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Thread: Re-writing formula

  1. #1
    Jun 2010

    Re-writing formula

    I'm trying to re-write the dividend-discount formula below so that rdiv is the result of the formula. tx is limited to x=3.

    Re-writing formula-naamloos.jpg

    I'm stuck at:
    dps1 - (dps3/r^3) = (P0 - P3)(r-1)

    Could you please help me out?
    Last edited by Yvginkel; Jun 20th 2010 at 01:52 AM.
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  2. #2
    MHF Contributor
    May 2010
    are you sure thats the right formula? The denominator in your sum appears to be applying the same discount factor to all dividends, even though they happen at different times.

    I think the formula you want is:
    \displaystyle P_0 = \left( \sum \frac{dps_t}{r_{div}^t} \right)  + \frac{P_{t_x}}{r_{div}^{t_x}}

    whichever formula you use, provided r_{div} is constant you can write s=\frac{1}{r_{div}}. You may be able to factorise depending on the values of dps_t and P_{t_x}. Otherwise you have a cubic in s to solve, time to find a computer...
    Last edited by SpringFan25; Jun 20th 2010 at 04:18 AM.
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  3. #3
    Jun 2010
    Sorry, you're right it should be \displaystyle P_0 = \left( \sum \frac{dps_t}{r_{div}^t} \right)  + \frac{P_{t_x}}{r_{div}^{t_x}}

    {r_{div}} is constant;
    the sum is maxed for 3 periods; and
    x = 3

    Hence s=\frac{1}{r_{div}} won't work as the sum has only three periods.

    I got to {dps_1} - \frac{dps_3}{r_{div}^3} = ({P_0}-{P_3})(r-1) by eliminating {dps_2} and {dps_3}.
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