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The current price of a stock can be modeled by $P_0 = \frac{D_{1}}{r-g}$ where $D_1$ is the expected dividend, $r$ is the rate of return, and $g$ is the expected growth rate in the perpetuity. If $r<g$, then

$\displaystyle P_0 = \sum_{t=1}^{N} \frac{D_{0}(1+g)^{t}}{(1+r)^{t}} + \frac{P_N}{(1+r)^{N}}$.

Is there anyway to simplify this?

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Yes, using $\sum_{k=0}^{n-1} x^k = (1-x^n)/(1-x)$. –  Raskolnikov Dec 12 '10 at 20:29
The sum is a geometric series, so you can use the formula for the sum of a geometric series. –  Arturo Magidin Dec 12 '10 at 20:29
I guess $D_0=D_1$, but what is $P_N$? Some face value? –  AD. Dec 12 '10 at 21:27

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