Robert Allen Schwartz's recent article on transitioning to dividend growth investing provided a good description of the advantages of dividend growth investing. It presented and modeled three scenarios for an individual stock: 1) 10% increase in stock price each year for 30 years, followed by an investment in a dividend-paying stock; 2) a dividend growth strategy without reinvesting dividends; 3) a dividend growth strategy that includes reinvesting dividends. Scenarios 1 and 2 were equivalent, since in the absence of taxes and transaction costs, total return does not vary according to the proportion provided by capital gains versus dividends. Scenario 3 provided significantly better results, showing that reinvested dividends significantly contributed to overall returns. However, Mr. Schwartz made a crucial assumption in describing scenario 3 that significantly and unrealistically improved returns. This article will describe that assumption, why it is unrealistic, and what more realistic modeling would show.

In calculating the returns of a dividend growth stock over time, the price at which dividends are reinvested is crucial to determining the growth of shares and dividends received. Mr. Schwartz made the approximation that the share price doesn't change over time. For short time periods, this may make sense - share prices in the short term are variable and difficult to predict. But for long time periods, share prices more closely track with earnings and or dividends. In the case of dividend growth stocks, over the long term, dividends cannot grow substantially more quickly than earnings if the dividend payout ratio is not low. And with a dividend reinvestment strategy, an increasing share price over time *reduces* the dividends received. Figure 1 demonstrates this, by graphing the dividend income for each year for two different hypothetical stocks. In both cases, the initial investment is $1000, the share price is $10, the initial dividend rate is 3%, and the dividend increases by 10% annually. The only difference is that for the blue line, the share price is held at a constant $10 for all 30 years. For the red line, the share price simply increases in line with the dividend - the dividend is held at a constant 3%. As you can see, the models diverge quite substantially, to the point that are year 20, there is nearly a threefold difference in dividends received. And at year 31, the models differ by a factor of 50!

The two models grow increasingly far apart over time. While this is easily visible in Figure 1, Figure 2 makes the distinction even clearer. Figure 2 shows the same two models; this time they are projected out 40 years and plotted on a logarithmic scale.

Mr. Schwartz's assumption also substantially impacts total returns. Although many dividend growth investors plan never to touch their "principal," concerning themselves only with dividends received, there are many other investors who appreciate and follow the dividend growth investing strategy who also care deeply about total returns. I plotted the value of stock over time for each of the two models in Figure 3. Since I am showing values over a long period of time, a logarithmic plot is easier to visualize (each factor of 10 on the vertical axis is the same distance). Since the model of increasing share price has uniform prices and dividend increases, the total value increases at a constant rate of 13.3% annually (1.03 x 1.10 = 1.133). The constant share price model, however, has much slower growth at first because the only returns come from a 3% dividend in year 1, a 3.3% dividend in year 2, etc. But they cross over around year 28, where the constant share price model shows a dividend of 43%. In year 37, the dividend would be more than 100%!

The price paid for additional shares of stock from reinvested dividends is quite important. To demonstrate this, I developed two additional price functions that either were accelerated from the constant rate (this model has larger price increases in the early years), or delayed from the constant rate (this model has smaller price increases in the early years). These functions are displayed in Figure 4. In each case, dividends still increase by 10% annually and the final share price is the same. The number of shares and total value for these scenarios are shown in Figure 5, while the dividend income from each is shown in Figure 6. From both a total return and dividend growth standpoint, investors are much better off if increases in share price occur later. This allows dividends to reinvest at optimal shares prices, boosting both future dividend streams and total return.

Obviously, an unrealistic constant share price model is ill equipped to show the advantages of a dividend growth investing strategy. Assuming a constant yield with increasing dividend growth gives a better, if still simplistic, model. But stocks, like life, are complicated. To add an additional level of complexity, I ran three models that introduced some randomness into the calculations. In these, the initial stock price is still $10, the initial dividend is still 3%, and the dividend still increases at 10% annually. The stock price increases on average 10%, but I also added an element where the stock price varies randomly by up to 30% (up or down) each year as well. I've plotted the share price and total value for each year in Figure 7. Can you predict which scenario would provide the greatest dividend income in year 41?

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