# 3.2.2. Gordon Growth Model (GGM)

In the Dividend-Discount Model it was assumed that the dividends wouldn’t grow in the future. That is not very likely, especially if you take into consideration economic growth and inflation rates. The most probable is the amount of dividend paid by a company may increase through time. The most used growth model is Gordon Growth Model (by Myron Gordon and Eli Shapiro). It assumes a constant growth rate throughout the perpetuity.

- \(P=\frac{{Div}_1}{{(1+r_e)}^1}+\frac{{Div}_2}{{(1+r_e)}^2}+\frac{{Div}_3}{{(1+r_e)}^3}+\dots +\frac{{Div}_{\infty }}{{\left(1+r_e\right)}^{\infty }}\)

Where:

- g
_{div}: dividend’s constant growth rate.

Transforming the initial equation to a Div0 basis:

- \(P=\frac{{Div}_0.{(1+g_{div})}^1}{{(1+r_e)}^1}+\frac{{Div}_0.{(1+g_{div})}^2}{{(1+r_e)}^2}+\frac{{Div}_0.{(1+g_{div})}^3}{{(1+r_e)}^3}+\ldots+\frac{{Div}_0.{(1+g_{div})}^\infty}{\left(1+r_e\right)^\infty}\)

- \(P=\frac{{Div}_0(1+g_{div})}{r_e-g_{div}}=\frac{{Div}_1}{r-g_{div}}\)

To calculate the cost of equity through the dividend growth model one needs to invert the equation.

- \(r_e=\frac{{Div}_1}{P}+g_{div}\)

It is acceptable for companies with a high dividend that the estimated growth rate of the dividend may be constant. But for companies that pay small dividends (companies with a low payout ratio due to needs of reinvestment of results) it is not likely that these companies will keep dividends within low levels. In such cases if you assume a high constant growth rate you may be overvaluing future dividends (at least those for the closer years), but a low constant growth rate may undervalue future dividends that are further away in time when the payout ratio may be higher.

The answer to two different stages of dividend growth can be made through a multi-period version of the Gordon’s model.

- \(P=\sum_{t=1}^{n}\frac{{Div}_0{(1+g_{div,\ 1})}^t}{{(1+r_e)}^t}+\frac{{Div}_0\times\left(1+g_{div,1}\right)^n\times\left(1+g_{div,2}\right)}{\left(1+r_e\right)^n\times\left(r_e-g_{div,2}\right)}\)

Where:

- g
_{div,1}: growth rate of the initial stage; - g
_{div,2}: growth rate of second stage.

Do not forget that Gordon’s growth model and the use of the dividend-discount model as an all, is quite sensitive to the assumptions that you use, particularly in what refers to the growth rate and to the perceived cost of equity. For that reason, this model is more adequate for companies where foreseen growth is slow.

Next Section: 3.2.3. Capital Asset Pricing Model (CAPM)