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15 January, 07:06

Find the duration of a 7.6% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6.0%. What is the duration if the yield to maturity is 12.0%? Note: The face value of the bond is $100

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  1. 15 January, 07:57
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    What is given:

    Semiannual coupon payments [7.6%*100/2 = 3.8]

    n = 3*2 = 6 periods

    YTM = 6%; 12%

    Calculations:

    YTM = 6%

    Cash-flows during periods 1-5 = 3.8 and pays 103.8 at the end

    PV of CF1 = 3.68932

    PV of CF2 = 3.581864

    PV of CF3 = 3.477538

    PV of CF4 = 3.376251

    PV of CF5 = 3.277913

    PV of CF6 = 86.93087

    Price (Total of CFs) = 104.3338

    Weighted CF1 = 3.8

    Weighted CF1 = 2*3.8 = 7.6

    Weighted CF2 = 3*3.8 = 11.4

    Weighted CF3 = 4*3.8 = 15.2

    Weighted CF4 = 5*3.8 = 19

    Weighted CF5 = 6 * 103.8 = 622.8

    PV of Weighted CF1 = 3.68932

    PV of Weighted CF2 = 7.163729

    PV of Weighted CF3 = 10.43261

    PV of Weighted CF4 = 13.505

    PV of Weighted CF5 = 16.38957

    PV of Weighted CF6 = 521.5852

    Sum of weighted CFs = 572.7654

    Duration 2.744871

    YTM = 12%:

    PV of CF1 = 3.584906

    PV of CF2 = 3.381986

    PV of CF3 = 3.190553

    PV of CF4 = 3.009956

    PV of CF5 = 2.839581

    PV of CF6 = 73.1749

    Price (Total of CFs) = 89.18189

    Weighted CF1 = 3.8

    Weighted CF1 = 2*3.8 = 7.6

    Weighted CF2 = 3*3.8 = 11.4

    Weighted CF3 = 4*3.8 = 15.2

    Weighted CF4 = 5*3.8 = 19

    Weighted CF5 = 6 * 103.8 = 622.8

    PV of Weighted CF1 = 3.584906

    PV of Weighted CF2 = 6.763973

    PV of Weighted CF3 = 9.57166

    PV of Weighted CF4 = 12.03982

    PV of Weighted CF5 = 14.19791

    PV of Weighted CF6 = 439.0494

    Sum of weighted CFs = 485.2077

    Duration 2.720326
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