# Math Help - Dividend discount formula

1. ## Dividend discount formula

Hello,

I'm trying to convert the formula attached in the .bmp file to Rt = ....
I was wondering if someone could help me with this? Divt is not equal in time and for simplicity can be seen as Div * g^t.

I hope someone can help me with this. Thank you very much in advance!

2. More information is needed here. Specifically, you have to make assumptions about $r_t$ and $g$

I assume you want g to be constant and $r_t = (1+i)^t$ where i is a constant?

if so, and assuming you are at time 0, and dividends are payable once per period starting at time 1, and assuming dividends grow at the constant rate g you can write:

Define:
Div = the first dividend payment (I've assumed this happens at time 1)
g = the constant growth rate of dividends

$P_0 = \frac{Div }{1+i} + \frac{Div \times g}{(1+i)^2} + \frac{Div \times g^2}{(1+i)^3} + ...$

$P_0 = \frac{Div}{g} \times \left( \frac{g}{1+i} + \frac{g^2}{(1+i)^2} + \frac{g^3}{(1+i)^3} + ... \right)$

You can recognise this as a geometric progression. The sum is then;
$P_0 = \frac {\frac{Div}{1+i}}{1-\frac{g}{1+i}}$
$P_0 = \frac {Div}{1+i-g}$

You should be able to simplify and rearrange this for $i$
Then you have $r_t$ from our assumption $r_t = (1+i)^t$

3. Not sure I can follow. Not assuming that i > g, I come to:

Po = ( Div - ( (Div*g^indefinite) / 1+i^indefinite) ) / i

and then I'm kind of stuck...

4. We seem to have a background barrier. I think you are going to have to try your best to describe what it is you are doing and why you are doing it.

"trying to convert the formula" is not a good description. It may be impossible, depending on what it is you are doing.

We can keep guessing at what you want or you can just tell us.