## What is Dividend Discount Model (DDM)?

Dividend payments are generally paid to investors or shareholders of a company when the company earns profit for the year, thus representing growth. The dividend discount model is an important method used to forecast the price of a company’s stock. It is based on the computation methodology that the present value of all its future dividends is equivalent to the value of the company.

To recap, the present value theory postulates that $1000 today is more valuable than $1000 in the future. This represents the time value of money, which represents that the value of money is associated with time. Present value is computed by discounting future cash flows with the interest rate. This dividend discount model formula takes all expected future dividends that the company is expected to receive and calculates its present value using a discounted or interest rate. Upon computing the present value of DDM, analysts compare it to the present value of the stock to understand whether the stock is valued correctly, or overvalued or undervalued.

## Estimating Future Dividends

Shareholders require a certain compensation for the efforts and money invested. This is represented by the firm’s cost of capital (equity) where the shareholders are the investors who are given compensation in the form of dividends. The rate at which they are determined is through the Dividend Growth model or the Capital Asset Pricing Model. The company’s future dividends are generally estimated through different methods and assumptions, such as by analyzing trends and other statistical computations. Some assumptions suggest that one could use a steady dividend growth rate and identical cash flow to compute future dividends. The difference between the rate of return and the rate of dividend growth will be the rate of discount used to effectively compute the NPV.

**Computing using the dividend discount model**

The DDM is a valuable tool in the analyst’s and investor’s arsenal especially because it helps in ascertaining the theoretical fair price of a stock. The DDM computes the intrinsic value of the stock.

$$\text{FV}=\text{PV}\times \left(1+\text{r}\right)$$**Here,**

**FV = **Future value of all cash flows

**PV = **Present value of cash flow

**r = **Rate of return on investment

This can be derived into:

$$\text{PV}=\frac{\text{FV}}{1+\text{r}}$$The formula for computing the rate of return (RoR)

$$\text{RoR}=\left(\frac{\text{ExpectedDividend}}{\text{StockPrice}}\right)+\text{GrowthRate}$$Let us compute this with an example. Assume that Google’s shares are trading at $60 per share. Google’s expected annual dividend for the next year is $1.5, and on average, has increased its dividends by 7.5%.

Therefore, the rate of return for Google is:

$$\begin{array}{c}\text{RoR}=\left(\frac{\$1.5}{\$60}\right)+7.5\%\\ =10\%\end{array}$$We can determine the stock price by using the following formula.

$$\text{Stockvalue}=\frac{\text{ExpectedDividendperShare}}{\left(\text{RateofReturn\u2013GrowthRate}\right)}$$

From the above example, the stock value would be:

$$\begin{array}{c}\text{StockValue}=\frac{\$1.5}{10\%-7.5\%}\\ =\$60\end{array}$$Assuming the investor wants a rate of return of 9%, then the stock value will be:

$$\begin{array}{c}\text{StockValue}=\frac{\$1.5}{9\%-7.5\%}\\ =\$100\end{array}$$## Types of DDM:

There are several types of dividend discount modeling.

The first is the **Gordon Growth Model (GGM)**. The GGM growth model assumes that the dividends will grow at a constant rate for an infinite period of time. This is extremely important in computing DDM for steady companies with steady cash flows and dividend growth.

The formula for computing the GGM- DDM is:

$${\text{V}}_{0}=\frac{{\text{D}}_{1}}{\text{r}-\text{g}}$$Here,

V_{0} = Fair value of stock

D_{1} = Dividend payment at the end of one year

r = Cost of equity

g = Constant growth rate of the company’s dividends

The second is the One-period DDM which assumes that the stock is held by the investor only for a year. The sum of the future dividend payment and the estimated price at which it will be sold will have to be discounted to the present values.

$${\text{V}}_{0}=\frac{{\text{D}}_{1}}{1+\text{r}}+\frac{{\text{P}}_{1}}{1+\text{r}}$$Here,

V_{0} = Fair value of stock

D_{1} = Dividend payment at the end of one year

r = Cost of equity

P_{1} = Price of stock in one year (or respective period)

The third is the **Variable growth DDM** or multi-stage DDM which accounts for the initial booming growth rate, the slower growth rate as the company reaches maturity, and later as the company ages a steady and more mature growth rate. In this case, each phase is computed separately with their respective DDMs and then added together.

Here,

V_{0} = Fair value of stock

D_{1} = Dividend payment at the end of one year

D_{2} = Dividend payment at the end of two year

D_{n} = Dividend payment at the end of n year

r_{1} = Cost of equity in the first year

r_{2} = Cost of equity in the second year

r_{n} = Cost of equity in n^{th} year

P_{n} = Price of stock in the n^{th} year (or respective period)

**Problems with the DDM:**

There are several issues with the DDM and its computation. They are as follows:

- The Gordon Growth model is the most popular one which does not account for major fluctuations in the rate of dividends.
- The model is most helpful for companies with steady growth rates and dividend disbursements and does not often consider companies with high-paced growth rates and small-scale organizations.
- The formula is very variable-sensitive and any minor changes to the variables can impact the outcome in a large possible way.
- It may not be the most useful marker of the company’s earnings, where companies may want to see a regular track of the growth of dividends and measures of dividend growth.
- It is most favorable for blue-chip stock companies as opposed to startups and those with inconsistent dividend growths and dividend distribution.
- While it may offer an overall picture of the state of the dividends that a company disburses, it may not offer the entire picture or the true story.
- It heavily relies and rests on assumptions, thus making it not a foolproof method to make and rest investment decisions.

**Advantages of the DDM:**

- The DDM is a model that is theoretically and mathematically sound model that eliminates ambiguity and guesswork that is common with deducing stock prices and rates of dividend, which is the most important part of influencing the stock price.
- DDM, while applies to companies paying dividends, can also be determined for companies that do not pay dividends (or profits to their shareholders) by determining how much they could pay.

## Context and Application:

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for:

- Bachelor of Business Administration
- Bachelor of Commerce
- Master of Business Administration
- Master of Commerce
- Chartered Financial Analyst

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