In an earlier section of their 2014 book, "Strategic Value Investing: Practical Techniques of Leading Value Investors," authors Stephen Horan, Robert R. Johnson and Thomas Robinson discussed the dividend discount model, a type of discounted cash flow (DCF) analysis, for stock valuations.

These models, among others, are used to estimate the present value of a stock by discounting back future cash flows. Present value tells us how much these future income streams are worth to us today, based on the idea that current dollars are always worth more than dollars in the future (in turn, that reflects the ability to invest that dollar available today and earn interest from it).

In the current section, they pointed out it is difficult to estimate future dividends accurately for some companies. One of the ways they work around this is by estimating earnings per share and assuming a fixed dividend payout ratio.

It's also important to remember that dividends rarely grow in a straight line, and the longer the forecast, the less likely it is to be accurate. "Some solace can be drawn, however, from the fact that near-term cash flows generally represent a greater portion of the value of a firm, due to present-value considerations," they wrote.

To illustrate, they set out to estimate a dividend growth rate for Johnson & Johnson (NYSE:JNJ). They call it a perfect example because it has consistently increased dividends every year for more than 50 years.

In a brief diversion, they explained that companies such as Johnson & Johnson (as well as Abbott Labs (NYSE:ABT), Pitney Bowes (NYSE:PBI), PPG Industries (NYSE:PPG) and Automatic Data Processing (NASDAQ:ADP)) are called "ruler stocks." The reason? Their dividends and dividend growth are so consistent that, "If you placed a ruler from the starting point in the series to the ending point in the series on a graph, most of the points would be very close to the ruler."

Getting back to the estimates, and based on data from 2012, these facts were available:

- A current dividend (2012) of $2.40 per share.
- Historically, a five-year constant dividend growth rate of 8.17%.
- An appropriate interest (or discount) rate of 12%.

First, they solved the equation for present value; when the data above was plugged into a constant growth dividend model, this was the present value:

The present value, then, was $67.78, while the market price, as of mid-March 2013, was about $75 per share. Comparing the price from the model, as the intrinsic value, with the market price showed the stock was overvalued to some degree, because the market price is higher than the model price. As the authors added, "Certainly there is no margin of safety for a value investor purchasing the stock at a price of around $75 per share."

Getting back to the dividend growth rate, they calculated it in the context of asking what growth rate would justify paying $75 per share:

When using the constant growth model, it may be necessary to *estimate* the dividend growth rate and the appropriate interest rate. The authors explained how to do that estimate, using Johnson & Johnson as an example: "To compute a historical growth rate of dividends for the past 5 years, we need to simply calculate the compound annual growth rate that equates a value of $1.62 at time 0 to a value of $2.40 at time 5 (in five years). That calculation yields a growth rate of 8.17 percent."

Could an analyst go back 15 years instead of five years? Yes, according to the authors, who added, "There certainly is no magical number of years on which to base an assumed growth rate."

Still on the topic of sustainable long-term growth rates, the authors asked how much a company can grow by internally reinvesting its profits. Assuming no profits at all are distributed as dividends, then capital reinvested will grow equity at the ROE (return on equity) rate. In other words, if ROE grows by 15%, then book value (equity) will also grow 15%.

The following formula provides a measure of long-term, sustainable growth rates in earnings or dividends:

**Two-stage dividend growth model**

For "ruler" companies, a constant dividend growth model may be sufficient, but for others, it may not. One of the tools available for non-constant companies is the two-stage dividend growth model. For example, you might assume Johnson & Johnson will grow by 12.15% for the first three years, then drop to 8% in all following years. Again, you assume the "current" annual dividend payout is $2.40 and the appropriate discount rate is 12%. Plugging this data into the two-stage formula we get:

In this model, the present value is still below the stock price of $75, but higher than the $67.78 price generated by the constant dividend growth model.

Rather than calculate the constant-growth or two-stage formulas "by hand," GuruFocus members may use its DCF calculator after selecting any stock.

**Conclusion**

In this section of chapter seven, the authors explained the application of the constant growth dividend model and the two-stage dividend growth model.

Looking under the hoods of these models gives us a greater understanding of their relevance and power.

Disclosure: I do not own shares in any company listed, and do not expect to buy any in the next 72 hours.

Read more here:

Strategic Value Investing: Dividend Discount Models

Strategic Value Investing: Absolute and Relative Valuations

Strategic Value Investing: The Valuation Process

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This article first appeared on GuruFocus.

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