DIVIDEND DISCOUNT MODEL / GORDON GROWTH MODEL
DEFINITION
The dividend discount model is a method of valuing the price of a company's share. Under this model the share price is calculated as the present value of all future dividend payments that the investor expects to receive from the share held. It is assumed that the dividends are paid in perpetuity (forever) and that the dividends grow at a constant rate each year. This model is also called the Gordon Growth Model, named after Myron Gordon.
CALCULATOR

#### Enter the following details:

Current dividend amount:

Expected dividend growth rate: (%)

Expected rate of return or yield: (%)

Share price:
FORMULA AND DERIVATION:
Let $$P$$ be the price of the share (that has to be calculated).
Consider that a dividend of amount $$D$$ is paid now. It is assumed that dividends are paid in perpetuity (paid forever) and also that the dividends would grow constantly at the rate $$g$$.

So, the future dividends would be:
$D\left(1+g\right),D{\left(1+g\right)}^2\dots \dots \dots D{\left(1+g\right)}^t$
The share price P is simply the present value or discounted value of all these future dividends. So, at rate $$i$$,

$P=D\left(1+g\right){\left(1+i\right)}^{-1}+D{\left(1+g\right)}^2{\left(1+i\right)}^{-2}\dots \dots \dots$ $\ \ \ =D\left[\frac{\left(1+g\right)}{\left(1+i\right)}+\ \frac{{\left(1+g\right)}^2}{{\left(1+i\right)}^2}\dots \dots \dots \ \right]$
The terms inside the square bracket form an infinite geometric progression. Using summation of an infinite geometric progression, these terms can be simplified to be written as $$\frac{\left(1+g\right)}{\left(i-g\right)}$$. Therefore,
$P=D\frac{\left(1+g\right)}{\left(i-g\right)}$
It can be noted here, that if $$g$$ is greater than $$i$$, i.e. if growth rate of dividends is greater than the interest rate used to discount the dividends, then, it gives a negative value. So, the dividend growth rate is assumed to be less than $$i$$, in this model.

EXAMPLES
Example 1
An investor wishes to purchase a share which has just received a dividend of $$\textrm{₹}\ 8$$ . It is expected by him that the company will steadily increase the dividend payments by $$3\ \%$$ every year. The investor expects a yield of $$10\ \%$$ p.a.

Here,
D = $$\textrm{₹}\ 8$$ (current dividend)
g = $$3\ \%$$ p.a. (dividend growth rate)
i = $$10\ \%$$ p.a. (yield)

So, the share price would be calculated as follows:
$P=D\frac{\left(1+g\right)}{\left(i-g\right)}$ $\ \ \ =\ 8\frac{\left(1+0.03\right)}{\left(0.1-0.03\right)}$ $\ \ \ =8\frac{\left(1.03\right)}{\left(0.07\right)}=117.71$
RELATED TOPICS
Present value