Question

Find the duration of a 3% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6.1%. What is the duration if the yield to maturity is 10.1%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

YTM	Duration
6.1% YTM
10.1% YTM

Answer 1

1

K = N

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

k=1

K =3

Bond Price =∑ [(3*1000/100)/(1 + 6.1/100)^k]     +   1000/(1 + 6.1/100)^3

k=1

Bond Price = 917.29

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($917.29)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	30.00	1.06	28.28	28.28
2	30.00	1.13	26.65	53.30
3	1,030.00	1.19	862.36	2,587.09
			Total	2,668.67

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

=2668.67/(917.29*1)

=2.9093

2

K = N

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

k=1

K =3

Bond Price =∑ [(3*1000/100)/(1 + 10.1/100)^k]     +   1000/(1 + 10.1/100)^3

k=1

Bond Price = 823.74

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

=2391.99/(823.74*1)

=2.9038

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($823.74)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	30.00	1.10	27.25	27.25
2	30.00	1.21	24.75	49.50
3	1,030.00	1.33	771.75	2,315.24
			Total	2,391.99