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The Gordon Growth Model, often synonymous with the Dividend Discount Model, is a straightforward method used to determine the intrinsic value of a stock that pays dividends. It assumes that dividends will increase at a constant growth rate endlessly, which makes it particularly useful for companies with stable dividend growth patterns. The formula for the Gordon Growth Model is:

• \[ P_0 = \frac{D_1}{r - g} \]

where:

• \(P_0\) = Current stock price
• \(D_1\) = Dividend for the next year
• \(r\) = Required rate of return
• \(g\) = Growth rate of the dividend

This model is particularly useful for valuing mature companies with predictable dividend growth. It's important to note that for the model to work effectively, the required rate of return must be greater than the growth rate (\(r > g\)). Otherwise, the formula would not be applicable.

The required rate of return is the minimum percentage return an investor expects to receive on an investment. This rate compensates for the risk undertaken and is critical in valuing stocks using the Gordon Growth Model. To derive this rate for a stock, you can rearrange the Gordon Growth Model formula as shown below:

• \[ r = \frac{D_1}{P_0} + g \]

In the practical example given, the solution involved back-calculating the required rate of return by inputting known values into the Gordon Growth Model. By knowing the current stock price \(P_0\), the expected dividend \(D_1\), and the dividend growth rate \(g\), you rearrange to find:

• \( r = 0.155 \text{ or } 15.5\% \)

Understanding this rate helps investors decide if the stock return aligns with their investment objectives.

Stock price calculation, via the Gordon Growth Model, involves estimating the future price of a stock based on expected dividends and growth rates. The process hinges on the assumption that dividends will grow at a consistent rate. To calculate the expected stock price one year from now, the formula used is:

• \[ P_1 = \frac{D_1}{r - g} \]

Here, you use the dividend for the next year \(D_1\), and subtract the growth rate \(g\) from the required rate of return \(r\). The example provided shows that:

• Given \(D_1 = 1.10\), \(r = 0.155\), and \(g = 0.10\), the stock price calculated is \(P_1 = 20\).

This calculation illustrates that, despite changes in dividends, the price expectations might stabilize when growth and interest rates remain constant. By evaluating expected prices, investors can make informed decisions about holding or selling stocks.