# Explaining the Dividend Discount Model

*This column was originally published on *RealMoney*. It's being republished as a bonus for *TheStreet.com* readers.*

In my

recent column on pairs trading, I mentioned using the dividend discount model as a method of valuing a company. I got several emails from readers who had never heard of the dividend discount model or how it is used, so here's an explanation of this commonly used valuation technique.

If you've ever taken an introductory finance or accounting course, you'll recall that the value of an asset is the present value of the expected future cash flows from that asset, discounted at a rate appropriate to the level of risk of the cash flows. Analysts can use a number of different "cash flows" to determine an asset's worth, including dividends, operating cash flow or free cash flow to equity.

When valuing a stock, dividends are the most clear-cut way of defining cash flows; they're actual cash flows that go directly to the investor. Therefore, while the discounted cash flow valuation methods are important, we'll focus here on the dividend discount model, which is the basic and most common method of valuing equity.

### Assessing the Inputs

In the simplest form of the dividend discount model, there are only three required inputs: the expected dividend, the dividend growth rate and the equity discount rate. To determine the expected dividends, you must make certain assumptions about future earnings and payout ratios. In order to keep this uncomplicated, let's assume that dividends infinitely grow at a constant rate.

So what rate do we use to determine the discounted present value of these cash flows? This equity discount rate is also sometimes called the required return, or the cost of equity. You can determine this rate in a number of different ways -- nothing is ever easy, is it? -- but to simplify things for this column, I'll share one common method, called the capital asset pricing model approach.

The equity discount rate is the difference between the expected rate of return on the overall market (usually the

**S&P 500**

is used for the market return) and the risk-free rate, multiplied by the stock's beta. This figure is added to the risk-free rate to arrive at the equity discount rate.

OK, if you've gotten this far without falling asleep, I congratulate you. Let's say we have a company that will pay a dividend next year and then increase its dividend at a constant rate forever. Also, using the equation above, we've determined the equity discount rate for this company.

Drum roll, please. I now present to you the constant growth dividend discount model:

For the purposes of this column, I've made some oversimplifying assumptions, which are probably unrealistic in the real world. For many companies, the assumption of constant dividend growth just isn't appropriate because some companies have an increasing level of growth in their dividend rate for a number of years, after which the growth becomes constant. Other companies have one constant growth rate in the near term, followed by a different constant growth rate later. Still other companies have nothing constant at all with their growth rates, as their dividends are highly variable.

In these cases, consider two types of cash flows: the dividends received each year, and the price at which you sell the stock after some finite time horizon. The dividends each year must be estimated or the growth rates must be projected. Alternatively, the earnings and payout ratios can be estimated. The expected price of the stock at the end of the holding period -- the price you sell the stock for -- is itself determined by the discounted stream of dividend payments. These cash flows are then discounted back using the equity discount rate.

This is called the two-stage (or finite horizon) dividend discount model and looks like this:

Now that we've gotten this far, there are two important limitations to point out. First, this valuation technique, as well as any of the other discounted cash flow measures, is very sensitive to the inputs: the growth rate of the dividends (and the duration of the growth) and the discount rate used. A small change in any of these inputs has a great influence on the estimated value. Second, the dividend discount model is difficult to apply to growth businesses that do not pay dividends during periods of high growth because they can earn rates of return on investments that are above their required return.

There are a few places on the Internet that offer dividend discount models of one kind or another. Two sites that I found after a five-minute search are

DividendDiscountModel.com and

MoneyChimp. For a quick valuation, I typically use Bloomberg to run my dividend discount models.

### Valuations

So using Bloomberg, I ran a dividend discount model for every company in the S&P 500 to determine the most overvalued and undervalued companies in the index. To do this, I kept all the assumptions that Bloomberg uses.

Obviously, this is just one measure that is typically used in conjunction with other research. In fact, it would be more appropriate to go through each name individually and determine the appropriate inputs. But in any event, here are the results of my screen:

Using the degree of overvaluation or undervaluation of every member of the S&P 500 and the weights, you can easily determine how the S&P 500 index as a whole is valued. This methodology results in the S&P 500 being marginally undervalued by roughly 2%.

This is a pretty in-depth subject that could be covered in a semester or more of coursework. I've attempted to summarize the basic principles in one column so that you have a better sense of this common technique in security analysis.

At time of publication, Norton's fund was long Dynegy, though positions may change at any time.

Charles L. Norton, CFA, is a principal of GNI Capital, Inc., a registered investment adviser that manages a hedge fund, GNI Partners, L.P., as well as discretionary private client accounts. Norton had been a vice president in the equity research department of a New York-based hedge fund, where he was also a registered representative managing discretionary private client accounts. Prior to his experience on the buy side, Norton worked in the investment banking division of Salomon Smith Barney, where he was an analyst in the health care group, reporting directly to the head of the group. Under no circumstances does the information in this column represent a recommendation to buy or sell stocks. While Norton cannot provide investment advice or recommendations, he

welcomes your feedback.