Question

Using a two year semiannual 8% coupon bond, 1000 par, with a 5% YTM. For this question find all answers to at least the 6th decimal place.

Calculate the price of this bond

Calculate duration and modified duration

Price the same bond with a YTM of 6% and 10% as you did in the first part

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =3x2

Bond Price =∑ [(8*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^3x2

k=1

Bond Price = 1082.62188

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,082.62)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	40.00	1.03	39.02	39.02
2	40.00	1.05	38.07	76.15
3	40.00	1.08	37.14	111.43
4	1,040.00	1.10	942.19	3,768.75
			Total	3,995.36

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

=3995.36/(1082.62188*2)

=1.845222

Modified duration = Macaulay duration/(1+YTM)

=1.85/(1+0.05)

=1.800217

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =3x2

Bond Price =∑ [(8*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^3x2

k=1

Bond Price = 1054.171914

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =3x2

Bond Price =∑ [(8*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^3x2

k=1

Bond Price = 949.243079