Question

Consider two risk-free coupon bonds A and B both having a maturity of 10 years and a $1000-face value. Bond A has 6% annual coupons while Bond B has 12% annual coupons. Suppose that the yield to maturity decreases from 10% to 8%. (15pts)

(a) Calculate the price of each bond with a 10% YTM and an 8% YTM respectively. What is the percentage change in the price of each of these two bonds (A and B) resulting from the change in the YTM? Show your work. (5pts)

(b) What conclusion can you reach? Explain your result.

Answer 1

Bond price = PV of annual coupon + PV of face value

Annual coupon, bond A = 1000 x 6% = 60

Annual coupon, bond B = 1000 x 12% = 120

(a)

(1) YTM = 10%

Price, bond A = 60 x P/A(10%, 10) + 1000 x P/F(10%, 10) = 60 x 6.1446 + 1000 x 0.3855 = 368.68 + 385.5 = 754.18

Price, bond B = 120 x P/A(10%, 10) + 1000 x P/F(10%, 10) = 120 x 6.1446 + 1000 x 0.3855 = 737.35 + 385.5 = 1122.85

(2) YTM = 8%

Price, bond A = 60 x P/A(8%, 10) + 1000 x P/F(8%, 10) = 60 x 6.7101 + 1000 x 0.4632 = 402.61 + 463.2 = 865.81

Price, bond B = 120 x P/A(8%, 10) + 1000 x P/F(8%, 10) = 120 x 6.7101 + 1000 x 0.4632 = 805.21 + 463.2 = 1268.41

(3)

% change in price, bond A = (865.81 / 754.18) - 1 = 1.148 - 1 = 0.148 = 14.8%

% change in price, bond B = (1268.41 / 865.81) - 1 = 1.465 - 1 = 0.465 = 46.5%

(b)

A decrease in YTM leads to an increase in price of a bond.