Question

Consider a(n) Six-year, 14 percent annual coupon bond with a face value of $1,000. The bond is trading at a rate of 11 percent.

a. What is the price of the bond?

b. If the rate of interest increases 1 percent, what will be the bond’s new price?

c. Using your answers to parts (a) and (b), what is the percentage change in the bond’s price as a result of the 1 percent increase in interest rates? (Negative value should be indicated by a minus sign.)

d. Repeat parts (b) and (c) assuming a 1 percent decrease in interest rates.

Answer 1

a

Current price

Bond

K = N

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

k=1

K =6

Bond Price =∑ [(14*1000/100)/(1 + 11/100)^k]     +   1000/(1 + 11/100)^6

k=1

Bond Price = 1126.92

b

Change in YTM =1

Bond

K = N

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

k=1

K =6

Bond Price =∑ [(14*1000/100)/(1 + 12/100)^k]     +   1000/(1 + 12/100)^6

k=1

Bond Price = 1082.23

c

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

%age change in price = (1082.23-1126.92)*100/1126.92

= -3.97%

d

Bond

K = N

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

k=1

K =6

Bond Price =∑ [(14*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^6

k=1

Bond Price = 1174.21

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

%age change in price = (1174.21-1126.92)*100/1126.92

= 4.2%