Question

Assume a company has issued an 8-year zero coupon bond with a yield of 6% and a par value of $1000.

a. What is the bond price?

b. What is the duration of the bond?

c. Based on duration, what is the estimated bond price if interest rates rise to 7%?

d. Determine the new price exactly if interest rates rise to 7%?

Answer 1

a

K = N

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

k=1

K =8

Bond Price =∑ [(0*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^8

k=1

Bond Price = 627.41

b

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($627.41)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	-	1.06	-	-
2	-	1.12	-	-
3	-	1.19	-	-
4	-	1.26	-	-
5	-	1.34	-	-
6	-	1.42	-	-
7	-	1.50	-	-
8	1,000.00	1.59	627.41	5,019.30
			Total	5,019.30

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=5019.3/(627.41*1)

=8.00003

Modified duration = Macaulay duration/(1+YTM)

=8/(1+0.06)

=7.547198

c

Using only modified duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-7.55*0.01*627.41

=-47.35

%age change in bond price=Mod.duration prediction/bond price

=-47.35/627.41

=-7.55%

New bond price = bond price+Modified duration prediction

=627.41-47.35

=580.06

d

K = N

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

k=1

K =8

Bond Price =∑ [(0*1000/100)/(1 + 7/100)^k]     +   1000/(1 + 7/100)^8

k=1

Bond Price = 582.01