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Math Help - Bond Pricing - Changing Coupon

  1. #1
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    Bond Pricing - Changing Coupon

    If you have a 1,000 face value bond that is 20 years to maturity, with a 5% coupon rate for the first 10 years and a 6% coupon rate for the last 10 years and a yield to maturity of 6% with interest assumed to be paid semi-annually how do you get the correct value of the bond? Because the coupon is <= the YTM i would assume that this is a discount bond however on my calculator i keep getting a premium, but in excel i get a discount.

    I set it up in 3 parts, the 1,000 / 1.03^40 since it's semi annual i doubled time period and halved the YTM

    then I added two annuities being 25 ( 1- (1/1.03^20)) / .03

    and 30 ( 1-(1/1.03^20))/.03

    What am I doing wrong on my calculator?
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  2. #2
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    Quote Originally Posted by ugakid View Post
    then I added two annuities being 25 ( 1- (1/1.03^20)) / .03
    and 30 ( 1-(1/1.03^20))/.03
    All's correct, EXCEPT you need to PV your last expression:

    [30 ( 1-(1/1.03^20))/.03] / 1.03^20 ; kapish?
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  3. #3
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    why do u discount the second annuity and not the first?
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  4. #4
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    Because the 2nd annuity starts in 10 years, not now.
    When you're calculating it, you're doing so at at 10 years from now.
    So you need to discount the result for 10 years (or 20 periods).
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