Dividend discount formula

• Jun 3rd 2010, 02:38 PM
Yvginkel
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!
• Jun 4th 2010, 12:30 PM
SpringFan25
More information is needed here. Specifically, you have to make assumptions about $\displaystyle r_t$ and $\displaystyle g$

I assume you want g to be constant and $\displaystyle r_t = (1+i)^t$ 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

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

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

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

You should be able to simplify and rearrange this for $\displaystyle i$
Then you have $\displaystyle r_t$ from our assumption $\displaystyle r_t = (1+i)^t$
• Jun 4th 2010, 01:34 PM
Yvginkel
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...
• Jun 4th 2010, 07:00 PM
TKHunny
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.