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# Dividend discount model

The dividend discount model is a means of estimating (not calculating) the value of company based on its dividend payouts, assuming certain increases to the dividend and growth in the company.

## Expanded Definition

Theory says that the value of a company is the value of all its future cash flows paid to its owners discounted back to the present at an appropriate discount rate. Warren Buffett has often said this, too, so theory must be right in this case!

In order to understand this, one must first grasp the concept of the time value of money. If you're not familiar with that, please go there and wrap your head around it, then come back here. Don't worry, this page won't disappear into the void or get eaten by space warthogs while you're gone.

In the case of the dividend discount model (DDM, for short), the cash flows under discussion are dividends. Thus, this model is less useful (not necessarily useless, see below) for estimating companies that don't pay dividends. It also assumes that the dividends being paid are substantial in terms of the company's net income.

### Basic form

Suppose that you have a company that pays a $1.00 annual dividend and that this dividend and the company are not growing. How much should you pay to be guaranteed that payment every year from now until forever? Well the answer is the dividend divided by the expected rate of return (the discount rate). If that is 5%, then you should pay no more than$20 for that stream of cash flows.

$Value = \frac{Dividend}{Discount\ rate} = \frac{1.00}{0.05} = 20.00$

Well, a guaranteed stream of identical cash flows from now into perpetuity is nothing more than a perpetual annuity and that equation is the same one as is used to calculate the value of such an annuity.

$V_0 = \frac{Div_1}{1 + r} + \frac{Div_1}{(1 + r)^2} + \frac{Div_1}{(1 + r)^3} + ... = \frac{Div_1}{r}$

Here, "Div" is the dividend and "r" is the discount rate. Note that it begins with next year's dividend (because it is discounted back to the present).

### Growth

Trouble is, most companies are expected to grow over time, or at least grow their dividends. (And the company better grow, too, to support the growing dividends.) So, we can modify the above equation to reflect this.

$V_0 = \frac{Div_0*(1 + g)}{1 + r} + \frac{Div_1*(1+g)}{(1 + r)^2} + \frac{Div_2*(1 + g)}{(1 + r)^3} + ... = \frac{Div_1}{r - g}$

Here, "g" is the expected growth rate of the dividend. This is called the Gordon growth model, after Myron Gordon who first created it. Note, again, that it begins with next year's dividend (because it is discounted back to the present).

So, if that $1.00 paying dividend company is expected to grow its annual dividend by 3% per year, then you would expect to pay no more than$50.00 for the privilege of owning it.

$V_0 = \frac{Div_1}{r - g} = \frac{1.00}{0.05 - 0.03} = 50.00$

### Multi-stage models

It is possible to expand the general equation back out to the long hand version and apply different growth rates to each term. This Fool article does exactly that, illustrating a two-stage model. Note, though, that even in this case, the vast majority of the estimated value comes from the "terminal" situation where growth is said to be constant.

### Warnings

#### Assumptions

The DDM is highly dependent on what assumptions go into it. For instance, if the discount rate is changed slightly, say from 5% to 6%, a mere one percentage point increase, the value become \$33.33. That's 33% lower from a single percentage point change in the discount rate!

#### Small differences

The numbers become less reliable (as if they were ever 100% reliable in the first place) the closer the growth rate is to the discount rate. If r = 6% and g = 5%, then the expected value of the company is 100 times the dividend. But if g = 5.5%, then the expected value is 200 times the dividend. It gets worse the smaller the difference is between "r" and "g."

#### High growth companies

If g is ever greater than r, such as a 20% per year grower and a discount rate of 15%, then the DDM model won't work at all. You are not allowed to have answers below zero dollars per share which is what you would get in this case (r - g = -5%). Sorry.

#### "Exact" value

Because of the difficulty in predicting growth out for several years, never think that the price being kicked out is the "true" price. It's an estimate only, based on the growth rate assumptions put in. Before Washington Mutual collapsed, you could have used this model to calculate a value based upon its then nice dividend, looked at the trading price and thought you were getting a bargain. Well, as you know, the company slashed its dividend. Oops! There go all those nice, beautiful future cash flows your model relied upon and the stock price collapsed, eventually leading to the company disappearing.

### Benefit of using the DDM

Despite the warnings given above, the model is still useful for companies that pay a reliable dividend (such as utilities, but not even them all the time).

It also is a good exercise to force you to look at your assumptions and consider whether or not they are reasonable. If you are putting in outrageous numbers just to get the calculated price close to where it is currently trading to justify buying the stock, well, don't say you weren't doing something totally un-Foolish.