**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:

\[P=D\frac{\left(1+g\right)}{\left(i-g\right)}\]
\[\ \ \ =\ 8\frac{\left(1+0.03\right)}{\left(0.1-0.03\right)}\]
\[\ \ \ =8\frac{\left(1.03\right)}{\left(0.07\right)}=117.71\]