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17 March, 18:04

Page Enterprises has bonds on the market making annual payments, with nine years to maturity, and selling for $948. At this price, the bonds yield 5.9 percent. What must the coupon rate be on the bonds?

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  1. 17 March, 19:25
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    Coupon rate is 5.17%

    Explanation:

    Yield to maturity is the annual rate of return that an investor receives if a bond bond is held until the maturity.

    Assuming Face value of the bond is $1,000

    Face value = F = $1,000

    Selling price = P = $948

    Number of payment = n = 9 years

    Bond Yield = 5.9%

    The coupon rate can be calculated using following formula

    Yield to maturity = [ C + (F - P) / n ] / [ (F + P) / 2 ]

    5.9% = [ C + ($1,000 - $948) / 9 ] / [ ($1,000 + $948) / 2 ]

    5.9% = [ C + $5.78 ] / $974

    5.9% x $974 = C + $5.78

    $57.466 = C + $5.78

    C = $57.466 - $5.78 = $51.686

    Coupon rate = $51.686 / $1,000 = 0.051686 = 5.17%
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