the bond’s YTM remains unchanged at the previous year’s (Year one) level. If you sell the bond immediately after receiving the second year’s coupon, calculate i) the 2-year CGY ii) the total interest incomes (coupon and reinvestment of coupons) for the two years iii) the 2-year holding period/total yield.

Answer 1

a). Purchase price: FV = 1,000; N = 30; PMT = 2%*1,000 = 20; rate = 3%, solve for PV.

Purchase price = 804.00

b-i). Current yield = annual coupon/purchase price = 20/804 = 2.49%

b-ii). Selling price of the bond: FV = 1,000; N = 29; PMT = 2%*1,000 = 20; rate = 2.5%, solve for PV.

Selling price = 897.73

Capital gains yield = (selling price/purchase price) -1 = (897.73/804) -1 = 11.66%

b-iii). Total holding period return = current yield + capital gains yield = 2.49% + 11.66% = 14.15%

c-i). Selling price of the bond: FV = 1,000; N = 28; PMT = 2%*1,000 = 20; rate = 2.5%, solve for PV.

Selling price = 900.18

Capital gains yield = (selling price/purchase price) -1 = (900.18/804) -1 = 11.96%

c-ii). Total interest income over 2 years = Year 1 coupon + Year 2 coupon*(1+2.5%) = 20 + 20*(1+2.5%) = 40.50

c-iii). 2-year holding period return = (capital gains + interest income)/purchase price = (96.18 + 40.50)/804 = 17.00%