Question

Question 21

Consider the following two bonds issued by a corporation:
(i) Bond A with 6% coupon and 10 years of maturity and (ii) Bond B with 9% coupon and 10 years of maturity. What would happen to the prices of these bonds if interest rate in the economy increases by 0.5%?

		Price of Bond A will increase more than price of Bond B
		Price of Bond A will fall more than price of Bond B
		Price of Bond B will fall more than price of Bond A
		Price of Bond B will increase more than price of Bond A

Answer 1

Option b is correct Price of Bond A will fall more than price of Bond B
because lower the coupon and higher the maturity higher is the fall in the price of bond with increase in YTM  Since Bond A has lower coupon rate there will be higher decrease in the price of bond as maturity of both A and B bond are same.

Let par value of Bond A =1000
Assuming 10% YTM
Coupon = 6%*1000 = 60
PV of Bond at 10% YTM = 60*(1-(1+10%)^-10)/10%+1000/(1+10%)^10 =754.22
PV of Bond at 10.5% YTM =60*(1-(1+10.5%)^-10)/10.5%+1000/(1+10.5%)^10 =729.34

Percentage Fall in price =(754.22-729.34)/729.34 = 3.41%

For Bond B
Assuming 10% YTM
Coupon = 10%*1000 = 100
PV of Bond at 10% YTM = 100*(1-(1+10%)^-10)/10%+1000/(1+10%)^10 =1000
PV of Bond at 10.5% YTM =100*(1-(1+10.5%)^-10)/10.5%+1000/(1+10.5%)^10 =969.31

Percentage fall in price =(1000-969.31)/1000 =3.01%

Hence price of bond a has fallen higher