Understanding the Dividend Growth Rate Calculation

This problem requires us to determine the implied dividend growth rate for a company's stock, given its current market price, the most recent dividend paid, and the required rate of return (capitalization rate). This type of problem is typically solved using the Gordon Growth Model, a fundamental concept in equity valuation.

Applying the Gordon Growth Model

The Gordon Growth Model (also known as the Dividend Discount Model with Constant Growth) provides a way to value a stock based on the assumption that dividends are expected to grow at a constant rate indefinitely. The model's formula links the stock's current price to its expected future dividends, the required rate of return, and the dividend growth rate.

The formula is expressed as:

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

Where:

• \(P_0\) represents the current market price of the stock.
• \(D_1\) is the expected dividend per share at the end of the next period (usually one year from now).
• \(K_e\) is the required rate of return, often referred to as the capitalization rate or cost of equity.
• \(g\) is the constant annual dividend growth rate.

Since we are usually given the most recent dividend paid (\(D_0\)), we relate \(D_1\) to \(D_0\) using the growth rate \(g\):

\(D_1 = D_0 (1 + g)\)

Identifying the Given Information

Based on the question, we have the following values:

• Current Share Price (\(P_0\)) = Rs. 60
• Current Dividend Per Share (\(D_0\)) = Rs. 4
• Capitalization Rate (\(K_e\)) = 12% or 0.12

We need to calculate the Dividend Growth Rate (\(g\)).

Step-by-Step Calculation to Find Dividend Growth Rate

We substitute the expression for \(D_1\) into the Gordon Growth Model formula:

\(P_0 = \frac{D_0(1 + g)}{K_e - g}\)

Now, plug in the given values:

\(60 = \frac{4(1 + g)}{0.12 - g}\)

To solve for \(g\), we first multiply both sides of the equation by \((0.12 - g)\):

\(60 \times (0.12 - g) = 4(1 + g)\)

Distribute the terms on both sides:

\(60 \times 0.12 - 60g = 4 \times 1 + 4 \times g\)

\(7.2 - 60g = 4 + 4g\)

Now, rearrange the equation to isolate the terms involving \(g\). Move the \( -60g \) term to the right side and the \( 4 \) term to the left side:

\(7.2 - 4 = 4g + 60g\)

Combine the terms on both sides:

\(3.2 = 64g\)

Finally, solve for \(g\) by dividing both sides by 64:

\(g = \frac{3.2}{64}\)

\(g = 0.05\)

To express the dividend growth rate as a percentage, multiply the decimal by 100:

\(g = 0.05 \times 100\%\)

\(g = 5\%\)

The calculated dividend growth rate is 5%.

Calculation Result Summary

Based on the provided inputs and using the Gordon Growth Model, the implied dividend growth rate is 5%.

Revision Table: Essential Finance Formulas

Here are some related finance formulas often used in stock valuation and required rate of return calculations:

Additional Information: Insights on Dividend Growth Rate and Valuation

The dividend growth rate is a key driver of stock value according to dividend discount models. A higher expected growth rate, assuming other factors remain constant, generally leads to a higher stock price. However, the Gordon Growth Model has limitations, primarily its assumption of a constant growth rate forever and the requirement that the growth rate must be less than the required rate of return.

In practice, companies rarely achieve perfectly constant dividend growth. More complex multi-stage dividend discount models exist to handle varying growth rates over different periods. Despite its simplicity, the Gordon Growth Model is valuable for understanding the fundamental relationship between dividends, growth, required return, and stock value, and for quickly estimating values or implied growth rates as shown in this problem.