# Dividend Discount Model: A guide

The dividend discount model is based on the theory that the price of a share should be equal to the present value of the future dividend payments. The dividend discount model is widely used as a method to value stocks and therefore companies.

The dividend discount model is also referred as dividend valuation model, Gordon’s Growth Model or dividend growth model.

## Dividend Discount Model Formula

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

## Constant Growth Dividend Discount Model

In order 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 just paid \$0.5 as an annual dividend. The dividend growth for the past five years has been 5% and is predicted 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 are trying to value preference shares that might offer predetermined annual dividends. Since there is no growth, the formula becomes:

### Dividend Discount Model with Constant Dividends Example

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

## Multi-Stage Dividend Discount Model

In reality, the 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 they have.

For example, it a common for a company to choose to have a high dividend growth rate for some years (after the introduction of a new product for example) which is then expected to be decreased.

## Earnings Retention Model-Ratio

Finding the dividend growth rate is not always an easy task. As an alternative, 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 are not distributed. These funds are invested in projects that will increase the profits generated and therefore the dividends distributed.

The growth based on the retention model-ratio can be calculated 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 the projects that 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 in the beginning of this post, the dividend discount model is widely used. 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.
• 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 is based on the 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 own stock. If a company chooses to reinvest their profits instead of distribute them, chances are that the market will react positively (all things being equal). Therefore, the dividend discount model will be unable to “capture” the increase of the stock price as there will be no increase in the dividends paid.

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