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Thread: Calculating the coupon rate

  1. #1
    New Member
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    Jan 2015
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    Calculating the coupon rate

    I am stuck trying to figure out how to calculate the coupon rate. The examples I have found do not have it as an unknown.
    Please help! You don't need to use my numbers. I just want to know how to solve.

    Here's what is given:
    14.5 years to maturity, semi-annual payments
    CURRENT price of the bond is $1038
    YTM = 6.1%

    Question: what must be the coupon rate?

    Thank you SO much in advance.

  2. #2
    Elite Member
    Join Date
    Jul 2014
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    3,344
    Quote Originally Posted by valval View Post
    I am stuck trying to figure out how to calculate the coupon rate. The examples I have found do not have it as an unknown.
    Please help! You don't need to use my numbers. I just want to know how to solve.

    Here's what is given:
    14.5 years to maturity, semi-annual payments
    CURRENT price of the bond is $1038
    YTM = 6.1%

    Question: what must be the coupon rate?

    Thank you SO much in advance.
    Given the YTM (=0.061 or 6.1%), the Bond Price (P=1038) is given by
    P = I PVa(YTM/2, 29) + M PVs(YTM/2, 29)
    where I is the periodic bond income (= M * semi-annual coupon rate), M is the maturity value (I would assume $1000), PVa is the Present Value for an annuity
    PVa(i,n) = [tex]\frac{1 - (1+i)^{-n}}{i}[/tex]
    and PVs is the simple present value
    PVs(i,n) = [tex]\frac{1}{(1+i)^{n}}[/tex]
    while i is the period interest rate and n is the period. Solve that equation for the semi-annual coupon rate and convert it to an annual rate.

    You might want to look at
    http://www.investopedia.com/terms/y/yieldtomaturity.asp

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