Question

Consider a 7-year bond with face value $1,000 that pays an 8.4% coupon semi-annually and has a yield-to-maturity of 6.9%. What is the approximate percentage change in the price of bond if interest rates in the economy are expected to increase by 0.40% per year? Submit your answer as a percentage and round to two decimal places. (Hint: What is the expected price of the bond before and after the change in interest rates?)

Can you please explain with FV, PV, Rate, PMT method? Someone has answered a question like this but used a forumla and I didn't quite understand nor get their answer. Thanks!!

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(8.4*1000/200)/(1 + 6.9/200)^k]     +   1000/(1 + 6.9/200)^7x2

k=1

Bond Price = 1082.18

=-PV(6.9/200,7*2,8.4*1000/200,1000)

Change in YTM =0.4, new YTM = 6.9+0.4 = 7.3%

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =7x2

Bond Price =∑ [(8.4*1000/200)/(1 + 7.3/200)^k]     +   1000/(1 + 7.3/200)^7x2

k=1

Bond Price = 1059.46

=-PV(7.3/200,7*2,8.4*1000/200,1000)

%age change in price =(New price-Old price)*100/old price

%age change in price = (1059.46-1082.18)*100/1082.18

= -2.1%