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Math Help - Yield to Maturity of a bond

  1. #1
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    Question Yield to Maturity of a bond

    I'm having trouble understanding how to calculate the yield of maturity of a bond.
    Here is an excerpt from my textbook.
    Suppose that the current term structure has the following yields on zero coupon bonds

    Term ___________ Zero Coupon Bond Rate
    1/2 Year______________8%
    1 Year________________9%
    1 1/2 Year____________10%
    2 Year________________11%


    Find the price per $100 face amount and yield to maturity of each of the following 2-year bonds (with semi-annual coupons):
    (i) zero coupon bond
    (ii) 5% annual coupon rate
    (iii) 10% annual coupon rate
    Then it has them solutions listed below

    (i) Price is 100(1+.055)^-4= 80.72 and yield to maturity is (nominal) 11%

    (ii) Price is 2.5[(1.04)^-1+(1.045)^-2+(1.05)^-3]+102.5(1.055)^-4= 89.59
    Yield to maturity is (nominal) 10.9354%

    (iii) Price is 5[(1.04)^-1+(1.045)^-2+(1.05)^-3]+105(1.055)^-4= 98.46
    Yield to maturity is (nominal) 10.8775%
    I understand how they calculated the price, but I have look throughout my whole notes and the book and it never explains how they calculated the yield to maturity.
    If anyone knows how, i would highly appreciate it, final exam is tomorrow!
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  2. #2
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    Sep 2010
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    after searching around the internet for a while i found a video on a website that showed me how to do it in EXCEL
    if anyone else runs into a problem like this just check this out.
    How to get yield to maturity (YTM) with Excel
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  3. #3
    Member
    Joined
    Jan 2009
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    Punjab, Pakistan
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    88

    Bond Price Calculation for Non Zero Coupon Bonds

    Quote Originally Posted by fenderic View Post
    I understand how they calculated the price, but I have look throughout my whole notes and the book and it never explains how they calculated the yield to maturity.
    I do understand how the author may have computed the YTM, but I am unable to understand the way the author is calculating the bond prices for 5% 2 yr and 10% 2 year $100 bonds

    The table you show on top gives yields for Zero Coupon bonds maturing in 6 months, 1 year, 1 and half year and 2 years

    Why is the author using these yields to solve for Bond prices of ii) and iii)

    The formula for Bond Price discounts each interest payment at period t and adds it to the discounted terminal value of the bond

    The formula he is using is right but I am unable to understand why the author is using semi annual yields from the table to discount each of the interest payments.

    Price of the Non Zero Coupon Bond Formula (Semi Annual Compounding)

    P = INT x PVIFA(YTM%/2, 2N) + Par Value x PVIF(YTM%, 2N)

    which is equivalent to what the author has it

    P = SIGMA T=1->2N-1 [ INT/(1+YTM%/2)^T ] + (INT+Par Value)/(1+YTM%/2)^2N
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