# How to Calculate the Value of a Stock Using Dividend Discount Model (DDM)

## How can we calculate the value of a stock using the Dividend Discount Model (DDM)?

Let's break down the steps involved in calculating the value of a stock using the Dividend Discount Model (DDM).

## Calculating the Value of a Stock using DDM

In order to calculate the value of a stock using the Dividend Discount Model (DDM), we need to follow a series of steps:

The dividend of a stock just paid was $2.08. It is expected to grow at 24.89% for the next five years and then at 4.27% thereafter. The required return on the stock is 11.62%. To determine the value of the stock, we will use the Dividend Discount Model (DDM) which focuses on calculating the present value of all future expected dividends.

## Step 1: Calculate the Expected Dividend for the Next Five Years

- The current dividend is $2.08.

- The dividend is expected to grow at a rate of 24.89% for five years.

- To calculate the expected dividend for each year, we multiply the previous year's dividend by (1 + growth rate).

Year 1: $2.08 * (1 + 0.2489) = $2.59

Year 2: $2.59 * (1 + 0.2489) = $3.23

Year 3: $3.23 * (1 + 0.2489) = $4.03

Year 4: $4.03 * (1 + 0.2489) = $5.03

Year 5: $5.03 * (1 + 0.2489) = $6.27

## Step 2: Calculate the Present Value of the Expected Dividends

- We discount each future dividend by dividing it by (1 + required return) raised to the power of the number of years in the future.

- The required return on the stock is 11.62% or 0.1162.

Present Value of Year 1 dividend: $2.59 / (1 + 0.1162) = $2.32

Present Value of Year 2 dividend: $3.23 / (1 + 0.1162)^2 = $2.68

Present Value of Year 3 dividend: $4.03 / (1 + 0.1162)^3 = $2.67

Present Value of Year 4 dividend: $5.03 / (1 + 0.1162)^4 = $3.18

Present Value of Year 5 dividend: $6.27 / (1 + 0.1162)^5 = $3.85

## Step 3: Calculate the Present Value of All Future Dividends

- Add up the present values of all expected dividends.

Present Value of all future dividends = $2.32 + $2.68 + $2.67 + $3.18 + $3.85 = $14.70

## Step 4: Calculate the Present Value of the Perpetual Growth

- The dividend is expected to grow at 4.27% indefinitely after year 5.

We can use the Gordon Growth Model to calculate the present value of the perpetual growth.

Perpetual Growth = Year 5 dividend * (1 + perpetual growth rate) / (required return - perpetual growth rate)

Perpetual Growth = $6.27 * (1 + 0.0427) / (0.1162 - 0.0427) = $107.08

## Step 5: Calculate the Value of the Stock

- The value of the stock is the sum of the present value of all future dividends and the present value of the perpetual growth.

Value of the stock = Present Value of all future dividends + Present Value of the perpetual growth = $14.70 + $107.08 = $121.78

Now you have learned how to calculate the value of a stock using the Dividend Discount Model (DDM). Understanding this model is crucial for making informed investment decisions in the stock market.