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17 August, 07:30

Gabriele Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $964. At this price, the bonds yield 6.7 percent. What must the coupon rate be on the bonds?

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  1. 17 August, 07:39
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    Coupon rate = 5.8%

    Explanation:

    The price of a bond is the present value (PV) of the future cash flows discounted at its yield.

    So we will need to work back to ascertain the coupon rate

    Step 1

    Calculate the PV of redemption value and PV of interest payments

    PV of Redemption

    = 1.067^ (-5) * 1000

    =723.06

    PV of the annual interest rate

    = price of the bond - PV of redemption

    = $964 - 723.06

    = 240.934

    Step 2

    Calculate the interest payment

    Interest payment = PV of redemption value / annuity factor

    Annuity factor = (1 - (1+r) ^ (-n)) / r

    Annuity factor at 6.7% for 5 years

    Factor = (1-1.067^ (-5)) / 0.067

    = 4.1333

    Interest payment = PV of the annual interest rate / Annuity factor

    Interest payment=

    =240.93/4.1333

    =58.290

    Step 3

    Calculate the coupon rate

    Coupon rate = interest payment / par value

    Coupon rate = (58.290/1000) * 100

    = 5.8%

    Coupon rate = 5.8%
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