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Math Help - Re-writing formula

  1. #1
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    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; June 20th 2010 at 12:52 AM.
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  2. #2
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    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; June 20th 2010 at 03:18 AM.
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  3. #3
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    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}}

    Where:
    {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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