Dividend Discount Model
There are many methods which people use to value a stock. For a dividend investor interested mainly in the dividends paid by companies, it makes sense to tie the value of the stock to the value of the dividends paid. A company which pays no dividend is essentially worthless to a dividend investor. The value of a dividend stock, then, is the value of all future dividend payments. In order to calculate this value, we use the Dividend Discount Model.
The Value Of Future Payments
When an investor is looking to make an investment, he or she typically has a minimum rate of return in mind. For instance, let's say I was looking to buy a house and rent it out. I decide that I want at least a 10% annualized return on my investment. I find a house that I can buy for $200,000 and can reasonably rent out for $1,400 per month, or $16,800 per year. This gives me an annual return of 8.4%, which is below my minimum. But what if raise the rent by 5% every year? Clearly, my rate of return will increase as the years pass. How do I calculate the value of these future rent payments? The payments need to be discounted by my minimum rate of return, or my discount rate. Ten years from now I will be receiving $27,365 in yearly rent. How much is this payment worth to me today? We simply discount this payment back ten years using my 10% rate of return.
In other words, if I were to invest $10,550 today and receive a 10% annual rate of return on that investment then after ten years my investment would be worth $27,365. So calculating the value of all future rent payments involves simple summing the discounted value of each future rent payment. The general formula is
where the numerator is the rent in year i. This formula is illustrated in the plot below.
As the real rent increases the discounted rent decreases due to the time value of money. If we take N to be very large, essentially infinite, then the result of this equation is that the current value of all future rent payments discounted at 10% is $352,000. So buying the house for a measly $200,000 is a steal.
Valuing Dividends
Dividend payments are no different than rent payments from the example above. A dividend stock pays a certain amount today, given by it's yield, and we expect that payment to grow over time. Therefore we define the fair value of a dividend stock as
Where P is the current annual dividend payment, G is the growth rate, and r is the discount rate. Notice that for the growth rate I wrote G(i) in the equation. This means that the growth rate is a function of the year - the growth rate is not simply a constant value. This is important because if we project a high growth rate into infinity the answer that we get will be inflated. This equation defines the dividend discount model.
Let's use this equation to calculate the fair value of a dividend stock. XYZ stock is trading at $40 per share and has a current dividend yield of 2.875%, resulting in an annual dividend payment of $1.15. Over the past ten years the dividend has grown at a fast pace, roughly 12% annually. I like to use a discount rate of 8% for the dividend discount model, which is roughly the long term return of the stock market as a whole. If we simply assume that the dividend will grow at 12% perpetually we run into a big problem - the result is infinite!. This is because the growth rate overpowers the discount rate. This is clearly unrealistic, since eventually the company's growth will stagnate and the dividend growth will necessarily slow. There are a couple of options to deal with this problem. One option is to introduce a multi-stage growth model. For example, a two-stage growth model may set the growth rate for the next ten years at 12% and then 3% for all following years. A three-stage growth model would split time into three distinct periods with different growth rates, a four-stage model into four distinct periods, and so forth. What I prefer to use is a decaying growth model. This involves using 12% as the initial growth rate and allowing that rate to decay over some number of years to a perpetual value, say 3%. The following table illustrates the different approaches regarding growth assumptions in the dividend discount model.
| Year | 2-Stage Growth Rate | 4-Stage Growth Rate | Decaying Growth Rate |
|---|---|---|---|
| 1 | 12% | 12% | 12% |
| 2 | 12% | 12% | 11.55% |
| 3 | 12% | 12% | 11.10% |
| 4 | 12% | 12% | 10.65% |
| 5 | 12% | 12% | 10.20% |
| 6 | 12% | 9% | 9.75% |
| 7 | 12% | 9% | 9.30% |
| 8 | 12% | 9% | 8.85% |
| 9 | 12% | 9% | 8.4% |
| 10 | 12% | 9% | 7.95% |
| 11 | 3% | 6% | 7.50% |
| 12 | 3% | 6% | 7.05% |
| 13 | 3% | 6% | 6.60% |
| 14 | 3% | 6% | 6.15% |
| 15 | 3% | 6% | 5.70% |
| 16 | 3% | 3% | 5.25% |
| 17 | 3% | 3% | 4.80% |
| 18 | 3% | 3% | 4.35% |
| 19 | 3% | 3% | 3.90% |
| 20 | 3% | 3% | 3.45% |
| 21+ | 3% | 3% | 3% |
Using the decaying growth model allows us to gradually decrease the dividend growth over twenty years. It does make the calculation more complicated, but spreadsheets simplify the task. Using these parameters and plugging them into the fair value formula I arrive at a fair value of $48.09 per share of XYZ. This means that shares of XYZ are trading at a discount to their fair value and the future dividends will give you a rate of return greater than your discount rate.
Conclusion
The dividend discount model is a reasonable valuation technique for those interested mainly in dividends. The key to using it correctly is being conservative about growth projections and using a reasonable discount rate. Being too optimistic will lead to inflated values and a poor rate of return.
