Question

Find the duration of a 8.4% 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 11.0%? Note: The face value of the bond is $100. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Answer 1

1)

Coupon payment = 100 x 8.4% x 1/2 = 4.2 $

Required rate = 6%/2 = 3%

n = 3 x 2 = 6

Statement showing duration of bond

Time	Cash flow	PVIF @ 3%	PV	Weight	Weight x time
1	4.2000	0.9709	4.0777	0.0383	0.0383
2	4.2000	0.9426	3.9589	0.0372	0.0743
3	4.2000	0.9151	3.8436	0.0361	0.1083
4	4.2000	0.8885	3.7316	0.0350	0.1402
5	4.2000	0.8626	3.6230	0.0340	0.1701
6	104.20	0.8375	87.2659	0.8194	4.9164
			106.5006	1.0000	5.4475

Thus duration of bond = 5.4475/2 = 2.7238 years

2)

Coupon payment = 100 x 8.4% x 1/2 = 4.2 $

Required rate = 11%/2 = 5.5%

n = 3 x 2 = 6

Statement showing duration of bond

Time	Cash flow	PVIF @ 5.5%	PV	Weight	Weight x time
1	4.2000	0.9479	3.9810	0.0426	0.0426
2	4.2000	0.8985	3.7735	0.0404	0.0807
3	4.2000	0.8516	3.5768	0.0383	0.1148
4	4.2000	0.8072	3.3903	0.0363	0.1450
5	4.2000	0.7651	3.2136	0.0344	0.1718
6	104.20	0.7252	75.5706	0.8082	4.8491
			93.5058	1.0000	5.4041

Thus duration of bond = 5.4041/2 = 2.7020 years