Results 1 to 4 of 4

Thread: Calculating the coupon rate

  1. #1
    New Member
    Join Date
    Jan 2015
    Posts
    1

    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
    Feb 2004
    Location
    Ottawa, Ontario
    Posts
    16,803
    Not sure how much help you're asking for...

    YTM = 6.1% means annual return (or effective annual) rate.

    Are you able to calculate the equivalent semi-annual rate?
    I'm just an imagination of your figment !

  3. #3
    Elite Member
    Join Date
    Jul 2014
    Posts
    3,386
    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

  4. #4
    Elite Member
    Join Date
    Feb 2004
    Location
    Ottawa, Ontario
    Posts
    16,803
    Problem can be treated as a loan of $1038.00, calling for 29 semiannual
    payments of $32.03, leaving exactly $1000.00 owing after 29th payment;
    in bank statement format, it'll all look a bit like this:
    Code:
     N      PAYMENT    INTEREST      BALANCE
     0                               1038.00
     1      -32.03       31.19       1037.16
     2      -32.03       31.16       1036.29
    ...
    28      -32.03       30.16       1001.92
    29      -32.03       30.11       1000.00
    The payments are really the coupon amounts.
    The interest is assumed as 6.1% annual effective,
    thus ~3.00486% compounded semiannually:
    (1 + i)^2 = 1.061
    i = 1.061^(1/2) - 1
    i = .0300485....

    Calculation of coupon amount is this way:
    (c=coupon amount, i=semiannual interest rate)

    u = present value of 1000: 1000 / (1 + i)^29
    v = present value of coupons: c[1 - 1/(1 + i)^29] / i
    u + v = 1038 : solve for c

    Hope that helps....and that Sir Jonah agrees...
    Last edited by Denis; 01-14-2015 at 10:06 PM.
    I'm just an imagination of your figment !

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •