**Introduction**

If you read enough finance articles it won't take you long to hear a statement that is along the lines of the following, which I read in a recent article*:

"A total return predicted using this method can have various combinations of yield and growth. For example, a 3% yield plus 7% growth implies the same total return as a 7% yield and a 3% growth…"

* I have chosen not to directly cite this article as it is not my intention to specifically refute any of its conclusions.

The origin of this and related phrases comes from the Gordon Growth Model [GGM] which states, after some simplifying assumptions**, that

Price = Dividend/[(Discount rate) - (Dividend growth rate)]

where Dividend is the expected dividend one year in the future, usually computed as

Dividend = (Current Dividend) * (1 + Dividend growth rate).

Now, if we rearrange the GGM and write it in terms of "Discount rate", we find that

(Discount rate) = (Dividend Yield) + (Dividend growth rate).

The term "Discount rate" is an often used term in finance and investing. In this context, it can most readily be thought of as the required rate of return for an equity investor to put money into a particular company. Rate of return in the context of a dividend issuing company is known as total returns, defined as:

Total returns = Capital gains + Dividends.

**The Controversy**

I have long taken issue with the idea that total returns could be equated to dividend yield + dividend growth, even in a long run sense. For one, the units are not comparable as dividend growth is the (geometric) rate of the dividend. In physics, an object's velocity is the rate of change of its position. Hence, an analogous statement to "dividend yield + dividend growth" is to say "position + velocity", a nonsensical phrase***. Note that even the concept of total returns itself can be critiqued via the same argument as outlined in the provocative article "Why Total Return Is Like Trying To Add Apples And Bananas".

But, along the lines of the George E. Box quote "all models are wrong, but some are useful", these quibbles of mine would be substantially minimized if the relationship "total returns = dividend yield + dividend growth" turns out to provide reasonable predictions. In general, there is reason to believe that total returns and dividends should be related. For the types of companies covered by the GGM (see footnote **), both total returns and dividends are driven by earnings****. As the dividend grows, either the yield or the stock price will increase, which is associated with an increasing total returns. Note that neither dividend growth nor dividends cause price increases, however. But how does it work in practice?

**The Data**

To investigate this further, I have performed the following experiment. For The Coca-Cola Co (NYSE:KO), Johnson & Johnson (NYSE:JNJ), and Proctor & Gamble Co (NYSE:PG), I computed the 3 year dividend growth rate and the next year's projected dividend yield for each day over the last 40+ years. I compare this to the annualized total returns experienced by an investor from each day to today. Note that these were the first three companies I analyzed. I picked them based on them being dividend aristocrats with stable (non-cyclical) business models. Here are the three plots, where CAGR is the compound annual growth rate of total returns experienced by an investor from each day to today (dividends not reinvested) and GGM is the total returns predicted by the Gordon Growth Model:

The Coca-Cola Co:

Johnson & Johnson:

Proctor & Gamble Co

For these companies, there is really no discernible relationship between the two curves over time. For instance, The Coca-Cola Co

in the early to mid 1990's experienced a steadily increasing "yield + growth" but a steadily decreasing total returns. For Johnson & Johnson, the relationship is even more tenuous.

**The Conclusion**

On philosophical grounds, I have always been uncomfortable with the oft-used short cut of predicting total returns by adding dividend yield and dividend growth. After directly comparing the results predicted by this model to historical returns, I'm even more doubtful of its utility in practice. Note that I have developed a much more refined, but still easy to use, prediction of total returns that I have used successfully many times in past. I wrote about it here and here.

** The assumptions boil down to the company having a constant dividend growth rate into perpetuity and that the growth rate is low to moderate. Essentially, that we are looking at a mature dividend growth company.

*** In more detail, position is commonly in terms of meters [m] and velocity is in terms of meters per second [m/s]. Hence, writing "position + velocity" necessitates m + m/s having meaning.

**Disclosure:** I am/we are long KO, JNJ.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.