Question

1. A five-year bond with a yield of 11% (compounded annually) pays an 8%

   coupon at the end of each year.

   1. (a) What is the bond’s price?

   2. (b) What is the bond’s duration?

   3. (c) Use the duration to calculate the effect on the bond’s price of a 0.2% de-

      crease in its yield.

   4. (d) Recalculate the bond’s price on the basis of a 10.8% per annum yield and

      verify that the result is in agreement with your answer to (c).

Face Value is $100 and five-year bond

Answer 1

a

K = N

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

k=1

K =5

Bond Price =∑ [(8*100/100)/(1 + 11/100)^k]     +   100/(1 + 11/100)^5

k=1

Bond Price = 88.91

b

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($88.91)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	8.00	1.11	7.21	7.21
2	8.00	1.23	6.49	12.99
3	8.00	1.37	5.85	17.55
4	8.00	1.52	5.27	21.08
5	108.00	1.69	64.09	320.46
			Total	379.28

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

=379.28/(88.91*1)

=4.265942

Modified duration = Macaulay duration/(1+YTM)

=4.27/(1+0.11)

=3.843191

c

Using only modified duration

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

=-3.84*-0.002*88.91

=0.68

New bond price = bond price+Modified duration prediction

=88.91+.68

=89.59

d

K = N

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

k=1

K =5

Bond Price =∑ [(8*100/100)/(1 + 10.8/100)^k]     +   100/(1 + 10.8/100)^5

k=1

Bond Price = 89.6