# Valuing Stocks Using Dividends

Investors looking to generate income pursue stocks with high and stable dividend yields. But how does one know whether or not the yield itself is cheap? Here's a good way to work it out.

A stock represents a small part of a company. It is part of the equity (ownership) of the underlying company and provides the holder with a vote (usually one per share) and potential capital appreciation, as well as dividends. This ownership stake fluctuates and is valued daily in the market. But how does one determine what the correct stock price valuation is?

The value of a stock in its simplest sense is the present value of the cash flow expected to be provided by that stock. Cash flow usually takes the form of a dividend, declared by the company’s Board of Directors. It follows that a stock can then be valued as the present value of future dividend payments.

The rate at which the dividend is discounted is called the discount rate. Assuming dividends grow at a constant rate to eternity (a rather absurd assumption – investors usually use this model for certain time periods of say ten or twenty years), the stock can be valued using this growth rate and the discount rate.

The dividend discount model, a formula used widely in stock valuation, uses the future value of dividends to determine the current value of a stock. The formula to produces such valuation says that price is equal to the dividend divided by the discount rate less the growth rate of that divided. It can be written P=D / (k-g), where k is the discount rate and g is the dividend growth rate.

The discount rate is the measure of risk that must be assumed when purchasing a stock. For example, if one is buying shares of Coca-Cola (KO), which has predictable cash flows and dividends, the discount rate will be low, say 10%. However when one is buying a company with uncertain cash flows and dividends, the rate will be high, say 15%. This rate is a subjective measure and is effectively the rate required to assume the risk of investing in the stock.

Now for an example:

Johnson & Johnson (JNJ) currently trades at \$64.90. An investor in search of a dividend yield wants to know if this is a fair value for the stock, in order to avoid over-paying. The current dividend on Johnson & Johnson is \$1.93. If an investor, being conservative as he is, decides that a dividend growth rate of 7% annually into eternity is appropriate, then g would be 7%, or 0.08. As for the discount rate, Johnson & Johnson is a great company with strong historical dividends and cash flows, and it’s almost certain the business will continue to generate cash in future years. As such a discount rate of 10% is probably appropriate (in the formula this would be 0.1).

Using the dividend discount model, P=D / (k-g), we substitute the above variables as: P=1.93 / (0.1-0.07). Solving this equation produces an answer of \$64.33, or almost exactly the current stock price. Using this logic, Johnson and Johnson is a good purchase at the current price for dividend-seeking investors.

This model also allows investors to protect themselves from overpaying for expected dividend streams. Assume Merck’s (MRK) dividend to increase at 5% per annum from the 2009 payout of \$1.52. Given the risks facing Merck of increased competition from generic producers, a cautious investor would use a higher discount rate, say 15%, to compensate for the increased risk of owning the company. Using the formula, P=1.52 / (0.15-0.05), and therefore P=15.2. Compare this to the current Merck price of \$33 and one can see that this dividend stream may be expensive.

The dividend discount model is in no way a sure-fire guaranteed way to accurately value stocks. It does, however, provide the cautious dividend seeking investor some idea of the true value of a future dividend stream and can prove valuable in not overpaying for this stream. Conservative estimates should always be used ahead of more optimistic appraisals, and of equal importance is the financial strength of the company, which can be attained by a quick look through the balance sheet.

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• #### Jozef

May 13, 2010

Solving the equation P=1.93 x (0.1-0.07) produces an answer 0.0579. I have no clue how the author came up the price \$64.33. Some details are probably missing.

• #### Sean Riskowitz

May 13, 2010

The equation is P=1.93 / (0.1-.07), and produces an answer of \$64.33.

• #### rypatel

May 14, 2010

Nice post, good to see some academic based valuation models on the site...

In the article above, you wrote:

"Johnson & Johnson (JNJ) currently trades at \$64.90. Solving this equation produces an answer of \$64.33, or almost exactly the current stock price. Using this logic, Johnson and Johnson is a good purchase at the current price for dividend-seeking investors."

I just wanted to mention that according to your model JNJ is worth no more than \$64.33.

You mentioned that using this logic (your equation), JNJ is a good buy at \$64.90, but again, the equation is telling you that JNJ is not worth a penny over \$64.33. Therefore, if you are following this model, it would be a bad buy to acquire JNJ because you would be overpaying.

Just something readers should keep in mind!
Ryan

• #### Sean Riskowitz

May 15, 2010

Ryan, your comments are duly noted.

Valuation by it's nature is a range bound practice and as such any valuation is approximate. Given the above assumptions on J&J, the fair value of the dividend stream is approximately \$64.33. This does not mean that \$64.90 is too high - rather I would suggest when working something like this out one does not stick rigidly to the valuation but allows some leeway.

For example, if I had input J&J's dividend growth rate at 7.5% terminally instead of 7%, I'd get a valuation of \$77.20. A 7% change in the dividend growth rate results in a 20% change in valuation. As such, valuation models are range approximate and not defined absolute values.

Clearly J&J's dividend stream is worth somewhere in the range of the current stock price, whereas Merck's is not. That really is the point I'm trying to convey.

Happy Investing!

Sean

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