Question

Find the duration of a 8% coupon bond making annual coupon payments if it has 3 years until maturity and has a yield to maturity of 10%. Note: The face value of the bond is $1,000. (Do not round intermediate calculations. Round your answers to 3 decimal places.) 10% YTM: Duration = ________ years

Answer 1

K = N

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

k=1

K =3

Bond Price =∑ [(8*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^3

k=1

Bond Price = 950.26

Duration

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($950.26)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	80.00	1.10	72.73	72.73
2	80.00	1.21	66.12	132.23
3	1,080.00	1.33	811.42	2,434.26
			Total	2,639.22

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

=2639.22/(950.26*1)

=2.78

Modified duration = Macaulay duration/(1+YTM)

=2.78/(1+0.1)

=2.52