Question

Consider a three-year bond trading at $110.83 that pays a 10% coupon semi-annually and has a yield to maturity (YTM) of 6%.
a)   Calculate the duration of this bond.
b)   What will be the final price if the YTM increases from 6% to 7%?

Answer 1

	Answer
a	Asset A - Bond
	Par Value	100	Assumption
	Coupon Rate	10%
	Maturity	3	Years
	YTM	6%
	Semi Annual Coupon Payments	100*10%*6/12
		5
	Current Market Price	110.83
	Bond Market Value	PVAF(3%,6 periods)*5+PVF(6%,3rd Year)*100
	PVAF(3%,6 Periods)	1-(1+r)^-n/r
		(1-(1.03)^-6)/0.03
		5.4172
	PVF(6%,3rd Year)	1/(1+r)^n
		1/(1.06)^3
		0.8396
	Bond Market Value	(5*5.4172)+(100*0.8396)
		111.046
	Duration	Discounted future casflows/Current Market Price
		111.046/110.83
		1.00
b	Asset A - Bond
	Par Value	100	Assumption
	Coupon Rate	10%
	Maturity	3	Years
	YTM	7%
	Semi Annual Coupon Payments	100*10%*6/12
		5
	Bond Market Value	PVAF(3.5%,6 periods)*5+PVF(7%,3rd Year)*100
	PVAF(3%,6 Periods)	1-(1+r)^-n/r
		(1-(1.035)^-6)/0.035
		5.3286
	PVF(6%,3rd Year)	1/(1+r)^n
		1/(1.07)^3
		0.8163
	Bond Market Value	(5*5.3286)+(100*0.8163)
		108.27