## What Is the Gordon Growth Model?

The Gordon Growth Model (GGM) is used to determine the intrinsic value of a stock based on a future series of dividends that grow at a constant rate. It is a popular and straightforward variant of a dividend discount mode (DDM).

Given a dividend per share that is payable in one year and the assumption the dividend grows at a constant rate in perpetuity, the model solves for the present value of the infinite series of future dividends. Because the model assumes a constant growth rate, it is generally only used for companies with stable growth rates in dividends per share.

## The Formula for the Gordon Growth Model Is

$\begin{aligned} &P = \frac{ D_1 }{ r - g } \\ &\textbf{where:} \\ &P = \text{Current stock price} \\ &g = \text{Constant growth rate expected for} \\ &\text{dividends, in perpetuity} \\ &r = \text{Constant cost of equity capital for the} \\ &\text{company (or rate of return)} \\ &D_1 = \text{Value of next year's dividends} \\ \end{aligned}$

#### Gordon Growth Model

## What Does the Gordon Growth Model Tell You?

The Gordon Growth Model values a company's stock using an assumption of constant growth in payments a company makes to its common equity shareholders. The three key inputs in the model are dividends per share, the growth rate in dividends per share, and the required rate of return.

Dividends (D) per share represent the annual payments a company makes to its common equity shareholders, while the growth rate (g) in dividends per share is how much the rate of dividends per share increases from one year to another. The required rate of return (r) is a minimum rate of return investors are willing to accept when buying a company's stock, and there are multiple models investors use to estimate this rate.

The Gordon Growth Model assumes a company exists forever and pays dividends per share that increase at a constant rate. To estimate the value of a stock, the model takes the infinite series of dividends per share and discounts them back into the present using the required rate of return. The result is the simple formula above, which is based on the mathematical properties of an infinite series of numbers growing at a constant rate.

The GGM attempts to calculate the fair value of a stock irrespective of the prevailing market conditions and takes into consideration the dividend payout factors and the market expected returns. If the value obtained from the model is higher than the current trading price of shares, then the stock is considered to be undervalued and qualifies for a buy, and vice versa.

## Example Using the Gordon Growth Model

As a hypothetical example, consider a company whose stock is trading at $110 per share. This company requires an 8% minimum rate of return (r) and currently pays a $3 dividend per share (D_{1}), which is expected to increase by 5% annually (g).

The intrinsic value (P) of the stock is calculated as follows:

$\begin{aligned} &\text{P} = \frac{ \$3 }{ .08 - .05 } = \$100 \\ \end{aligned}$

According to the Gordon Growth Model, the shares are currently $10 overvalued in the market.

## Limitations of the Gordon Growth Model

The main limitation of the Gordon growth model lies in its assumption of a constant growth in dividends per share. It is very rare for companies to show constant growth in their dividends due to business cycles and unexpected financial difficulties or successes. The model is thus limited to firms showing stable growth rates.

The second issue occurs with the relationship between the discount factor and the growth rate used in the model. If the required rate of return is less than the growth rate of dividends per share, the result is a negative value, rendering the model worthless. Also, if the required rate of return is the same as the growth rate, the value per share approaches infinity.