Question

An 8% coupon bond with 3 years to maturity has a yield of 7%. Assume that coupon is paid semi-annually and face value is $1,000.

(a) Calculate the price of the bond. (Keep 2 decimal places, e.g. 90.12)
(b) Calculate the duration of the bond. (Keep 4 decimal places, e.g. 5.1234)
(c) Calculate this bond's modified duration. (Keep 4 decimal places, e.g. 5.1234)
(d) Assume that the bond's yield to maturity increases from 7% to 7.2%, estimate the new price of the bond. (Keep 2 decimal places, e.g. 90.12)

Answer 1

a

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =3x2

Bond Price =∑ [(8*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^3x2

k=1

Bond Price = 1026.64

b

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,026.64)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	40.00	1.04	38.65	38.65
2	40.00	1.07	37.34	74.68
3	40.00	1.11	36.08	108.23
4	40.00	1.15	34.86	139.43
5	40.00	1.19	33.68	168.39
6	1,040.00	1.23	846.04	5,076.24
			Total	5,605.63

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

=5605.63/(1026.64*2)

=2.7301

c

Modified duration = Macaulay duration/(1+YTM)

=2.73/(1+0.07)

=2.6378

d

Using only modified duration

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

=-2.64*0.002*1026.64

=-5.42

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

=-5.42/1026.64

=-0.53%

New bond price = bond price+Modified duration prediction

=1026.64-5.42

=1021.22