# Constant Growth Dividend Discount Model

The constant growth dividend discount model theory states that the share price should be equal to the present value of the future dividend payments. The dividend discount model provides a method to value stocks and, therefore, companies.

We also refer to the dividend discount model as the dividend valuation model, Gordon’s Growth Model or dividend growth model.

## Dividend Discount Model Formula

As explained above, the stock value should be the same as the discounted future dividend payments. We can apply the dividend discount model to scenarios where dividend distribution is constant when there is continuous growth or even when the growth of the dividends changes. For example, most stocks do not have a constant dividend growth but change their dividends based on profitability or investment opportunities.

## Constant Growth Dividend Discount Model

To keep things as simple as possible, we assume that there is a constant dividend growth rate. In other words, the dividends are growing at a constant rate per year.

## Constant Growth Dividend Discount Model Example

We will use company “A” as an example who paid \$0.5 as an annual dividend. The dividend growth for the past five years has been 5 per cent, and we expect it to stay the same. Finally, we were able to use the capital asset pricing model and calculate the cost of equity which is 10%.

Based on the above, the price of one share should be 0.5*(1+0.05)/(0.1-0.05)=\$10.5 per share.

## Dividend Discount Model with Constant Dividends

The dividend discount model can be used to value a share when the dividends are constant over time. This case can be applicable when you value preference shares that might offer predetermined annual dividends. Since there is no growth, the formula becomes:

Using the same example above, we expect the price of one stock to be lower as the total dividends that a firm will distribute are lower.  Therefore, the value of one share is (\$0.5/0.1)=\$5.

## Multi-Stage Dividend Discount Model

In reality, dividend growth is rarely constant over time. Most companies increase or decrease the dividends they distribute based on the profits generated or based on the investment opportunities.

For example, it is common for a company to choose to have a high dividend growth rate for some years (after introducing a new product, for example), which we would expect to decrease.

## Earnings Retention Model-Ratio

Finding the dividend growth rate is not always an easy task. Alternatively, you can use the earnings retention ratio to “benchmark” the dividend growth rate. The assumption is that the dividend growth comes from reinvesting funds that the firm doesn’t pay to shareholders. Instead, the firm invests these funds in projects that increase profits and dividends.

We can calculate the growth based on the retention model ratio as the rate of return multiplied by the percentage of the profits retained and not distributed.

For example, if a company distributes 40% of its profits and retains 60% while projects the company runs yield a 7% rate of return, the growth of the dividends is 0.6*0.07=0.042 or 4.2%.

## Dividend Discount Model Uses

As mentioned at the beginning of this post, analysts use the dividend discount model worldwide. Some of its uses are:

• To develop a forecast for the price of a stock;
• To calculate the fair value of a stock;
• To value a company;
• To calculate the cost of equity if we know the dividend growth rate, the price of the stock (for listed companies) and the annual dividend paid, and;
• To calculate the beta of a stock using the capital asset pricing model (by finding the cost of equity).

## Dividend Discount Model Limitations

The dividend discount model has a theory that the price of a stock should be the same as the present value of the future dividends. In reality, companies might choose not to pay dividends (Apple, for example) or might choose to repurchase their stock. If a company decides to reinvest their profits instead of distributing them, the chances are that the market will react positively (all things being equal). Therefore, the dividend discount model will be unable to “capture” the increase in the stock price as the firm will pay no increase in the dividends.