Question

1. Assume a bond that has a $5000 par value, pays annual coupon interest of 10%, matures in three years, and has a yield to maturity of 12%? What is the duration (i.e., Macaulay’s Duration) of this bond? (Round your answer to 5 decimal places).

2. If the yield to maturity on this bond increases by 125 basis points, what will be the percent change in the price of the bond (according to the answer(s) you calculated above)? Record your answer as a percent rounded to 2 decimal places.

Answer 1

1)

Calculation of Duration: Formula of Duration is given as below: Macau layDurati on PV(C.) 10 Where, Ct is cash flow at time t, PV(C) is the present value of cash flow at time t and T is the total time horizon 12 Calculation of Cash Flow of Bond: Face Value of Bond Maturity Period Coupon rate 14 15 16 17 $5,000 3 years 10.00% 12.0% Annual Coupon $500.00 D14 D16 19 Cash Flow of the Bond will be as follows: Year Cash Flow 2 $500.00 $500 $ 00 $5,500.00 24 Calculation of Duration: Year (t Cash FLow (Ct) YTM (i) Present value factor (P/F,i,n) for each year PV (Ct) = (Ct)*(P/F,i,n 26 27 2 500.00$500.00 $5,500.00G23 12.00% 0.71-1/((1+SD28)AG26) 0.89 0.80 $446.43$398.60 $3,914.79G27 G29 PV (Ct) Fraction of total Value [PV(Ct)/Σ PV $4,759.82 31 0.82-G30/SD31 3.00-G26 2.47 G32 G33 32 0.09 1.00 0.09 0.08 2.00 0.17 35 36 37 38 Duration 2.72868-SUM(E34:H34 Hence Duration of the bond is 2.72868 Years