It is often useful to combine metrics to gain insight into "what is really going on" in the investment world. A combination of yield (Y) and dividend growth (DG) would help in envisioning how dividends can grow over time. Of the three simple combinations -- adding, multiplying, and dividing -- multiplying seems to hold the most promise as a "figure of merit." Of equal importance are a lower yield/higher dividend growth vs. a higher yield/ lower dividend growth. The last is useful in early retirement, and the first in later years.

Let's see what we can make of this. Basically, there are two main types of dividend growth, exponential and linear. Exponential dividend growth is where each yearly value has the same percentage increase. Linear dividend growth is where each yearly dividend is increased by the same amount of dollars. In the exponential case, there are an increasing dividend dollar amount each year. In the linear case, the percentage dividend growth decreases each year. One can find cases, like Proctor & Gamble (NYSE:PG), where actual dividend payouts are almost purely exponential, and other cases, like Enterprise Products Partners (NYSE:EPD), where the payments are quite linear.

Generally speaking, low yield/high dividend growth stocks (consumer staples, etc.) have exponential characteristics, and high yield/low dividend growth stocks (LPs and REITs) are in the linear category. The percentage dividend growth for Proctor & Gamble from 2000 vs.1999 to 2011 vs. 2010 is as follows: 7.2, 9.0, 8.2, 9.5, 13.0, 11.5, 11.0, 12.4, 14.0, 11.0, 9.6, and 9.1. The dividend for Enterprise Products Partners varied from 0.925 in 1999 to 2.405 in 2011. Yearly increases in dividend were as follows: 0.12, 0.12, 0.12, 0.13, 0.12, 0.135, 0.1475, 0.07, 0.115, 0.1713, 0.1313, and 0.10. These data were taken from David Fish's U. S. Dividend Champion and Contender spreadsheets. These data are outstanding, given they include two major stock market declines. While most stocks may not be as pristine as these, they generally fall in one of the two categories.

A Seeking Alpha centurion contributor, David Van Knapp, is an advocate of yield on cost (YOC), where the current dividend is divided by the original cost. He uses this metric to gauge the goodness of dividend accumulations over time, setting a "bar" of a 10% YOC in 10 years. If we assume a range of initial yields, we can calculate the dividend growth required to meet this goal for both exponential and linear cases of dividend growth. Results are shown in the table for the 10%/- year/exponential case:

| 2 | 2.5 | 3 | 3.5 | 4 | 5 | 7 |

| 17.5 | 14.9 | 12.8 | 11.1 | 9.6 | 7.2 | 3.63 |

| 35.0 | 37.3 | 38.4 | 38.9 | 38.4 | 36.0 | 25.4 |

*Both initial yield and dividend growth are expressed as a percentage.*

We see that in this first case, a very good approximation that satisfies the goal is the product of initial yield and dividend growth. This is particularly true for values of yield between 2% and 4%, consistent with most of the stocks in this category. The average Y*DG is in this range is 37.6. Any Y*DG in excess of this would clear the "bar." This gives us a very simple method for selecting dividend growth stocks for future dividend potential. We can see the Rule of 72 at work here. From that formula, to find the number of years required to double your investment at a given compound rate, divide the compound return into 72. Here, 72/7.2 equals 10 years, dividends double from a 5% yield to 10%.

This 10/10 goal is fairly severe. In David Fish's U.S. Dividend spreadsheets (for end of year 2011), using one year dividend growth values, only 10/102 made the grade for Champions, 74/200 for Challengers, and 24/146 for Contenders. Results from lowering the "bar" from 10% YOC to 7.5%/10 year/exponential are shown in the table below:

| 2 | 2.5 | 3 | 3.5 | 4 | 5 | 3.75 |

| 14.13 | 11.61 | 9.60 | 7.92 | 6.49 | 4.14 | 7.18 |

| 28.3 | 29.0 | 28.8 | 27.7 | 26.0 | 20.7 | 26.9 |

Average Y*DG from 2% to 4% initial yields is 27.95, a fair bit below the 37.6 in the 10% case. The Rule of 72 is shown in the last column, rounding 7.18 up to 7.2. There will be more candidates from David Fish's lists using this lower criteria.

I don't look at dividend growth stocks as related to YOC. For stocks with exponential (or nearly so) dividend growth, I use the Y*DG metric as one of several in selecting stocks, with "the higher the better" as a gauge. I use one-year values as this metric, like all others, changes with time. It is my intention to write another article on dividend growth where more will be said about this time variance. The Y*DG metric should be used only for low yield/high dividend growth stocks. It allows one to explore lower yield stocks with higher dividend growth. There may be one there just below your normal yield cutoff point that would be a real zinger in the out years.

For the linear dividend growth case, it gets a little more complicated. The Initial Yield and Dividend Growth pairs were found for the 10%/10 year/linear case in a similar fashion as above. Results are shown in the table below:

| 2 | 2.5 | 3 | 3.5 | 4 | 5 | 7 |

| 40.0 | 30.0 | 23.3 | 18.6 | 15.0 | 10.0 | 4.286 |

*Values are in percents.*

The formula that fits these loci is a little more involved, but it is exact. The relationship is Y*(DG + 10) = 100. The corresponding equation for the 7.5%/10 year/linear case is Y*(DG + 10) = 75. The metric to use for high yield/low dividend growth stocks is Y*(DG + 10); the higher the values, the better. This is interesting because it allows comparison with stocks/bonds that have no dividend growth.

Be careful not to mix the numbers between the exponential and linear formulas. Their numeric values have no correlation.