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26 December, 07:51

g Your grandfather purchased a $1,000 face-value bond 10 years ago. When he purchased the bond, it had 30 years to maturity and a coupon rate of 5% paid annually. Now you want to sell the bond and read that the yield on similar bonds is 4.93%. What can you sell the bond for today

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  1. 26 December, 08:13
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    You can sell the bond for $1,008.78 today

    Explanation:

    We need to calculate current value of the bond & its coupon

    Face value: $1,000

    Left tenor: 20 years ( = 30 years to maturity - 10 years ago)

    Coupon rate: 5%

    Yield to maturity: 4.93%

    Total coupon to be paid every year = $1,000 * 5% = $50

    To calculate the current value of coupon received in every of 20 years, we use formula PV in excel or manually as below:

    PV = 50 / (1+4.93%) ^20 + 50 / (1+4.93%) ^19 + ... + 50 / (1+4.93%) ^1 = $626.83

    The current value of face value after 20 years = $1,000 / (1+4.93%) ^20 = $381.95

    So the value of bond = $626.83 + $381.95 = $1,008.78
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