In: Finance
You are interested in purchasing a bond with three years to maturity and semiannual interest payments. The bond has a 7% coupon rate and a 9% yield to maturity. The bond has a $1,000 par value. What is the bond’s duration in years?
K = Nx2 |
Bond Price =∑ [( Coupon)/(1 + YTM/2)^k] + Par value/(1 + YTM/2)^Nx2 |
k=1 |
K =3x2 |
Bond Price =∑ [(7*1000/200)/(1 + 9/200)^k] + 1000/(1 + 9/200)^3x2 |
k=1 |
Bond Price = 948.42 |
Period | Cash Flow | Discounting factor | PV Cash Flow | Duration Calc |
0 | ($948.42) | =(1+YTM/number of coupon payments in the year)^period | =cashflow/discounting factor | =PV cashflow*period |
1 | 35.00 | 1.05 | 33.49 | 33.49 |
2 | 35.00 | 1.09 | 32.05 | 64.10 |
3 | 35.00 | 1.14 | 30.67 | 92.01 |
4 | 35.00 | 1.19 | 29.35 | 117.40 |
5 | 35.00 | 1.25 | 28.09 | 140.43 |
6 | 1,035.00 | 1.30 | 794.77 | 4,768.63 |
Total | 5,216.07 |
Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year) |
=5216.07/(948.42*2) |
=2.749871 |