Question

A $1,000 face value has a 8% annual coupon rate. The next coupon is due in one year and the bond matures in 11 years. The current YTM on the bond is 4.8%. What is the dollar value of the price change if the bond's YTM increases to 5.6%? Round to the nearest cent. ​[Hint: 1) If the price drops, the change is a negative number. 2) Do not compute duration. You can calculate the precise impact of a yield change on the bond's price by comparing the prices under the two scenarios.]

Answer 1

Current price

Bond

K = N

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

k=1

K =11

Bond Price =∑ [(8*1000/100)/(1 + 4.8/100)^k]     +   1000/(1 + 4.8/100)^11

k=1

Bond Price = 1268.62

Change in YTM =0.8

Bond

K = N

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

k=1

K =11

Bond Price =∑ [(8*1000/100)/(1 + 5.6/100)^k]     +   1000/(1 + 5.6/100)^11

k=1

Bond Price = 1193.22

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

%age change in price = (1193.22-1268.62)*100/1268.62

= -5.94%