I have on occasion seen the equation put forth here on Seeking Alpha that Dividend Yield plus Dividend Growth equals Return. This is a mathematical fallacy. To quote the ever wise David Van Knapp: it's like "adding the speed of a car to its acceleration--the result makes no sense."

But why do some dividend investors continue to cite this as a metric? I considered my own previous article in this series. In this article, I analyzed something that I know dividend investors intuitively understand...there is an inverse mathematical relationship between dividend yield and dividend growth. In other words, to end up with an equal result over some time period, a stock with a lower current dividend yield must have a higher growth rate than a stock with a higher current yield. Unfortunately, I think a few investors (perhaps understandably) extrapolate this relationship to conclude that it is perfectly symmetric...i.e. at the end of the day, a 3% dividend yield growing at 6% per annum equals a 6% dividend yield growing at 3% per annum.

So let's take a quick look at this to put this notion to bed. Let's say I have two $10,000 investments: one with a 3% yield and a 6% dividend growth rate and the other with a 6% yield and a 3% dividend growth rate. The annual dividend amount is on the vertical axis and the number of years is on the horizontal axis.

(Click charts to expand)

As the graph shows, there is one distinct point in time (the crossover point), somewhere between years 25 and 26, that they are equivalent. Past that, they head to infinity never to cross paths again. Bottom line, for the one distinct point in time that they are "equal," there is an infinite number of times that they are not.

Nonetheless, I believe there is significant diagnostic value in "pairing" (not adding) dividend yield and dividend growth rate. As I demonstrated in my previous article, if you choose a particular point in time in the future (a so-called "Investment Horizon"), there are a series of pairings of dividend yields and minimum corresponding dividend growth rates that will result in allowing an investor to achieve an income target. But choosing different investment horizons will alter these results.

To demonstrate this, rather than providing the detailed model that I have in the two previous articles, I will presume that you either trust or don't trust my model at this point and will instead simply give you some results from it. Let's assume there are three people: Larry is still 55 years old, Jan is 50 and Peter is 45. They all have $300,000 in an IRA and are planning to add $10,000 per annum to it. All three are dividend growth investors and want to have $40,000 of income from dividends in current dollars from their IRA when they turn 65. Assuming 2.5% inflation, this means Larry will need about $50,000 of income, Jan $58,000 and Peter $65,500. Share price growth is assumed to be 3% per annum but this is for reinvestment purposes only. So what are the pairings that will allow each of them to achieve this goal? The following chart sets the dividend yield and indicates what corresponding minimum dividend growth rate will be required:

Dividend Yield | ||||||

Investment Horizon | 2.00% | 3.00% | 4.00% | 5.00% | 6.00% | |

Larry | 10 Years | 16.70% | 11.47% | 7.81% | 5.00% | 2.72% |

Jan | 15 Years | 10.48% | 7.05% | 4.62% | 2.72% | 1.16% |

Peter | 20 Years | 7.58% | 5.01% | 3.16% | 1.71% | 0.51% |

Looking at this graphically (dividend yield on the horizontal axis and dividend growth on the vertical axis), you can see that this data are points along a polynomial curve. Any pairings on or above their respective curves would allow Larry, Jan or Peter to achieve their income target...below, they would fall short.

You will note that Peter's "curve" reflecting the longest investment horizon is not only lower, but is also flatter than Larry's or Jan's. Being lower, it indicates why, everything else being equal, Peter has more overall pairings available that would allow him to reach his income target. Being flatter, it shows why it may be more advantageous for him to invest lower yielding, higher dividend growth stocks than their higher yielding, lower dividend growth counterparts as there are relatively more pairings available to him in this lower yielding range. Putting it in other terms, a portfolio with the Procter & Gamble (NYSE:PG), Johnson & Johnson (NYSE:JNJ), Exxon Mobil (NYSE:XOM) and McDonald's (NYSE:MCD) would probably work nicely for Peter but the AT&T (NYSE:T), Waste Management (NYSE:WM), Consolidated Edison (NYSE:ED) and Eli Lilly (NYSE:LLY) arrangement is probably a better choice for Larry.

Conclusion: Every dividend growth investor using a portfolio of dividend growth stocks to build toward a certain income level at a certain point in time has a unique polynomial curve reflecting the pairings of dividend yields and corresponding minimum dividend growth rates required to achieve this goal. Provided this is your investment approach, having a sense of what your personal curve is will give you a valuable tool to determine from time-to-time what combinations of actual dividend stock investments will produce blended pairings of dividend yield and dividend growth that will allow you to achieve an income target.

In my next article in this series, I will discuss some portfolio management and investment strategies that could result from this analysis and I will introduce some real world data to assist in this process.