1. ## 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.

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

2. 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...

3. 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 ${dps_3}$.