What Is the Dividend Discount Model?
The dividend discount model (DDM) or discounted dividend model is a model used to project the fair value of a stock based on the premise that the stock’s current price should be equal to the present value of all future expected dividends for the stock. This price is calculated using several assumptions, including next year’s dividend, perpetual dividend growth rate, and the cost of equity. The dividend discount model is frequently used to determine the value of mature companies with a consistent dividend history.
Understanding the Dividend Discount Model
Good businesses make profits, and some of them make a lot of it. The same businesses use investors’ money at the start of operations or in the interim based on their capital requirement. When the business starts making money, the investors also look to earn returns on their investments.
The investors get rewarded for their capital by capital appreciation – when the value of their investments increases and they sell their investments to another party for a profit. Another way to reward the shareholders is through dividends – a part of profits distributed to shareholders periodically.
In the dividend discount model, we assume that the investors get rewarded only through the dividends for the company’s entire life. We further assume that the company’s current value is the value of all its future dividends in current dollars – the present value of future dividends discounted at the investors’ required rate of return.
The most commonly used model in DDM is the Gordon Growth Model, named after Myron J. Gordon of the University of Toronto, who originally published it in 1959.
The entire premise of the dividend discount model is based on the time value of money principle, a concept we will discuss in the next section.
Time Value of Money
Time Value of Money (TVM) essentially states that the amount of money you have today is worth more than the identical sum of money at a future point. This is because money has an earning power, which is lost if it is not put to use.
For example, assume a friend owes you a sum of $1000, and he somehow has the capacity to pay you the entire $1000 now. He also gives you an option to take the same $1000 a year later.
Now, no matter how generous you are, you would take the first option because you know you will be without that money for a year and still get only what was due a year ago in the second option.
If you take your $1000 now and go to your bank, the banker will happily take that money and offer you interest to keep it in a deposit. Let’s assume that the bank pays you 5% interest. In that case, you will be $50 richer at the end of the year. You would not have the $50 if you took option 2.
In TVM, the future value of money is calculated as follows:
The additional $50 that you get in the above example is the increase in the value of money over time.
With this equation, you can also calculate how much your future money is worth in today’s dollars. This can be calculated by rearranging the Present Value equation (This is what most financial analysts mean when they refer to the present value of future cash flows).
The equation can be further rearranged to calculate the Interest Rate. The dividend discount model uses the TVM principle for dividends, essentially adding up the present values of all future dividends that the company will pay. Let’s see how we can calculate those future dividends.
Estimating future dividends can be extremely complex because it requires the company’s earnings forecast for its perpetual future and a payout ratio – the percentage of earnings paid out in dividends.
For the sake of simplicity, in the dividend discount model, we assume that the company will maintain a constant growth rate in dividends for its perpetual future. So, for example, if the company has paid a recent dividend of $2 and is expected to increase these dividends by 5% every year, we assume this 5% as the constant growth rate in dividends.
One should not assume very high perpetual growth rates for DDM. However, it should definitely be in sync with the long-term economic (GDP) growth rate because it is hard for businesses to maintain an exceptionally high growth rate for perpetuity.
The expected dividend is represented by “D” in the dividend discount model.
Earlier, we discussed how we could calculate the present value of money we will receive in the future. In the formula, we used a “discounting factor” expressed as (1+ Interest Rate) to arrive at the present value (or discounted cash flow value) from the future value.
While calculating the future value from the present value, the same expression (1 + Interest Rate) becomes the “compounding factor.”
The discounting and compounding factor we discussed in the TVM section was for single-period TVM calculations. In a multi-period model, the formula changes a little, and these factors are raised to the power with the appropriate number of years.
For example, if in the previous example, the bank deposit pays you 5% per year only if you leave your money in the account for three years. Then, the future value can be calculated as:
Similarly, the present value can be calculated as follows:
In the dividend discount model, we use a discounting factor formulated on similar lines to arrive at a cumulative present value of all the company’s future dividends.
Let’s see how it works.
The DDM discounting factor is expressed mathematically as follows:
The formula looks a lot different than the one we discussed above. One should note that this formula is used when we are discounting perpetual dividends and not the future dividends for a set number of years.
The first part of the above equation relates to the investor’s expected return rate from the investment. The best representation of the expected return rate for any business is the cost of its equity capital.
Though firms don’t pay a fixed rate on their equity capital, the cost of equity capital is the rate that investors demand to take the risk of investing in the firm. Investors then realize this rate of return through capital appreciation or dividends.
The expected return or cost of equity (r) is calculated using the Capital Asset Pricing Model (CAPM). The model calculates the expected rate of return using a premium that the investor should demand above the risk-free rate for taking the risk of investing in the company.
The premium is adjusted for the company’s market-specific volatility represented by a variable called Beta. In simple terms, Beta is the volatility of the company’s stock relative to the general market. A beta of less than 1 indicates that the stock is less volatile and risky than the market, while a beta of more than 1 indicates the opposite. Thus, the farther the Beta is from 1, the more volatile and risky the stock is, and the more premium investors should demand for holding the stock.
The expected rate of return or cost of equity (r) is calculated using the following formula.
r = Risk -free Rate + Beta * (Expected market return – risk-free rate)
The next pillar in the SSM discounting factor is the constant dividend growth rate (g). This growth rate can be computed as the product of the firm’s return on equity (ROE) and retention ratio.
The retention ratio is the part of the company’s profit that is not distributed to investors and retained for future growth.
As the firm can only pay out as much as it earns, the dividend payout ratio cannot be above 100%. Mathematically, when the dividend payout is 100%, the retention ratio will be 0%, and so is the constant dividend growth rate (g). The logic here is that the firm will not be able to grow its profits or dividends if it does not invest its residual profits.
While that’s true in theory, some firms can grow profits in the real world even without investing their residual profits in business.
The expected return on the investment or cost of common equity (r) should always be higher than the constant dividend growth rate (g). A lower “r” will return a negative discounting factor, which will distort the company’s present value using the dividend discount model.
Dividend Discount Model Formula
Once we have all the required variables, it is fairly straightforward to calculate a stock’s value using the following DDM formula.
We use the next year’s dividends in the formula because we discount the future dividends and therefore can’t use the current dividends. Using the current dividends in the formula will give us the stock value of a year ago, which will not be relevant.
One can calculate the expected next year’s dividend by simply applying the constant growth rate to the current divided. The formula is mainly applicable to firms that pay out regular dividends.
Dividend Discount Model Variations
There are three common variations of the DDM.
The first variation of the dividend discount model is the zero growth rate DDM, which assumes a zero growth rate in dividends. In the absence of the growth rate, the formula simply becomes a division of next year’s expected dividend (D1) and the cost of common equity (r).
The second and the most commonly used variation is called the Gordon Growth Model, also called the constant growth model or the constant growth dividend discount model. It is calculated using the following variables: next year’s dividend (D1), the cost of common equity (r), and constant dividend growth rate (g). While this methodology may be an acceptable estimate for a fairly high-yielding mature company, it incorrectly values stocks with high dividend growths but lower dividend yields. Here is the formula for the Gordon Growth Model:
The third variation of the dividend discount model is the Variable Growth DDM or multi-stage dividend discount model, which assumes one or more temporary stages of higher growth in dividends (the growth phases) and a stage of constant growth thereafter. In this variation, we add the present values of all the dividends in the temporary phase and then add a terminal value for the period of constant growth. This terminal value is calculated using the Gordon growth model discussed above.
Examples of the Dividend Discount Model
Here is a simple example of the DDM.
Assume a company paid a dividend of $2 this year and expects this dividend to grow at a constant rate of 5% per year (g) in perpetuity. The cost of common equity for the firm is 8% (r).
To calculate the stock’s value using the Dividend Discount Model, we need the next year’s dividend per share, which can be calculated by applying the growth rate to the current dividend.
$2 * (1+ 5%) = $2.1
We then calculate the value of the stock using the Gordon Growth DDM
$2.1 / (8% – 5%) = $70
Therefore, the current value of the stock is $70. If the same stock is trading below $70, it will be perceived to be undervalued, and if it is trading above $70, it will be perceived to be overvalued.
Shortcomings of Dividend Discount Model
Though DDM is known for its simplicity, this straightforward model does have some limitations.
The first shortcoming that the model has is that it assumes a constant growth rate in perpetuity. While this may be possible for some companies, it is not easily applicable to a large part of the investment universe. Many companies have fluctuating earnings and dividends, and many don’t even pay dividends. In such cases, the model is not as good a value forecaster as regular dividend-paying firms.
The second shortcoming of DDM is that the output is wildly susceptible to input assumptions. Even small changes in input assumptions, especially in “r” and “g,” will result in a significantly changed output value.
The model also falls flat when the cost of common equity (r) is less than the constant growth rate (g). For example, that can happen when a loss-making company continues to pay dividends.
Using the Discount Dividend Model for Investments
The dividend discount model is one of the simplest stock valuation models available at the investors’ disposal. One can calculate the stock’s intrinsic value using DDM and compare it with the current price to ascertain the over-or undervalued nature of the stock to make buy and sell decisions.
Because the focus is on dividends, DDM also facilitates the comparison between stocks in different industries. This can be helpful for an investor while deciding between two or more investments in different industries.
However, DDM has its own limitations, and sometimes its real-world application is not great. Luckily, investors have many other valuation models at their disposal that they can use to confirm the output of DDM and make them more confident with their investment choices.
Relying on the dividend discount model alone may not be an investor’s best bet in investing.
Further reading and sources:
Stephen H. Penham wrote an interesting research paper on A Synthesis of Equity Valuation Techniques and the Terminal Value Calculation for the Dividend Discount Model. (1998, University of California, Berkeley).