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Letting Dividends Do Their Work

The Dividend Discount Model for Dividend Investors – Part 1

by George L Smyth

The Dividend Discount Model is a means of valuing a stock price that is relevant to dividend investors because the theory is based on the sum of all of the stock’s future dividend payments. Part 1 of this article explains the formula and its shortcomings. The second part will speak to fixing those shortcomings and adding a margin of safety.

There are as many ways to evaluate stocks as there are notes on a piano – perhaps more – some better than others, some completely worthless.  There is one, however, that is primarily geared toward dividend growth stocks and that is the Dividend Discount Model (DDM).

This theory contends that a dividend stock is worth the discounted value of all dividend payments going into the future.  There is a bit more than initially meets the eye in that sentence so I will break it down.

"Life can only be understood backwards—but it must be lived forwards”

I have used this quote from Kierkegaard in the past and will almost certainly use it again because it is relevant to not only investing but also many other things in our life.  We can look into the past to build a model explaining events, but going into the future we cannot avoid the requirement of making a list of assumptions.

The DDM is no different.  Reasonable assumptions must be made when attempting to divine behavior that may or may not subsequently occur.  This involves a degree of risk, which can be mitigated through conservative estimations or augmented by stretching the premises.  We all have personal risk levels, so it is important to understand where one's level of comfort lies, and that should be kept in mind when considering this model.

The Dividend Discount Model is a derivation of the Discounted Cash Flow valuation method, which bases enterprise value on future cash flows.  The DDM one of the most conservative methods derived from this, and the most straightforward of these methods is called the Gordon Growth Model, which is what we will be examining.

Diving Into the Theory

To begin I will refer to the loaded word used above in the sentence that defines the model, which is "discounted".  Understandably, the value of a dividend stock might be worth all future dividends that are received, but the word "discounted" was used, which somewhat changes the picture.  The bottom line is that $1 a year from now is worth less than $1 right now.  Allow me to explain.

As an example let’s say that a friend asks you to loan them $100, which they will pay back in one year.  One year passes and they return the $100, so all is well, except for the fact that you know that you could have placed that $100 in a savings account that offered 5% interest (sure, not possible these days, but let’s make the math easy).  Whereas you could have had $105 from that Franklin note you now only have $100, so the $100 a year ago was worth more than it is today.

This is the idea of the term "discounted", the suggestion that future dividends are not worth as much as current dividends, and the further into the future those monies are, the less valuable they are.

If a company offers a $1 dividend per share right now, that $1 might only be worth $0.95 a year from now ($0.95 * 1.05 = $1), and $0.91 two years from now, $0.86 the following year, and so on.  Adding all of these discounted values going into the future yields the value of the stock if we are assuming that it is worth the sum of all future discounted dividends.

The below chart extends this example to 50 years.


Excel spreadsheet

Adding all future dividends of this example together comes to $19.17, in case anyone is interested.  Also, in case there is interest, in this example, year 100 eventually rounds to $0.

This, however, is one of the reasons why dividend growth is so important.  If a company raises its dividend by about 5% every year then that would cover the discount in the example above, allowing for a future dollar to be worth a current dollar.

The Formula

If you wish you may go the route of the scary formula:


From Wikipedia

Fortunately for us, it can be whittled down to something more manageable:

P = D1 / (r – g)

P is the fair price of the stock
D1 is next year’s expected dividend
r is the discount rate or required rate of return
g is the dividend growth rate. 

We can plug some example numbers into the formula to see how this works.

We see that a company is selling at $15 per share and are contemplating a purchase.  They currently offer an annual dividend of $0.95 and expect to increase it next year to $1 per share, and that will steadily grow 5% year over year.  We have a requirement to make 10% on our money because we know that we can make that elsewhere, so this would be the discount rate.  The question is whether or not that other place would offer a better investment than this company’s current valuation.

Entering values into the right side of the formula offers:
D1 = next year’s expected dividend = $1
r = discount rate or required rate of return = 10%
g = dividend growth rate = 5%
$1 / (10% – 5%) = $1 / 0.05 = $20.00

The $20 result is the proper value of the stock according to the DDM.  As it is higher than the current $15 value of the stock this indicates that the stock is underpriced by $5 and would offer a better value to the investor.

Note that the dividend growth rate is subtracted from the required rate of return.  If the former is larger than the latter then mathematically and logically we are done – mathematically in the respect that the result will be negative and a stock cannot have a negative value, and logically in the respect that if the growth rate is more than is required then the investment is proper.

Shortcomings

Of course, nothing is this easy – sure the math is easy but as is the case with anything looking into the future, complications exist.

For one, this formula is primarily suited for companies that have long-term stable growth.  High-growth stocks can post a problem with this model if the company’s growth rate exceeds the expected rate of return.  With this happening then the denominator will result in a negative value, resulting in a negative amount. This is meaningless, as noted above.

Another difficulty concerns the input of the values, or in the common lingo – garbage in, garbage out.  We are assuming a constant dividend growth rate and companies do not do this.  I grabbed a copy of the Dividend Champions spreadsheet and looking through over 800 companies saw none that had the same 3, 5, and 10-year growth rates.  There will always be some variation in this number.

The 800+ companies in this list are the best case examples, as they have a history of dividend growth.   Those without at least a handful of years of consistent dividend growth will offer extreme difficulty in determining realistic numbers that can be placed into this formula. 

An additional issue comes with the discount rate.  If you know what percentage increase you require then this is not a problem at all.  Perhaps you have an opportunity to safely invest somewhere that offers a fixed return and you are trying to decide between placing your money there or with a particular stock.  In that case, you know the discount rate.

However, if you are just guessing what the discount rate should be then you may as well not bother in the first place.  After all, if you select a discount rate that is too low then everything will look good and if you select one that is too high then nothing will qualify.

This is where the Capital Asset Pricing Model (CAPM) gains importance and it, along with margin of safety, will be the subjects of the conclusion of this article.

Other Articles of Interest

Dividend Champions Spreadsheet

Safe Stocks for Dividend Investors

Lessons Learned

 



This website is maintained by George L Smyth