Question

Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 7.7%. What is the duration if the yield to maturity is 11.7%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

YTM Duration 7.7% YTM 11.7% YTM

Answer 1

Calculation of Duration

PV Rate @ 7.7%
Following data are available
Face Value	1000	(Assume)
Coupon Rate	6%
Years to maturity	3	years
Redemption Value	1000
Yield to maturity	7.70%

First step : Calculate market price of bonds
60, present value 7.7% for 3 years)		60*2.59	155.4
1000, present value 7.7% for 3 years)		1000*.800	800
Market Price			955.4
Second Step: Calculation of bond
Year	PV @7.7%		Proportion of bond Value	Proportion of bond value x time
1	0.928	55.68	0.05828	0.05828
2	0.862	51.72	0.05413	0.10827
3	0.8	848	0.88759	2.66276
		955.4	1	2.82931
Duration of bonds is 2.8293 years

PV Rate @ 11.7%
Face Value	1000		(Assume)
Coupon Rate	6%
Years to maturity	3		years
Redemption Value	1000
Yield to maturity	11.70%
First step : Calculate market price of bonds
60, present value 11.7% for 3 years)		60*2.4113		144.678
1000, present value 11.7% for 3 years)		1000*.7162		716.2
Market Price				860.878
Second Step: Calculation of bond
Year	PV @11.7%			Proportion of bond Value		Proportion of bond value x time
1	0.8947	53.682		0.06236		0.06236
2	0.8005	48.03		0.05579		0.11158
3	0.7162	759.172		0.88185		2.64556
		860.884		1.00000		2.81949
Duration of bonds is 2.8195 years