Question

In: Finance

You are interested in purchasing a bond with three years to maturity and semiannual interest payments....

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?

Solutions

Expert Solution

                  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

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