Screening a universe of common stocks down to a manageable number for further analysis leads the investor to the question of valuation: Given the market price of the common stock, is the stock correctly valued? If, in your opinion, the answer is no and you believe the stock is either overvalued or undervalued, then a short position (a sale of stock) or long position (a purchase of stock) is indicated.

Determining whether the stock is correctly valued requires the investor to estimate the value of the stock and compare the estimated value to the current market price. Valuation of common stocks presents an immediate question—what do you value? Assuming that the appropriate view of the firm is as an on-going concern, and not a liquidation, merger, or takeover, then valuation of firm assets is not a productive approach. The investor’s concern is what those assets generate for the benefit of shareholders, or more directly, what those assets generate that affect common stock market prices.

At this point, there are two major directions that valuation can take—investors can use approaches that focus on either dividends or earnings. Rather than take up the debate of which is better, this workshop will survey some of the major approaches that use both dividends and earnings to value common stocks.

## A Look at the Variables

The major variables in valuation models are a required return, an expected growth rate, and expected generation of earnings or dividends. Of course, there are many factors behind each of these estimates. For example, in order to arrive at an estimate of required return, an analysis of the risk of the common stock is necessary, and growth estimates of earnings and dividends require analysis of sales, margins, debt and dividend policies, to name a few.

To concentrate just on the basic techniques of valuation, the example used to illustrate these techniques is the S&P 500 index, a proxy for the market. Through the second quarter of 2017, the S&P 500 stocks had total 12-month dividends of $47.22 and operating earnings of $115.92. The dividend yield was 1.97%—total dividends of $47.22 divided by the S&P 500 closing average for the second quarter of 2,397.97. The payout ratio—dividends divided by earnings ($47.22 ÷ $115.92)—was 40.7% and the price-earnings ratio—price per share divided by operating earnings per share (2,397.97 ÷ $115.92)—was 20.7. This information for the S&P 500 is from S&P and StockCharts.com.

## The Dividend Valuation Model

The first valuation model presented here reﬂects the present value of all expected future cash dividends. The theory is simply that cash dividends are the only cash ﬂow that investors receive, and value must ultimately be based upon cash ﬂows. Even expected future stock prices that determine capital gains or losses are based upon more distant expected future dividends.

Simplifying some of the assumptions reduces some of the mathematical requirements to an easily applied model. Simply stated, the model says that capitalizing the expected dividend by the difference between the required rate of return and the expected growth rate gives an estimate of common stock value.

Mathematically, this translates into the following:

Looking at the model, it is clear that as dividends and growth increase, or as the required return declines, the stock would take on a higher value, and be more valuable to the investor. The model assumes that the required return is greater than the expected growth in dividends. If the expected growth in dividends were greater than the required return, irrational valuations would result.

In the restated form of the model, the return on a common stock is defined as the dividend yield plus the expected growth in dividends, which also works out mathematically to be the expected capital gains. This statement is hard to argue with.

In the above model, it is necessary for the investor to determine a number of variables before the valuation can be made. The first variable is the required rate of return (r). This is somewhat complex, because it requires the investor to make a forecast of future returns and risk. The required rate of return for an investment is the return an investor should expect based on the level of risk undertaken. This boils down to the expected return on a risk-free asset, such as a Treasury bill, plus a premium that compensates for the risk. In mathematical terms, the model for determining r is:

Notice that beta is used in the formula. This adjusts the required return to the level of risk undertaken. Beta is a relative risk measure of how a stock reacts relative to the market. The beta of the market is always 1.0, but beta values of individual stocks can vary from values near zero to values near 3.0. Most beta values fall in the 0.5 to 1.5 range. A beta of 1.5 means a stock is 50% more volatile than the market; thus, if the market rose 10%, the stock would generally rise about 15%. A similar relationship would hold in a declining market. You can see from the formula that stocks with higher betas would have higher required returns to compensate investors for the additional risk. If the beta of an investment is zero, only a riskless return is required. If the beta of the investment is 1.0, the return required is the same as that of the overall market. Beta values are generally available from Value Line or brokerage reports.

We can use historical figures to determine the required return for our above example. Over the past 50 or so years, the equity risk premium, the amount by which the return on equities have exceeded the return on Treasury bills, has averaged roughly 5.1%. Taking today’s Treasury bill rate (1.3%) as a simple basis for deriving an expectation of future riskless rates, knowing that the beta of the S&P 500 is 1.0, and assuming that the historical equity risk premium will serve as an estimate of the future premium, the required return is:

**r = 1.3% + (1.0 × 5.1%)**

** r = 6.4%**

The second variable in the dividend valuation model—the growth rate (g)—must be estimated from a variety of factors. One approach, however, which we will use here, is to rearrange the dividend model and solve for g using current dividend yield (current dividends divided by the stock price today—or 1.97%, the current S&P 500 average, as noted above) rather than expected yield:

**g = 6.4% – 1.97%**

** = 4.43%**

As a long-term annual growth rate for dividends, this 4.43% is below the average annual growth rate of approximately 6.0% experienced by the S&P 500 in the 1989 to 2016 period, but it may embody expectations.

The remaining variable is the next expected annual cash dividend. This can be determined once the growth rate has been estimated, and is simply the current dividend times one plus the growth rate. Note that the latter figure, one plus the growth rate, must be raised to the first power, because you are estimating growth over one year. If the estimate was for growth over two years, one plus the growth rate would be squared; for three years it would be cubed, etc.

Now that the variables have been estimated, they can be substituted into the dividend valuation model to estimate the value for the S&P 500:

= [47.22(1.0443)^{1}] ÷ [(0.064 – 0.0443)]

= 49.311846 ÷ 0.0197

= 2,503.14

With the S&P 500 currently (at the end of September) around 2,500, this valuation would conclude that the S&P 500 is fully valued—a signal that you may want to be cautious with your stock purchases.

To value a single stock, the exact same procedure would be followed using the estimated values for that stock; the final value would then be compared with the current market price.

If the growth and required return estimates are more complex than you would care to do, a simpler approach is to use several different dividend expectations to determine a range of values. To do this, you must first rearrange the dividend model to highlight dividend yield:

As you can see from the equation, the difference between the required rate of return (r) and the dividend growth rate (g) is the expected dividend yield. Assume that you expect the dividend yield to be 2% (during 1989 to 2016 the S&P 500 dividend yield averaged 2.11%) and that next year you anticipate the total cash dividend on the S&P 500 to be $48.15. Substituting the dividend yield of 2% for r – g, and the total cash dividend of $48.15 for d, the valuation would be:

0.02 = 48.15 ÷ P_{0}

P_{0} = 48.15 ÷ 0.02

= 2,407.50

This produces a value that is slightly below the S&P 500’s current value. If instead of expected values, you were to substitute historical averages from the 1989 to 2016 period into the equation, a much different value would be produced:

0.0211 = [(47.22(1.06)^{1}] ÷ P_{0}

P_{0 }= [47.22(1.06)^{1}] ÷ 0.0211

= 2,372.19

The value here has fallen significantly below the current market. In other words, based on purely historical figures, the S&P 500 should be lower in value. The fact that it is not implies that the market expects dividend growth to be higher and/or dividend yields to be lower than historically. The use of different expectations is a good way to perform a sensitivity analysis to develop a most likely range of values.

## The Earnings Valuation Approach

The dividend valuation model is not useful for all stocks, particularly those that do not pay dividends currently or are considered primarily for their growth attributes. For those kinds of stocks, the earnings valuation approach may be more appropriate.

The most common earnings valuation approach is the price-earnings ratio approach. Let’s look at the price-earnings ratio for the S&P 500, based on the figures for the first quarter, given above:

p/e = 2,397.97 ÷ 115.92

= 20.7

Another way of viewing the price-earnings ratio is to fit it into the format of the dividend model, with a few adjustments. Dividing earnings into both sides of the equation accomplishes this:

Substituting for r – g, which you will recall is the dividend yield, and using current figures for the S&P 500, the price-earnings ratio can also be found:

p/e_{0} = 0.407 ÷ 0.0197

= 20.7

Using historical averages for dividend yield, the price-earnings ratio for the S&P 500 would be lower:

p/e_{0} = 0.407 ÷ 0.0211

= 19.3

The idea behind the price-earnings ratio approach is to arrive at the expected price-earnings ratio, to use this as a multiplier for the expected earnings, and to arrive at a valuation. Mathematically, this is:

An estimate of earnings for the next year can be produced by using historical growth rate figures, adding one and multiplying this by the current earnings. The 1989 to 2016 average annual growth rate in operating earnings for the S&P 500 was 6.57%. Substituting this into the equation, along with the price-earnings estimate based on historical ratios tends to undervalue the S&P 500:

= 19.3 × ($115.92 × 1.0657)

= 2,384.24

If, on the other hand, you used a 10% growth rate assumption and the historical price-earnings ratio, the S&P 500 valuation would be:

= 19.3 × (115.92 × 1.10)

= 2,461

If we went back to the original price-earnings ratio equation and used a 5% dividend yield, along with a 10% growth rate, the S&P 500 valuation that would be produced would be quite different:

p/e_{1} = 0.407 ÷ 0.05

= 8.14

P_{0} = 8.14 × (1.10 × 115.92)

= 1,037.95

These approaches are an introduction to valuation. The techniques can be readily adapted to the valuation of individual stocks, and provide investors with a tool to judge current prices.

The dividend and earnings valuation models form the nucleus of valuation from which all other fundamental valuation techniques spring.

*This is an updated version of an article written by John Markese for the October 1985 issue of the *AAII Journal. *At the time, Markese was director of research at AAII. He is also the former president of AAII** and currently serves as chairman of AAII.*

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