Question

Find the duration of a 7.0% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6.0%. What is the duration if the yield to maturity is 8.4%? Note: The face value of the bond is $100

Answer 1

1) when YTM=6%

Time	Cashflow	PVF@3%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	3.5	0.971	3.40	0.0331	0.03
2	3.5	0.943	3.30	0.0321	0.06
3	3.5	0.915	3.20	0.0312	0.09
4	3.5	0.888	3.11	0.0303	0.12
5	3.5	0.863	3.02	0.0294	0.15
6	103.5	0.837	86.68	0.8439	5.06

Duration of semi annual bond = (Time*Weight)/2

= 5.52/2

= 2.76 years

Note : Since the bond makes semiannual interest payments, total no. of period is 6 (3*2), cashflow per period is 3.5(100*7%/2) and cashflows are discounted at 3% (6/2)

2) when YTM=8.4%

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	3.5	0.960	3.36	0.0349	0.03
2	3.5	0.921	3.22	0.0335	0.07
3	3.5	0.884	3.09	0.0321	0.10
4	3.5	0.848	2.97	0.0308	0.12
5	3.5	0.814	2.85	0.0296	0.15
6	103.5	0.781	80.86	0.8392	5.04

Duration of semi annual bond = (Time*Weight)/2

= 5.52/2

= 2.76 years

Note : Since the bond makes semiannual interest payments, total no. of period is 6 (3*2), cashflow per period is 3.5(100*7%/2) and cashflows are discounted at 4.2% (8.4/2)

You can use the equation 1/(1+i)^n to find PVF using calculator