Dividend Growth Basics

Dividend growth strategies are based upon the Dividend Discount Model presented in the form of the Gordon Equation. The Gordon Equation calculates a discount rate R from a steadily growing income stream. If suitable reinvestments can be found for the dividends, the R is the overall return of a stock.

The Gordon Equation is: R = initial dividend yield + the growth rate of the dividends.

Suitable reinvestments are those that maintain the same rate of return as the stock when it was originally purchased. In short, the Gordon Equation assumes that the stock’s dividend yield and dividend growth rate remain steady on into the distant future. All dividends are reinvested to purchase additional shares.

Notice that it is neither the dividend yield nor the dividend growth rate that is important. It is their sum.

Add in some restrictions to assure quality and you have the foundation of a dividend growth strategy. All of this applies during the years of accumulation as well as during retirement. In addition, focusing on income streams helps psychologically. Steadily rising dividend income mitigates the unpleasantness often associated with short-term price fluctuations.

By focusing on income streams, a dividend growth strategy avoids the problem of selling shares during retirement. An income stream from dividends is inherently safe as long as the company is sound. Restrictions on quality require selling and reinvesting elsewhere before a company’s outlook deteriorates too severely. There can be losses. For the most part, a reliable dividend stream is a Safe Withdrawal Rate with an indefinite, but very long lifetime.

A retiree can choose to withdraw all or part of his dividend income stream. The best approach appears to be to reinvest at least a small portion to cover the occasional losses that are bound to occur.

A natural question arises as to the rate of return that applies to the dividends that are reinvested. A good guess might be to adjust the Gordon Equation by scaling the dividend yield. That is, if one reinvests 25% of his dividends, he would add a quarter of his dividend yield to the dividend growth rate. It is a good guess. But it is wrong.

The problem is that the growth rate term is no longer constant with respect to the initial withdrawal. Suppose, for the sake of illustration, that dividends double every year, starting at $1. The growth rate is 100% per year. The dividend amounts are $1, $2, $4, $8 and so forth. If you withdraw 75 cents each year, reinvesting 25%, the amounts to be reinvested are $0.25, $1.25, $3.25, $7.25 and so on. This is not a steady rate and the Gordon Equation does not apply.

But what about our guess? For the Gordon Model to apply, the reinvested amounts would have had to be $0.25, $0.50, $1.00, $2.00 and so on to maintain a growth rate of 100% per year. The actual amounts reinvested are higher, especially at first. We end up buying a lot more shares than expected. Scaling the dividend yield produces a low estimate of the return from reinvested dividends.

I think that this subtle mathematical point has helped to cloud discussions of dividend growth strategies. If it is natural to think in terms of a stock’s total return with reinvested dividends, it is natural to scale incorrectly when reinvesting only a portion.

Adding to the confusion is the insistence of those advocating dividend growth strategies to refer everything back to the initial investment. If there were no withdrawals, there would be only one number to apply. It would work in all cases and that would be that. When there are withdrawals, there is a different number for each withdrawal amount. The growth rate term has been affected. The corrections are pleasant. The income stream increases faster than anticipated (when scaling only the dividend yield).

What about risk? Dividends are much more amenable to analysis and projection than prices and total return. Notice that their expected return is highly predictable, especially in the short-term. This is in radical contrast to price behavior, which is almost entirely unpredictable in the short-term but reasonably predictable in the long-term. Dividend yields fluctuate considerably. Dividend amounts do not. It still makes sense to buy only at a good price. But retirees are under no pressure to sell when relying on dividend income. They may choose to do so when prices are ridiculously high.

I cannot over-emphasize this latter distinction. It is important. Some things are predictable in the short-term. Other things are predictable in the long-term. Safe Withdrawal Rate analysis is only beginning to take advantage of such distinctions.

Have fun.

John Walter Russell
I wrote this in August 5, 2004.