# Dividend Discount Model

Dividend Discount Model (DDM) is a technique used to estimate the market value of a company’s shares by discounting the projected dividends of the company at the rate of return required by investors. The model is based on the assertion that the stocks are worth the same as the value of all the future dividends expected.

It uses the concept of time value of money and present values the future dividends. It assumes that same amount of dividend is paid annually, and the most recent dividend payment has just been made. In this scenario the dividend payments resemble those of a perpetuity paying an equal sum for indefinite time periods.

## Formulas

If dividends are not expected to grow over the years, the value of a share is calculated as follows:

$$\text{Value}=\frac{\text{d}}{\text{r} _ \text{e}}$$

Where,

• d is the expected dividend for the year.
• re is the rate of return required by investors. It is the same as cost of equity.

If the dividends are expected to grow. The model also incorporate the expected growth rate in the calculation:

$$\text{Value}=\frac{\text{d}(\text{1}+\text{g})}{\text{r} _ \text{e}-\text{g}}$$

Where,

• d and re are same as above
• g is the annul expected growth in dividends

The growth rate may be calculated either using Gordon Growth Model or as a geometric mean growth of past dividends or other suitable method.

DDM formulas may either use dividend per share to arrive at the value of a single share. The total value of a company’s shares is the product of number of shares outstanding and value per share. Alternatively, DDM may take the total dividends of all shares as input. In that case, the the value obtained is the value of all shares.

## Example

A company has just paid a dividend per share of \$5. The rate of return required by the investors is 12%. Calculate the value of a share if the:

1. expected growth rate is zero
2. dividend is expected to grow as 5% annually

Solution

Expected growth rate is zero:

$$\text{Value}=\frac{\text{\5}}{\text{12%}}\approx \text{\41.7}$$

Dividend is expected to grow as 5% annually:

$$\text{Value}=\frac{\text{\5}\times(\text{1}+\text{5%})}{\text{12%}-\text{5%}}=\text{\75}$$