# How does the Dividend Discount Model value stocks?

*"A cow for her milk. A hen for her eggs, And a stock, by heck, For her dividends" (John Burr Willams) *

As valuation techniques go, the dividend discount model ("DDM") is basically a more conservative cousin of discounted cash flow analysis.

It is to be contrasted with asset-based intrinsic valuation techniques like tangible book value or net net working capital, or residual income-based valuation techniques like EVA.

The DDM approach seeks to value a stock **by using predicted dividends and discounting them back to their present value**. The idea is that, when you buy stock in a publicly listed firm, the only cash flow you receive directly from this investment are expected dividends. The dividend discount model builds from this to argue that the value of a stock should therefore be the present value of all its expected dividends over time.

This valuation model was popularlised by John Burr Williams who published "The Theory of Investment Value" in 1938. Williams was writing back in the 1930s, when people like him and Ben Graham were trying to establish a science of investing after getting burned by the irrational exuberance of the roaring twenties. Williams decided that focusing on reported earnings was like buying "bees for their buzz" instead of their honey. He argued that the only return you could really believe in was the dividend:

"a stock is worth the present value of all the dividends ever to be paid upon it, no more, no less... Present earnings, outlook, financial condition, and capitalization should bear upon the price of a stock only as they assist buyers and sellers in estimating future dividends".

While many analysts have moved away from the dividend discount model, arguing that its focus on dividends is too narrow, it does have the advantage of simplicity & logic. This model seems a good starting point for valuing stocks, since it sensibly connects dividend payments and growth to the stock price. Dividends after all represent the only cash flow from the firm that is tangible to investors. Ideas like free cash flows to equity (FCFE) are most abstract and prudent investors may legitimately argue that they cannot lay claim to these cash flows. Another key advantage is that there are only a few assumptions involved, whereas deriving forecasted free cashflow involves estimates of capex, depreciation and working capital.

## How a DDM Model Works

The basic version of the DDM model is the constant growth or perpetuity DDM. This known as the "Gordon model" after its creator, Myron Gordon, who originally published it in 1959. The Gordon growth model is:

Price = DPS / r −g.

This relates the price of a stock to: i) its expected dividends in the next time period ("DPS"), ii) the cost of equity ("r") and iii) an expected growth rate in dividends ("g"). To illustrate this, let's say that you think company X's expected dividend of £1 will grow by 2% annually, and that the risk profile of the company merits a 7% return on your money. On this basis, the company's equity valuation would be £1 / (.07 - .02) = £20. The Gordon growth model works best when valuing a mature company which has well established dividend payout policies, such as a utility company.

Of course, this model still requires us to estimate the dividend growth rate and the required rate of return, which is not easy. As we've discussed elsewhere, the dividend growth rate can be estimated by using the historical growth rate or relying on management/analysts. However, it is probably best done by using the "sustainable growth" equation. i.e. taking the return on equity (ROE) and multiplying it by the retention ratio (which is 1-the payout ratio).

## The High-Growth Problem

One quirk of the Gordon growth model is its inability to deal with high-growth stocks. If the company's dividend growth rate exceeds the expected return rate (e.g. a company with a dividend growing at 12% while the expected return rate is only 6%), a value cannot be calculated because we would get a negative denominator in the formula. When growth is expected to exceed the cost of equity in the short run, then usually a multi-stage DDM (discussed below) is used to get around this issue.

## Multi-Stage Dividend Discount Models

As discussed, the DDM assumes that dividends will grow at a constant rate forever, but this assumption of a stable dividend growth rate is unrealistic for many firms. However, if we assume that growth will eventually be constant, then we can modify the DDM model to move a step closer to reality by assuming that the company will experience differing growth phases.

For example, a multi-stage DDM might predict that a company will have a dividend that grows at 6% for seven years, 4% for the following two years and then at 2% going forward. Typically, analysts use either a two stage or a three stage model - i.e. an initial period of higher growth and a subsequent period of stable growth, or an initial period of stable high growth, a second period of declining growth and a third period of low growth that lasts forever.

These approaches do however bring even more complexity into the model - they still require estimates as to when and by how much a dividend will change over time, which is not straightforward.

## What if the Stock doesn't pay Dividends?

Of course, one issue is that many publicly traded companies don't pay a dividend, choosing to retain all of their earnings so they can grow. The conventional wisdom is that the dividend discount model cannot be used in this situation. However, this is not the case - a non-dividend paying firm can still be valued based upon dividends that it is expected to pay out when the growth rate declines. Consider an investor with a required return of 7% looking at a stock that is not expected to pay dividends for the next five years, but that will pay a £1 dividend in year six and the dividend is expected to grow 5% annually thereafter. All that needs to be done is to compute the Gordon growth value at year 5, then discount it back for five years. Of course, you do need to make some pretty tenuous assumptions about when a company will start paying a dividend and how much they'll pay.

## Does the DDM Model work?

Empirical tests of the model suggest that, in the long term, undervalued (overvalued) stocks from the dividend discount model outperform (under perform) the market index on a risk adjusted basis. A simple study of the dividend discount model was conducted by Sorensen and Williamson, where they valued 150 stocks from the S&P 400 in December 1980, using the dividend discount model. The undervalued portfolio had a positive excess return of 16% per annum between 1981 and 1983, whereas the overvalued portfolio had a negative excess return of 15% per annum.

However, it is unclear how much the model adds in value vs. other investment strategies that use PE ratios or dividend yields to screen stocks. According to Damodaran, a study by Jacobs and Levy indicated that the marginal gain was relatively small. They found that using a low PE approach added 0.92% to your quarterly returns, whereas using the dividend discount model just added a further 0.06% to quarterly returns.

## Model Criticisms

Although it has the advantage of simplicity and its intuitive logic, there are also some drawbacks to using the dividend discount model.

**1. Assumption Dependent **- One flaw of the dividend discount model (or any valuation model, for that matter) is that it requires numerous assumptions to be made (regarding growth rates, time frame, or the required rate of return), and the models can be very sensitive to those assumptions. Even a slight miscalculation in any of these inputs can result in dramatically overvaluing or undervaluing a stock.

**2. Ignores Buybacks - **One criticism of the model is that it does not incorporate other ways of returning cash to stockholders (such as stock buybacks). However, this issue can be addressed by adding them on to the dividends and compute a modified payout ratio. While this adjustment is relatively straightforward, the resulting ratio for any one year can be skewed by the fact that stock buybacks, unlike dividends, are not smoothed out. In other words, a firm may buy back a vast amount of stock in one year and not buy back stock for the next 3 years. For that reason, a much better estimate of the modified payout ratio is likely to be obtained by looking at the average value over a four or five year period.

**3. Too Conservative -** A more general criticism is that that the dividend discount model provides too conservative an estimate of value. One issue is that it does not reflect the value of 'unutilized assets' or intangibles, e.g. patents, brand names, and other intangible assets (although, as Damodaran points out, there is no reason why these unutilized assets cannot be valued separately and added on to the value derived from the dividend discount model). Beyond this, though, the dividend discount model’s strict adherence to dividends means that it will underestimate the value of the stock in firms that consistently pay out less than they can afford and accumulate large cash balances in the process (e.g. a company like Microsoft). While stockholders may not have a direct claim on the cash balances, they do own a stake in them. The dividend discount model essentially ignores equity claims on cash balances and, while adjustments can be made to assess potential dividends (or free cash flow to equity), rather than actual dividends, this is frankly a departure from the essence of the model.

## Conclusion

While the dividend discount model is fairly old-school and often criticized, it can still be surprisingly useful, not least because it can be reversed so that the current stock price are used to impute market assumptions for dividend growth and expected return. Because it counts only those cash flows that are actually paid out, it is a conservative "intrinsic value" model that finds fewer and fewer undervalued firms as the market price rises relative to dividends but that's arguably all part and parcel of the "margin of safety". The downside, however, is that observed dividends are not directly related to value creation within the company and therefore to future dividends - unless the pay-out policy is tied to the value generation within the company which it usually isn't. This missing link between value creation and value distribution is an issue as it can be difficult to forecast pay-out ratios.

## Further Reading

- The Dividend Discount Model: A Primer
- Damodaran on DDM
- Digging Into The Dividend Discount Model
- Damodaran on Valuation

Filed Under: Income Investing,

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