1. Bond A is a 5% semi-annual coupon bond with 5 years to maturity; its par valu
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1. Bond A is a 5% semi-annual coupon bond with 5 years to maturity; its par value is $1000; the YTM is 7%; there are 10,000 units of bond A held in the portfolio. Bond B is a 3-year 6% semi-annual coupon bond, $500 par value, and its YTM is 8%; you hold 5,000 units of Bond B. (You must keep 5 decimal places in all steps, eg. $5.67867, otherwise you get 0) [12 points] What is the duration of Bond A and Bond B? 1. Bond A is a 5% semi-annual coupon bond with 5 years to maturity; its par value is $1000; the YTM is 7%; there are 10,000 units of bond A held in the portfolio. Bond B is a 3-year 6% semi-annual coupon bond, $500 par value, and its YTM is 8%; you hold 5,000 units of Bond B. (You must keep 5 decimal places in all steps, eg. $5.67867, otherwise you get 0) [12 points] What is the duration of Bond A and Bond B? 1. Bond A is a 5% semi-annual coupon bond with 5 years to maturity; its par value is $1000; the YTM is 7%; there are 10,000 units of bond A held in the portfolio. Bond B is a 3-year 6% semi-annual coupon bond, $500 par value, and its YTM is 8%; you hold 5,000 units of Bond B. (You must keep 5 decimal places in all steps, eg. $5.67867, otherwise you get 0) [12 points] What is the duration of Bond A and Bond B?Explanation / Answer
Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $1,000 Annual Coupon % 5.00% Annual Coupon Amount $50.00 Semi Annual Coupon Amount $25.00 Step 2: Calculate number of years to Maturity Number of years to maturity =5 years Interest is paid semi annyally so total period = 5 Years * 2 = 10 Periods Step 3 : Caclulation of the duration of the Bonds A Market rate of interest or Yield to Maturity or Required Return = 7% Bonds interest is paid semi annualy means so discounting factor = 7 % /2= 3.5 % PVF = 1 / Discount rate = 1/ 1.035 Result of above will again divide by 1.035 , repeat this till last period Period (A) Cash Flow (B) PV of $ 1 at 3.5% ('C) Present Value of the Cash Flow (AXBXC) 1 $25.00 0.96618 24.15459 2 $25.00 0.93351 46.67554 3 $25.00 0.90194 67.64570 4 $25.00 0.87144 87.14422 5 $25.00 0.84197 105.24665 6 $25.00 0.81350 122.02510 7 $25.00 0.78599 137.54842 8 $25.00 0.75941 151.88231 9 $25.00 0.73373 165.08947 10 $25.00 0.70892 177.22970 10 $1,000 0.70892 7089.18814 8173.82983 Duration = 8173.82983 Divide By = "/"By Par Value = 1000 Duration = 8.17383 Step 1 : Calculation of Annual Coupon Payments Par value of the bond issued is = $500 Annual Coupon % 6.00% Annual Coupon Amount $30.00 Semi Annual Coupon Amount $15.00 Step 2: Calculate number of years to Maturity Number of years to maturity =3 years Interest is paid semi annyally so total period = 3 Years * 2 = 6 Periods Step 3 : Caclulation of the duration of the Bonds A Market rate of interest or Yield to Maturity or Required Return = 8% Bonds interest is paid semi annualy means so discounting factor = 8 % /2= 4 % PVF = 1 / Discount rate = 1/ 1.04 Result of above will again divide by 1.04 , repeat this till last period Period (A) Cash Flow (B) PV of $ 1 at 4 % ('C) Present Value of the Cash Flow (AXBXC) 1 $15.00 0.96154 14.42308 2 $15.00 0.92456 27.73669 3 $15.00 0.88900 40.00484 4 $15.00 0.85480 51.28825 5 $15.00 0.82193 61.64453 6 $15.00 0.79031 71.12831 6 $500 0.79031 2370.94358 2637.16927 Duration = 2637.16927 Divide By = "/"By Par Value = 500 Duration = 5.27434 Answer = Duaration of the Bonds A is = 8.17383 Duaration of the Bonds B is = 5.27434
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