Absolute Equity Valuation, Part II: Dividend Discount Model
Introduction:
In part1 of this series, we discussed the concept that a stock’s intrinsic value is the present value of its cash flows. Here in part2 we will introduce the general form of the present value model, and discuss the dividend discount model in more detail.
The present value model discounts all future cash flows to determine a stock’s present value, V_{0}, which is its intrinsic value at t=0. Discounting all future cash flows necessitates using the infinity sign (∞) in the summation. The foundational formula for the present value model is:
The Dividend Discount Model (DDM):
One specific measure of cash flow (CF_{t}) which we can discount is a stock’s dividend stream, hence the name “Dividend Discount Model” or DDM for short. The inputs to the DDM are the time horizon (t), the dividend stream (DIV_{t}), and an appropriate discount rate ^{1} or required rate of return (r). After substituting dividends for cash flow in the above equation, the formula now reads:
Discounting dividends into infinity presents an obvious problem. One approach to dealing with this problem is to use a twostage version of the model which changes our time horizon to one that is finite. We will discuss another approach that addresses the infinity problem directly in a subsequent article.
The TwoStage DDM:
A simplified twostage version of the DDM assumes a finite distribution period of dividends from t=1 to t=n, followed by a resale price, P_{n}. Essentially this is the present value of an income stream plus a terminal value. You can think of this terminal value as the discounted present value at t=n of all future cash flows into infinity, that is to say from t= n → ∞.
The dividend stream can be represented as a series of individual dividends [Div_{1}, Div_{2},…,Div_{n}], or as an initial value (Div_{0}) and a growth rate of dividends (g). Our basic present value formula can then be expanded into these two forms as follows:
By varying the inputs to the equation [Div, r, P_{n}], we can calculate a minimum/maximum range of values. Note that the infinite t=∞ has now become a finite t=n.
An Example:
Raytheon Company (RTN:NYSE) paid a dividend of $1.24 in the last fiscal year ^{2}. Over the past 5years, dividends grew at an annualized rate of 9.2%. Based on further analysis, let us say that you have estimated the following variables:
 The average dividend growth rate of 9.2% is sustainable for another 5 years.
 The fair sale price of RTN will be approximately $65/share at the end of the 5years.
 Your required rate of return is 15%
Plugging these variables into the two stage formula above, you calculate the intrinsic value as follows:
The present value of the dividend stream is $5.33 and of the terminal value is $32.32, or $37.65 total. Paying less than this for RTN will add a margin of safety. Note how that the terminal value is a large portion of the present value in this example.
“Rational men, when they buy stocks…would never pay more than the present worth of the expected future dividends.” — John Burr Williams ^{3}
Economic Rationale:
When using any valuation model, care must be taken in understanding the assumptions and economic rationale behind it and the application for which it is intended. Investors who use the DDM take a long term, noncontrolling ownership perspective at the stockholder level.
Common stockholders have an ownership claim on future cash flows. Dividends are actual distributions made to shareholders, a direct access to a company’s value. Dividends are more stable than earnings over the long term, and are less sensitive to short term fluctuations.
The DDM may be more appropriate for a mature, historically dividendpaying company with few investment opportunities. The company’s board of directors has established a consistent dividend policy that is related to profitability and that has a constant payout ratio.
Conclusion:
The DDM is one example of the present value model where dividends are the cash flow being discounted. In application, this is easier for bonds than it is for stocks where the magnitude and timing of cash flows and the proper discount rate are more difficult to determine.
In following articles we will present:
 The Gordon Growth Model which addresses the t=∞ issue
 Free cash flow and residual income applications
 Methods of calculating the terminal value, Pn
Thank you for reading this article. Your comments are welcomed.
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Footnotes:
 The discount rate can be a market rate determined by an analyst for the public, or a personal required rate of return determined by each individual investor. A different rate could be applied for each cash flow period being discounted. Lacking a defensible rationale, our formulas use the same rate in all periods. Determining the discount rate is beyond the scope of this series.
 Data for RTN compliments of the Charles Schwab equity research website.
 Williams, John Burr. The Theory of Investment Value. Fraser, 1997: p. 6.
Originally published in 1938, the full text of the quote is worth presenting.
“The definition for investment value which we have chosen is in harmony with the time honored method of economic theory, which always begins its investigations by asking, ‘What would men do if they were perfectly rational and selfseeking?’ The answer is that rational men, when they buy stocks and bonds, would never pay more than the present worth of the expected future dividends, or of the expected future coupons and principal; nor could the pay less, assuming perfect competition, with all traders equally well informed.”
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Absolute Equity Valuation, Part III: Gordon Growth Model  Sargon Y. Zia, merging fundamental analysis with technical analysis — August 19, 2010 @ 6:23 pm
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