It’s one of the basic applications of a financial theory that students in any introductory finance class must learn. Unfortunately, the theory is the easy part. The model requires loads of assumptions about companies’ dividend payments and growth patterns, as well as future interest rates. Difficulties spring up in the search for sensible numbers to fold into the equation.
The Dividend Discount Model
Here is the basic idea: any stock is ultimately worth no more than what it will provide investors in current and future dividends. Financial theory says that the value of a stock is worth all of the future cash flows expected to be generated by the firm, discounted by an appropriate risk-adjusted rate. According to the DDM, dividends are the cash flows that are returned to the shareholder. (We’re going to assume you understand the concepts of time value of money and discounting. You can learn more about these subjects here.)
To value a company using the DDM, you calculate the value of dividend payments that you think a stock will throw-off in the years ahead. Here is what the model says:
ZERO GROWTH : Po = Div/r
P= the price at time 0
r= discount rate
For simplicity’s sake, consider a company with a $1 annual dividend. If you figure the company will pay that dividend indefinitely, you must ask yourself what you are willing to pay for that company. Assume expected return, or, more appropriately in academic parlance, the ‘required rate of return‘ is 5%. According to the dividend discount model, the company should be worth $20.00 ($1.00 / .05).
How do we get to the formula above? It’s actually just an application of the formula for a perpetuity:
P0 = Div1/1+r + Div2/(1+r)^2 + ……..Div/r
The obvious shortcoming of the model above is that you’d expect most companies to grow over time. If you think this is the case, then the denominator equals the expected return less the dividend growth rate. This is known as the constant growth DDM or the “Gordon Model” after its creator, Myron Gordon. Let’s say you think the company’s dividend will grow by 3% annually. The company’s value should then be $1.00 / (.05 – .03) = $50.00. Here is the formula for valuing a company with a constantly growing dividend, as well as the proof of the formula:
Constant Growth : Po = Div/r-g
P0 = Div1/1+r + Div1 (1+g)/(1+r )^2 +………Div/r-g
The classic dividend discount model works best when valuing a mature company that pays a hefty portion of its earnings as dividends, such as a utility company.
Assumptions – The Problem of Forecasting
Proponents of the dividend discount model say that only future cash dividends can give you a reliable estimate of a company’s intrinsic value. Buying a stock for any other reason–say, paying 20 times the company’s earnings today because somebody will pay 30 times tomorrow–is mere speculation.
In truth, the dividend discount model requires an enormous amount of “speculation” in trying to forecast future dividends. Even when you apply it to steady, reliable, dividend-paying companies, you still need to make plenty of assumptions about their future. The model is subject to the axiom “garbage in, garbage out,” meaning that a model is only as good as the assumptions it is based upon. Furthermore, the inputs that produce valuations are always changing and susceptible to error.
The first big assumption that the DDM makes is that dividends are steady, or grow at a constant rate indefinitely. But even for steady, reliable, utility-type stocks, it can be tricky to forecast exactly what the dividend payment will be next year, never mind a dozen years from now.
To get around the problem posed by un-steady dividends, multi-stage models take the DDM a step closer to reality by assuming that the company will experience differing growth phases. Stock analysts build complex forecast models with many phases of differing growth to better reflect real prospects. For example, a multi-stage DDM may predict that a company will have a dividend that grows at 5% for seven years, 3% for the following three years and then at 2% in perpetuity.
However, such 