The Dividend Discount Model (DDM) is a simple and well known tool to value stocks by discounting to present value their future dividend distributions. In its simplest format, the DDM assumes a perpetual constant rate of dividend growth and calculates value simply as:

*V: Value*

*D: Next Year Dividend*

*r: Dividend Discount rate*

*g: Dividend Growth Rate*

Most of the time, however, investors are willing to assess scenarios where growth rates are not constant, and this has lead historically to the development of several variations of the DDM.

This article tries to address a very particular case of sustained growth where dividends are increased each year by a constant dollar amount * d* rather than by a constant percentage rate

**g.**A number of stocks can be found where dividends are grown by a constant amount for several years in a row, like AT&T (NYSE:T) has done by increasing its dividend 4 cents a year for the last five years. In that case, the growth rate is not constant as the DDM requires (it is in fact decreasing), so investors are left to their own devices in their attempts to guess the value of the stock.

Luckily enough, the DDM formula can be slightly tweaked to value stocks in this situation in an equally simple way (readers with an interest in calculus can see the derivation below), under the assumption that dividends will perpetually increase by the same amount in the future.

*V : Value*

*D: Next Year Dividend*

*r: Dividend Discount rate*

*d: Dividend Growth ($Fixed amount)*

Being a variation of the DDM, the proposed model will work best with stable dividend growth stocks. Among these there is no lack of stocks that show a pattern of increasing their dividends by a fixed amount. In fact 6-7% of David Fish list of dividend champions and contenders have followed this behavior for at least 5 years in a row (see complete list below).

**Example: AT&T valuation**

T is a dividend champion with an impressive track record of steady dividend increases. Its recent history shows the sort of dividend behavior suitable for the variation of DDM proposed above.

The following example uses an 8% discount rate (different investors may choose different values).

Year |
Dividend |
$ Amount Increase |
%Rate Increase |

2008 |
1.60 |
||

2009 |
1.64 |
0.04 |
2.50% |

2010 |
1.68 |
0.04 |
2.44% |

2011 |
1.72 |
0.04 |
2.38% |

2012 |
1.76 |
0.04 |
2.33% |

2013 |
1.80 |
0.04 |
2.27% |

2014E |
1.84 |
0.04 |
2.22% |

Dividend growth rate is declining year after year given that the amount increase is constant. An investor trying to value AT&T with the standard DDM would need to choose a growth rate assumption. In the case he sticks to the lowest most recent value g=2.22%, he would value T at $31.85 and conclude that T is fairly valued today.

But the variation discussed above allows our investor as well to value T under the assumption that the 4 cent increases continue forever into the future. By simply using the tweaked formula, he would value T at $29.25 and conclude that the stock is clearly overvalued unless the current pattern of dividend increases changes in the future.

As a conclusion, T seems to offer no margin of safety in the first case and seems overvalued in the second. Unless investors expect T to soon increase the 4 cents by which it grows its dividends every year, a price above $29.25 seems expensive from the DDM perspective discussed above.

**Appendix 1. Dividend Champions (7 cases out of 105 stocks)**

The full list of champion stocks with 5-year fixed-amount dividend growth.

- ABM Industries Inc. ABM
- AT&T Inc. T
- Energen Corp. EGN
- Middlesex Water Co. MSEX
- Old Republic International ORI
- Piedmont Natural Gas PNY
- Universal Corp. UVV

**Appendix 2. Dividend Contenders (14 cases out of 220 stocks)**

The full list of contender stocks with 5-year fixed-amount dividend growth.

- AGL Resources GAS
- Auburn National Bancorp AUBN
- Enterprise Bancorp Inc. EBTC
- First Robinson Financial Corp OTCPK:FRFC
- JB Hunt Transport Services Inc JBHT
- Laclede Group Inc. LG
- Linear Technology Corp. LLTC
- National Interstate Corp NATL
- Oil-Dri Corp. of America ODC
- RenaissanceRe Holdings RNR
- Robert Half International Inc. RHI
- Southern Company SO
- Thomasville Bancshares Inc OTCPK:THVB
- Urstadt Biddle Properties UBA

**Appendix 3. Formulae derivations**

Dividend Discount Model with constant growth rate g

DDM variant where dividends increase by a constant amount d

Subtract both series:

And then solve for V:

**Disclosure: **I am long T. 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.

Editor's Note: This article covers one or more stocks trading at less than $1 per share and/or with less than a $100 million market cap. Please be aware of the risks associated with these stocks.