# How to Find a Stock's Value Using the Dividend Discount Model

One of the most elusive questions in investing is, "What is the right price for this stock?"

There are a number of ways to calculate a stock's value, but one of the most elegant and relatively simple ways continues to be via the dividend discount model (DDM) individual investors can estimate the price they should be willing to pay for a stock or determine whether a given stock is undervalued or overvalued.

The dividend discount model starts with the premise that that a stock's price should be equal to the sum of its current and future cash flows, after taking the "time value of money" into account.

Now, there are two different concepts in that sentence, and both of them are vital to your understanding of investing. Let's walk through each one, and then discuss how they are joined together in the DDM.

**Estimating Current & Future Cash Flows**

The cleanest and most clear-cut measure of cash flow is the dividend. Hopefully this makes sense to you, but if it doesn't, consider that the dividend is the mechanism companies use to pay their investors. People invest in companies with the intention of getting their money back and then some. Dividends are one of the main ways companies return money to investors. Dividends are paid out in cash, and therefore are the most straightforward estimate of the future cash you can expect to receive.

Even if a company does not pay a dividend right now, the price of its stock is calculated under the assumption that at some point in time the company will begin paying one. If there is no hope of ever getting money back, investors would have no reason to buy a stock. It would be worth nothing.

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**The Time Value of Money**

Investing is a method of saving. Because you have extra money left over after paying your expenses, you can set it aside for future use. The whole point of investing is to turn a sum of today's money into a larger sum in the future.

Understanding the time value of money is of utmost importance to investing. Time value of money is a series of concepts that allows you to compare different options: Is it better to receive $24,000 today or $25,000 one year from today? If you understand the concept of present value, you can easily perform a calculation and come up with the right decision.

[Click here to read A Primer on Present Value and Its Many Uses]

The time value of money is directly relevant to the dividend discount model because the DDM's main objective is to put future cash flows into today's dollars. To do so, we'll use present value calculations.

**Using the DDM Formula**

Now let's get to the DDM formula itself. The dividend discount model is based on a basic valuation model that is the foundation for many other investing techniques. This basic valuation principle, used far and wide, combines expected future cash flows and the time value of money into one easy-to-use formula:

Stock Price = the Sum of the Present Value of All Future Dividends

Or, more precisely,

Price = ∑ (D_{t} / (1 + r)^{t})

where,

t = period

D_{t} = dividend during period t

r = required rate of return on the stock

If you don't understand the concept right now, it should get easier after looking at a couple of examples.

**Buy-and-Hold**

Let's look at the stock of hypothetical Company ABC. Stock ABC pays a $3 annual dividend. We decide that we must make 5% annually on this investment for it to be worth our while (this is known as the required rate of return, also known as the discount rate, or "r" in this tutorial). We're also planning on holding the stock for the very long term.

Luckily, when we talk about an infinite holding period and a constant dividend, the DDM simplifies to this formula:

Stock Price = D / r

So to calculate the price of Stock ABC, we plug in the numbers to get:

Stock Price = $3 / (0.05) = $60

This formula tells you that if you buy at $60, the $3 annual dividend will ensure you receive a 5% return on your investment. If Stock ABC is trading below $60 right now, it's a buy. If it's trading above $60, we should wait for the price to come down.

Calculating the value of a stock using the dividend discount model is easy if we assume the dividend will never change and we'll hold the stock forever. But in the real world, most investors expect companies to grow dividends. So let's look at another example.

**Factoring in Dividend Growth**

So what happens if Stock ABC has potential to grow its dividend? This isn't an unreasonable assumption at all. As long as a company can grow its earnings, it should be able to grow its dividend. Let's assume we think Company ABC can grow its dividend by 2% every year.

Adding this growth assumption gives us the "reduced form DDM" with the following formula:

Stock Price = D_{1} / (r - g)

where,

D_{1} = the dividend at year 1

g = the dividend growth rate

To calculate the dividend at year 1, all we need to do is multiply the current dividend ($3) by the dividend growth rate (2%): D_{1} = $3 x (1 + 0.02) = $3.06. Now we can plug it into the formula with the rest of our assumptions:

Stock Price = $3.06 / (0.05 - 0.02) = $102

Note how much more valuable Stock ABC comes if it is able to realistically grow dividends by 2% per year ($102 vs. $60).

The calculation gets more and more complicated as you add other assumptions. For example, what if you only want to hold the stock for 1 year, 5 years or 10 years? What if the dividend growth rate is expected to change over time? What if the company doesn't pay a dividend yet? These more advanced scenarios will be addressed in future tutorials.

For now, let's look at the pros and cons of the DDM to get even more insight into how and why the model is used.

**Model Advantages and Disadvantages**

The main advantage of the dividend discount model is that it is relatively easy to use. There are only a few calculations involved. This model is a good starting point for valuing stocks, since it connects dividend payments and dividend growth to the stock price.

The dividend discount model works best for companies that are experiencing stable growth. There is a version of the model that can be used for companies transitioning from rapid growth to more moderate growth, but the calculations are much more complicated.

There are also some drawbacks to using the dividend discount model. A major shortcoming of the model is that it works best for a stock that already pays dividends. But almost two-thirds of publicly traded companies don't pay a dividend. Instead, these companies retain all of their earnings so they can grow. You can use the DDM for non-dividend paying companies, but you need to make some pretty tenuous assumptions about when they will start paying a dividend and how much they'll pay.

Another flaw of the dividend discount model (and any model, for that matter) is that it requires numerous assumptions to be made. Investors must guess a company's growth rate as well as the required rate of return. The model is only as good as its inputs. Even a slight miscalculation in any of these inputs can result in dramatically overvaluing or undervaluing a stock.

An odd weakness of the model is that it cannot value a company if that company is growing its dividend faster than the required rate of return. If the dividend is growing faster, the denominator in the dividend discount model becomes a negative value. For example, suppose Stock A pays a $3 dividend, has a 15% growth rate and has a required rate of return of only 10%. According to the dividend discount formula, the value of Stock A = ($3 x 1.15) /(0.10-0.15) = -$69. That's not terribly useful.

Despite these flaws, the dividend discount model remains a worthwhile analytical tool. It's simple to use and the model's basic premise -- that the value of a stock is equal to the sum of current and future dividend payments -- is sound. The dividend discount model is a good starting point for valuing a stock since the model encourages investors to think about the relationship between risk, returns and growth.