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9 October, 05:31

Big Canyon Enterprises has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and a price of $969. At this price, the bonds yield 8.1 percent. What must the coupon rate be on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.)

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  1. 9 October, 07:17
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    Coupon rate = 3.8%

    Explanation:

    we know that:

    r = YTM = [C + (F-P) / n] / (F+P) / 2

    where r = bond yield rate = 8.1% =.081

    F = Face valye of bond = $1000

    P = Price of bond = $ 969

    n = number of periods to maturity = 17 years

    C = coupon payment = ?

    Solution:

    0.081 = C + [ (1000-969) / 17 ] / (1000+969) / 2

    0.081 = (C + 1.8235) / 492.25

    0.081 * 492.25 = C + 1.8235

    39.872 = C + 1.8235

    39.872-1.8235 = C

    C = 38.04 (coupon payment).

    we know that:

    Coupon rate = annualized interest (coupon) / par value of bond

    = 38.04 / 1000

    = 3.8%
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