"Is Your Dividend Growth Stock Coming or Going?"
This question asks, is DG improving or lagging  accelerating or decelerating?
I recently published an article here at SA concerning development of a metric for degradation in linear dividend growth stocks. When that was completed, the next project was to do the same for exponential DG stocks. As this study progressed, it became obvious that a more general unified approach made more sense.
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 analysis. This was relatively straightforward, but somewhat involved in that you had to copy data to an internet website 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 determining dividend growth degradation. This article attempts to address this last issue. Don't worry about the math being too difficult. All that is required is: follow simple directions and apply basic arithmetic.
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. [see 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 that includes overall dividend growth and its deviation from a linear or exponential standard, as applicable for each of the two types of growth.
Note 1: Dividend growth stocks (of both types) may exhibit short spurts of higherthannormal dividend growth due to acquisitions or other oneoff reasons. In moderate time frames, such as the 8year business cycle commonly used in analyses, expected growth is linear and exponential in appropriate cases. This is demonstrated later. The only parameter used in this analysis is the annual dividend amount. For dividend growth aficionados, it doesn't get more pure than that.
Linear Dividend Growth Case
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 percent increase. This difference is the incremental slope of the dividend curve. Those 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). The equation of the curve is unknown, which a linear regression analysis would provide, but it can be estimated. 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 step is 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) or averaged, 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 timeperiod 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. The two components can be melded into a composite metric involving both dividend growth and its variations.
The following outlines the steps taken for developing this metric:
1) Gather 8 years of dividends for the stock to be analyzed. Since there will be subtraction of numbers close together, care is required to insure that roundoff values are not used.
2) Determine the dividend increase in dollars by subtracting one year from the next. Average these 7 values, designated as DI$.
3) Divide DI$ by the latest dividend and multiply by 100. This is called DGRL for Dividend Growth Rate, Linear.
4) Subtract yeartoyear values of the dividend increase, this is called Accel. Average these 6 values and multiply by 100, designated as DAL for Dividend Acceleration, Linear.
5) Determine a metric DGAL, Dividend Growth Acceleration, Linear, using DGAL = DGRL (DAL + 5).
Example for Sunoco Logistics Partners LP (NYSE:SXL):
SXL 
2006 
2007 
2008 
2009 
2010 
2011 
2012 
2013 
Div. 
1.0083 
1.1083 
1.2217 
1.3700 
1.5050 
1.6099 
1.8350 
2.3475 
Div. Inc. 
0.1000 
0.1134 
0.1483 
0.1350 
0.1049 
0.2251 
0.5125 

Accel 
0.0134 
0.0349 
0.0133 
0.0301 
0.1202 
0.2874 
DI$ = 0.1913; DGRL = 100 * 0.1913/2.3475 = 8.15; DAL = 100 * 0.06875 = 6.88; DGAL = 8.15 *(6.88 + 5) = 97
To see how this comes about, the graph below depicts a cross plot between the acceleration and velocity components for 104 Linear Dividend Growth Companies (Source: David Fish's CCC Lists):
An eyeball average of these data would indicate a line along the horizontal axis. This means that for all dividend growth rates there is no acceleration (on average), meaning a constant slope for dividend increases, meaning a straight line for the dividend history over time  linear dividend growth.
It would be helpful to develop a metric using the two components, DAL and DGRL. Since a zero DAL value is acceptable, adding a constant to DAL will lift the plot up above the horizontal axis, as shown below:
The green curve represents a hyperbolic function (equilateral hyperbola) in the form of xz=constant=15. It represents the equation, DGAL = DGRL * (DAL + 5). Using this equation (metric), calculations will yield values for each stock whereby comparisons can be made. All stocks above the curve exceed the "limit", in this case 15. Obviously, both values 5 and 15 can be varied to divide the population of stocks into different pass/fail categories. It does present a simple way to do so. SXL at 97 is doing well. A minimum limit of 15 for DGAL means a minimum of 3 for DGRL with no acceleration.
Wellknown linear dividend growth stocks have the following DGAL values:
AT&T (NYSE:T) 15.5
Rogers Communications (NYSE:RCI) 48.5
BCE Inc. (NYSE:BCE) 48.5
HCP Inc. (NYSE:HCP) 14.5
Health Care REIT (NYSE:HCN) 26.7
National Heath Investors (NYSE:NHI) 33.7
Omega Healthcare Investors (NYSE:OHI) 40.3
Realty Income (NYSE:O) 38.6
Kinder Morgan Energy Partners LP (NYSE:KMP) 50.5
ONEOK Partners LP (NYSE:OKS) 34.6
TransMontaigne Partners LP (NYSE:TLP) 10.7
Enterprise Products Partners LP (NYSE:EPD) 27.7
Energen (NYSE:EGN) 17.2
NextEra Energy (NYSE:NEE) 41.1
Wisconsin Energy (NYSE:WEC) 82
Exponential Dividend Growth Case
A similar analysis can be executed for exponential dividend growth stocks. Here, the steps to follow are quite the same, the main difference is in the calculation of the velocity component. The percent dividend increase is used instead of the dividend increase in dollars. For exponential dividend growth, this percent increase should be constant (more or less) every year, providing a similar starting condition as above in the linear case. The coefficients in the final metric DGAE, Dividend Growth Acceleration, Exponential, are different.
The following outlines the steps taken for developing this metric:
1) Gather 8 years of dividends for the stock to be analyzed. Since there will be subtraction of numbers close together, care is required to insure that roundedoff values are not used.
2) Determine the percent dividend increase in dollars by the ratio of yearly dividends minus one. Average these 7 values, multiply by 100. This is called DGRE for Dividend Growth Rate, Exponential.
3) Subtract the yeartoyear values of the percent dividend increase, this is called Accel. Average these 6 values and multiply by 100, designated as DAE for Dividend Acceleration, Linear.
4) Determine a metric DGAE, Dividend Growth Acceleration, Exponential as DGAE = DGRE * (DAE + 7).
Example for Johnson & Johnson (NYSE:JNJ):
JNJ 
2006 
2007 
2008 
2009 
2010 
2011 
2012 
2013 
Div. 
1.4550 
1.6200 
1.7950 
1.9300 
2.1100 
2.2500 
2.400 
2.5900 
% Div. Inc. 
0.1134 
0.1080 
0.0752 
0.0933 
0.0664 
0.0667 
0.0792 

Accel 
0.0054 
0.0328 
0.0181 
0.0269 
0.0003 
0.0125 
DGRE = 100 * 0.086 = 8.6; DAE = 100 * 0.00571 = 0.571; DGAE = 8.6 *(0.571 + 7) = 55
The graph below shows a cross plot between these two variables for 290 stocks with exponential growth (Source: David Fish's CCC Lists). A line along the DAE = 7 horizontal line is a rough average of the population. Again, this means no acceleration, a constant average percent dividend growth, an exponential dividend history  exponential dividend growth. The green curve represents a limit of 50 for DGAE. The minimum DGRE is 7 with no acceleration.
As before, the constants 7 and 50 can be changed to satisfy different objectives. Common stocks in the exponential dividend growth category are, with their corresponding values of DGAE:
The Clorox Company (NYSE:CLX) 61
ConocoPhillips (NYSE:COP) 100
Darden Restaurants (NYSE:DRI) 76
Hasbro (NASDAQ:HAS) 71
Illinois Tool Works (NYSE:ITW) 41
Intel (NASDAQ:INTC) 69
Owens & Minor (NYSE:OMI) 84
Target (NYSE:TGT) 146
Procter & Gamble (NYSE:PG) 62
Sysco (NYSE:SYY) 42
Walgreen (WAG) 146
VF Corp. (NYSE:VFC) 77
Chevron (NYSE:CVX) 68
BHP Billiton (NYSE:BBL) 48
PepsiCo (NYSE:PEP) 49
Conclusions
I believe the metrics, DGAL and DGAE, developed here will be useful (with others) in determining those stocks to buy and/or hold in a portfolio. As in all metrics, they are not infallible, calculated values that are out of the ballpark will be the result of irregular input data. These may be discounted and corrected as the input data is reviewed. There is no substitute for graphing dividend history data.
As in most metrics, utility is increased by performing annual calculations to determine trends. The graph below shows an 8year running DGAE for P&G, Courtesy of Robert Allen Schwartz (an SA contributor) for dividend history. He has a storehouse of dividend data here .
I don't know how to interpret the dip in the '80s. Inflation was very high then. It maybe that their costs were going up faster than they could increase prices. After that, DGAE seems to follow the economy/market, finds a peak in 1999, a bottom in 2002, and a peak again in 2008. After 2009, the market has gone up (but maybe not the economy), while DGAE has consistently dropped. PG is not alone here. I have several stocks in my portfolio that are doing the same, the rest are doing just fine. Hence my interest in this arena.
Disclosure: I am long SXL. 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.
Additional disclosure: Of the stocks listed in the article, I am long SXL, RCI, BCE, NHI, OHI, HCN, OKS, O, TLP, EPD, CLX, DRI, HAS, INTC, OMI, TGT, PG, VFC, WAG, JNJ.