Calculating Equity Capitalization Rate using Dividend Growth Model

The question asks us to calculate the equity capitalization rate for a company's share. We are given the current market price of the share, the expected dividend next year, and the constant rate at which this dividend is expected to grow indefinitely. This information fits the assumptions of the Dividend Growth Model, also known as the Gordon Growth Model.

Understanding the Dividend Growth Model

The Dividend Growth Model is a method used to value a stock based on the assumption that dividends will grow at a constant rate. The formula relates the stock price to the expected future dividend, the required rate of return (equity capitalization rate), and the dividend growth rate.

The basic formula is:

\( P_0 = \frac{D_1}{r - g} \)

Where:

• \(P_0\) is the current market price of the stock.
• \(D_1\) is the expected dividend per share at the end of the next period (Year 1).
• \(r\) is the required rate of return on equity (equity capitalization rate).
• \(g\) is the constant growth rate of dividends.

Applying the Formula to Find Equity Capitalization Rate

We need to find \(r\). We can rearrange the formula to solve for \(r\):

\( P_0 \times (r - g) = D_1 \)

\( r - g = \frac{D_1}{P_0} \)

\( r = \frac{D_1}{P_0} + g \)

Identifying the Given Information

From the question, we have the following values:

• Current Share Price (\(P_0\)): Rs. 50
• Expected Dividend after one year (\(D_1\)): Rs. 3
• Expected Dividend Growth Rate (\(g\)): 8% or 0.08

Performing the Calculation

Now, substitute these values into the rearranged formula for \(r\):

\( r = \frac{3}{50} + 0.08 \)

First, calculate the dividend yield part (\( \frac{D_1}{P_0} \)):

\( \frac{3}{50} = 0.06 \)

This means the initial dividend yield is 6%.

Now, add the growth rate:

\( r = 0.06 + 0.08 \)

\( r = 0.14 \)

To express this as a percentage, multiply by 100:

\( r = 0.14 \times 100\% = 14\% \)

Result

The equity capitalization rate is 14 percent.

Revision Table: Key Concepts

Additional Information on Dividend Growth Model

The Dividend Growth Model is a simple and widely used model for stock valuation and determining the cost of equity. However, it relies on several key assumptions:

• Dividends are expected to grow at a constant rate (\(g\)) indefinitely. This assumption may not hold true for many companies, especially those in early growth stages or mature/declining industries.
• The required rate of return (\(r\)) must be greater than the dividend growth rate (\(g\)). If \(r \le g\), the formula would result in a non-sensical or infinite stock price.
• The company must pay dividends. The model cannot be directly applied to companies that do not currently pay dividends.
• The growth rate (\(g\)) is stable and predictable.

Despite these limitations, the model is valuable for stable, mature companies with a history of paying steadily growing dividends. The equity capitalization rate derived from this model represents the minimum return investors require from the stock, considering the expected future dividends and their growth.