Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|cite|improve this question
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.