I have had several articles published here at SA in the dividend growth arena on subjects of due diligence, monitoring portfolio performance and developing metrics. This article continues along those same lines. I had suggested one way to characterize dividend growth by using linear regression analyses. This was relatively straightforward, but somewhat involved in that you had to copy data to an internet web-site in a vertical (column) format. This was awkward and a little time consuming, particularly when working off a watch list of stock candidates for purchase. Also, it didn't provide a good clue for accessing dividend growth degradation. This article attempts to address this last issue, as applied to linear dividend growth stocks.

There are two kinds of dividend growth, exponential and linear. For the most part, C Corp (regular) companies exhibit exponential dividend growth where the Rule of 72 prevails. Utilities, REITs, MLPs and Telecoms have linear dividend growth. [Note 1]. Both types are subject to "droop", gradual degradation of dividend growth over time. It would be useful to develop a metric for a single composite measurement of overall dividend growth, and one for deviation from a linear or exponential standard, as applicable for each of the two types of growth.

Note 1: Linear dividend growth stocks may exhibit short spurts of higher than normal dividend growth due to acquisitions or other one-off reasons. You will notice that in moderate time frames, such as the 8 year business cycle commonly used in analyses, expected growth is linear. This is demonstrated later.

A salient characteristic in a linear function of time is that changes are constant in each increment of time. This provides a measure of goodness if we determine the annual dollar increase for each stock rather than the percent increase. This difference is the incremental slope of the dividend curve. Those of you who have studied differential calculus will recognize this as the first derivative, delta dividend/delta time (dd/dt) - there dt in this case is 1 (year). We don't know the equation of the curve which a linear regression analysis would provide, but we can estimate it. A simple metric could be the average of these data for each stock divided by the last dividend, a current dividend growth of expected future performance. An additional metric could be obtained by taking the second derivative, the difference in the "velocity" derivative incremental data just calculated. This provides the "acceleration" for each increment of time, which when integrated (summed over time), per integral calculus, results in a net acceleration/deceleration of dividend increases. A zero value of the sum of these second derivatives over a small time period means no net changes in dividend flow from the linear standard. Positive values means the dividends are trending up (above the linear) and negative trending down. We could establish a cutoff value for this acceleration metric as a means test for acceptance or rejection.

For those who think faster than you can read will recognize that all this could be done for exponential dividend growth stocks as well because there, DGR, Dividend Growth Rate, is constant year-to-year (or should be!). That would be the first derivative, summing those data would be an 8-yr DGR average (not CAGR). The second metric could be a summed net acceleration value as described above.

While all this may sound complicated, the above discussion is presented as a mathematical justification for the technique. Practical usage is simple, as shown in the example below for Enterprise Products Partners (NYSE:EPD):

EPD | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |

Dividend | 1.795 | 1.915 | 2.045 | 2.165 | 2.285 | 2.405 | 2.5325 | 2.7 |

Div Inc $ | 0.12 | 0.13 | 0.12 | 0.12 | 0.12 | 0.1275 | 0.1675 | |

Accel | 0.01 | -0.01 | 0 | 0 | 0.0075 | 0.04 |

The average of the Div Inc line is $0.129, so current dividend growth is 0.129/2.7 = 0.048 (4.8%). Since this rate will change (go down) every year because dividends are increasing, the rate is useful only in comparing with other stocks. The sum of the Accel line is 0.0475; a positive number means the dividends are trending up from a linear rate.

The next example is less neat. It features Shaw Communications (NYSE:SJR).

SJR | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |

Dividend | 0.258 | 0.541 | 0.646 | 0.735 | 0.851 | 0.925 | 0.963 | 0.991 |

Div Inc $ | 0.283 | 0.105 | 0.89 | 0.116 | 0.074 | 0.038 | 0.028 | |

Accel | -0.178 | -0.016 | 0.027 | -0.042 | -0.036 | -0.01 |

The average dividend increase was 0.1047 for a dividend growth of 0.1047/0.991, 10.6%. The summation of the Accel line was -0.255, showing significant dividend growth degradation.

This example illustrates the problem of characterizing dividend growth for erratic dividend history. The dividend increase (slope) has a value of 10.5%, while the l.r. calculation shows 9.03% for the same data. All the more reason for paying attention when it is used.

A new metric is introduced, Accel Sum Value [ASV]; it is the 4 year sum of Accel times 100. A value of zero indicates a straight line in dividend flow (over the 4 year time period). To analyze this metric using a larger data sample, David Fish's CCC Lists were reduced to the following stocks: Utilities, REITs, MLPs, Telecoms. The graph below shows the average dividend data, deleting 9 for lack of complete data:

101 Stocks | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |

Avg Div/sh $ | 1.302 | 1.417 | 1.492 | 1.565 | 1.659 | 1.757 | 1.87 |

Div Inc $ | 0.115 | 0.075 | 0.073 | 0.094 | 0.098 | 0.113 | |

Accel | -0.04 | -0.002 | 0.021 | 0.004 | 0.015 | ||

ASV | -1.7 | 3.8 |

The average dividend increase was 0.0947 giving a dividend growth of 5.06%. The 9.1% l.r. refers to the slope of the line which was determined to be 9.5% in the calculation above.

There are two variables here under consideration, the length of the summing period and a trigger point for testing performance. Arguments in favor of a longer period are that more smoothing is achieved. Arguments against are it takes a longer time to make a determination and once triggered, takes a longer time to clear through the system, assuming you are performing these calculations every year. Too low a trigger point means more false alarms, more failures indicated than warranted. I tried various schemes to ferret out the best time frame and trigger point. These included counting the number of "fails" in cells as conditions varied as well as exotic combinations of running ASVs over the 8 year time period. It only got more complicated until I decided to KISS it off. The best, simple approach is to use a 4 year summing period for the most recent 4 year time frame.

ASV numbers above 10 indicate companies with significant increasing dividend growth above a straight line (for linear dividend growth stocks). Seventeen companies that "passed" this test were: American States Water (NYSE:AWR), DCP Midstream Partners LP(NYSE:DPM), Essex Property Trust (NYSE:ESS), Kinder Morgan Energy Partners LP (NYSE:KMP), Lexington Realty Trust (NYSE:LXP), Magellan Midstream Partners LP (NYSE:MMP), National Health Investors (NYSE:NHI), NextEra Energy (NYSE:NEE), Omega Healthcare Investors (NYSE:OHI), OKE (NYSE:OKE), ONEOK Partners LP (NYSE:OKS), Plains Pan American Pipeline LP (NYSE:PAA), Realty Income (NYSE:O), Sunoco Logistics Partners LP (NYSE:SXL), W P Carey (NYSE:WPC), William Partners LP (NYSE:WPZ), Wisconsin Energy (NYSE:WEC).

ASV numbers below -10 indicate companies with significant decreasing dividend growth, again below a straight line. Seven companies in this category were: BCE (NYSE:BCE), Buckeye Partners LP (NYSE:BPL), China Mobile (NYSE:CHL), EV Energy Partners LP (NASDAQ:EVEP), NuStar GP Holdings (NYSE:NSH), UNS Energy (NYSE:UNS), Vanguard Natural Resources (NASDAQ:VNR). A note of caution, ASV can vary substantially year-to-year if the Accel numbers are large, both positive and negative, as they come on and drop off the summation window. There is no substitute for simply looking at the dividend flow over the 8 year period to determine what is going on. For this reason, using ASV as a screening metric should be approached with caution.

As an example of the complexities involved, I downloaded all dividend data for SJR from 1999 to 2013. This is shown in the chart below.

Moving ASVs for these data from 2004 to 2013 are: 4.5, 1.3, 13.5, 25.3, 5.0, 7.6, -1.9, -20.9, -6.7,-6.1. The indication in 2008 that the dividend increase had dropped was due to a big increase the year before. As time progressed, ASV varied somewhat, but still in the positive range. In 2010 it went negative. In 2011 it is time to take a close look at the situation. There is improvement in 2012 and 2013, but this is due (in part) to the big drop in Accel in 2008 dropping off the summation.

Think of it as if you were driving a car along this bumpy road. The car is 4 units long (dragging a 2 unit trailer). At first everything is OK because you are going up a hill. Bumps may occur along the way. Gradually it levels off, but you reach a point where you bottom out. This occurs when ASV goes negative, which it did in 2010. The bump you ran over that hit the chassis is the indication that dividend growth performance was not maintained.

Another stock that fails the test and has a long dividend history (per CCC) is Buckeye Partners LP :

ASVs starting in 2004 are: -12.5, 13.7, 15.0, 16.2, 10.0,1.3, 0, 0, -7.5, -12.5. Note that starting in 2008, ASV was dropping, then in 2012 went negative, and down again the next year. To return to a pass condition, one needs a higher dividend growth to boost positive acceleration. Remember, zero ASV is normal for true linear dividend growth.

Before leaving this discussion on linear dividend growth stocks, I want to try the ASV technique on an exponential dividend growth company. I have written in the past about Procter & Gamble (NYSE:PG), as deviating from exponential down thru linear and below. The dividend history curve is shown below:

Looking closely, you can see some droop in the last few years. ASVs from 2004 are: 5.9, 2.5, 2.8, 2.9, 0.9, -0.5, -1.4, -3.3, -6.5, -3.9. The scheme seems to work. Here I used the normal annual percentage dividend growth rate for the velocity part. For exponential dividend growth this should be constant year-to-year. The Accel part (the difference in percentage increases) and the 4 year ASV were calculated as before. One can easily see the degradation in ASV, more apparent than eye-balling the chart. I don't know (yet) if the trigger point is the same for exponential dividend growth stocks, this awaits further analysis. It may be that PG is dying a slow death. Maybe they hope if they decrease the increase slowly, we won't notice.

Exponential and linear dividend growth stocks should be analyzed differently. But with the ASV metric described here, some of that could be the same. Start with a level playing field (pun intended), dividend increases (linear) and percent increase (exponential).

**Disclosure: **I am long EPD. 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. Of the stocks referenced in the article, I am long EPD, SJR, BCE, EVEP, NHI, NEE, OHI, OKS, PAA, O, SXL, WEC