BONDS AND SINKING FUNDS Bond Price on Any Date参考.ppt

Chapter 15BONDS AND SINKING FUNDS 15.4 Bond Price on Any Date Solution : a, The number of days from the interest payment on January 15, 1996, to the April 10, 1996 valuation date was 86 The number of days in the full payment interval (from January 15 to July 15) was 182 The coupon interest that accrued over these 86 days was I = Prt = Fbt = $1000(0.038)86/182 = $17.96 Hence, $17.96 of the $965.21 flat price was accrued interest. * * | | | | | Preceding interest Next interest Maturity Present Value Bond price (FV) payment date payment date date bF Date of sale bF bF bF+F Step 1 Step 2 FV=PV(1+i)n i=market’s required rate of return/2 =p n=number of days since the proceeding interest payment total number of days in the full payment interval Step 1: Calculate the present value of the remaining payment on the preceding interest payment date. For the discount rate, use the market rate of return as of the date of sale. Step 2: The bond price is the future value of the step 1 result on the date of sale. Price of a Bond (between interest payment dates): The bond price is the future value, on the purchase date, of the remaining payment’s present value at the preceding interest payment date. Example 1 A $1000, 20-year, 11% coupon bond was issued on August 15, 1994. It was sold on November 3, 1996, to yield the purchaser 8.8% compounded semiannually until maturity. At what price did the bond sell? F=$1000 b=11%/2=5.5% p=8.8%/2=4.4% | | | Nov 3,1996 (Sale date) PV Bond price Aug 15,1996 Feb 15,1997 Aug 15,2014 (Fb) Fb Fb +$1000 Fb=$1000×5.5%=$55 P P Step 1: Calculate the present value of remaining payments on August 15, 1996. PMT FV n