# Gordon's growth model

Gordon's growth model is a method of valuing the share price of a company using constant growth and discounting the value of future dividends today. She is often known by her English name Gordon Growth model.

It is a dividend discount model that assumes that the growth that the company will experience is constant. It is based on the theory that the price of a share must be equal to the price of the dividends that the company is going to deliver, discounted to its net present value. Where:

- Vo = current value
- Div 1 = Dividend in year 1
- r = required return on shares
- g = expected dividend growth

If the price of the share in the market is lower than the result obtained by the discounted dividend model, the share is undervalued and therefore, it is advisable to buy. If, on the other hand, the market price is higher than that of the model, it is understood that the share price is too high.

It is known as Gordon after its author, Myron J. Gordon, of the University of Toronto, who published it in 1956 together with Eli Saphiro, which is why it is also known as the Gordon-Saphiro Model.

Present value## Calculation of the Gordon growth model

Since it is practically impossible to know what the value of the dividends will be during each of the future years, the Gordon model assumes that the value of each year is equal to the previous one plus a small increase. This small increase is considered constant as if it were the average of all those future growth. That is why it is also known as the constant dividend growth model.

Taking into account the value of each of the future dividends with constant growth, g, we will have the following formula:

If we solve this function we will have the formula that we have seen above: Observing the formula we can deduce that as the difference between r and g increases, the value of the stock decreases. In addition, the final value is very sensitive to this data, since small changes in this difference can cause large variations in the result.

To see how much of the final value is explained by growth (g), some analysts also calculate the formula assuming that growth is zero. So they will know the difference made by that growth.

To estimate the growth factor, you can choose the historical growth of the firm, the median growth of the industry, a growth estimate or even the country's GDP.

This model does not work for all companies, as obviously for companies that do not distribute dividends or for which negative growth is expected above the required return. However, it usually works very well for mature and stable companies that have a non-cyclical behavior.

## Gordon growth model assumptions

In order to simplify the valuation method, Gordon's growth model assumes the following assumptions:

- The constant growth of dividends and the discount rate used will never change in the future.
- Dividends are the appropriate measure of shareholder wealth.
- The discount rate must be greater than the growth, because otherwise the formula does not work.

## Gordon's growth model example

We are going to calculate the current value of a share that distributed € 1 in dividend last year, if it is expected that these will grow at a constant rate of 2% and the required return on the shares is 6%:

First we calculate the dividend 1 (DIV 1): Do (1 + g) = 1 (1 + 0.02) = 1.02

Now we apply the formula of the model:

If the price of the share in the market were, for example, 20 euros, we expect the price of the share to rise.

Financial asset valuation model (CAPM) Growth rate