Question

Consider two 30-year maturity bonds. Bond A has a coupon rate of 4%, while bond B has a coupon rate of 12%. Both bonds pay their coupons semiannually.

a. Compute the prices of the two bonds at each interest rate. (Round the bond price to 2 decimal places.)

b. Suppose Bond A is currently priced to offer a yield to maturity of 8%. Calculate the (percentage) capital gain or loss on the bond if its yield immediately changes to each value of yield to maturity. (Enter your answers as a percent rounded to the nearest whole percent.)

c. Suppose Bond B is currently priced to offer a yield to maturity of 8%. Calculate the (percentage) capital gain or loss on the bond if its yield immediately changes to each value of yield to maturity. (Enter your answers as a percent rounded to the nearest whole percent.)

d. Which bond’s price exhibits greater proportional sensitivity to changes in its yield? In other words, which bond has greater interest rate risk?

e. Which bond pays a high coupon rate has lower “average” or “effective” maturity than a bond that pays a low coupon rate?

Answer 1

		Bond A	Bond B
	Coupon rate	4%	12%
	Time(years)	30	30
	times coupon payment per year	2	2
	n= T*times coupon payment made per year	60	60
	Assumption 1-In the absence of Redeemable value and Market Price, YTM=Coupon rate
	Assumption 2- Face value	100	100
a)	YTM	4%	12%
	Bond Price (Interest*PVAF + RV*PVF)	100.00	100.00
		=(4*PVAF1.04^60)+(100*PVF1.04^60)	=(12*PVAF1.12^60)+(100*PVF1.12^60)
	Thus irrespective of coupon rate, if YTM=Coupon rate then Bond Price = Face value of bond
b)	YTM	8%
	Bond Price (Interest*PVAF + RV*PVF)	50.49
		=(4*PVAF1.08^60)+(100*PVF1.08^60)
	Mac D= sum of(PV * Year)/sum of PV	13.82
	Volatility= Mac D/(1+YTM)	12.80%
c)	YTM		8%
	Bond Price (Interest*PVAF + RV*PVF)		134.42
			=(12*PVAF1.08^60)+(100*PVF1.08^60)
	Mac D= sum of(PV * Year)/sum of PV		12.50
	Volatility= Mac D/(1+YTM)		11.57%
d)	Bond A is more sensitive to change in yield as its volatility is greater than Bond B. Thus, Bond A price exhibits greater proportional sensitivity to changes
e)	Bond A has higher Macaulay's duration then Bond B. Thus, Bond A pays a high coupon rate has lower “average” or “effective” maturity than a bond that pays a low coupon rate.