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The dividend yield is a vital metric for stock investors as it represents the portion of a company's annual earnings paid out to shareholders in dividends. It is expressed as a percentage of the stock's current market price. To calculate the dividend yield, you divide the annual dividend per share by the stock's price per share. It is defined mathematically as:\[\text{Dividend Yield} = \frac{D_1}{P_0}\]Where:

• \(D_1\) is the annual dividend per share next year.
• \(P_0\) is the current stock price.

The dividend yield helps investors understand how much return they are getting in dividends alone, without considering any stock price appreciation or depreciation. A higher dividend yield can be attractive for income-focused investors, but it's crucial to assess other aspects of a company's stability and growth potential too. Notably, in the exercise scenario, the dividend yield of 4.7% informs part of the process in determining the stock's overall expected return.

The Gordon Growth Model, also known as the Dividend Discount Model, is a popular method used to value a stock by assuming dividends will continue to increase at a constant growth rate. It is particularly useful for companies with a stable dividend growth pattern.The core formula of the Gordon Growth Model is:\[P_0 = \frac{D_1}{r - g}\]Where:

• \(P_0\) is the current stock price.
• \(D_1\) is the expected dividend next year.
• \(r\) is the required rate of return.
• \(g\) is the dividend growth rate.

Using this formula, investors can solve for the stock's intrinsic value or, as in our original exercise, use it to find the stock’s required rate of return when given a constant dividend growth rate and dividend yield. In this particular equation setup, by rearranging terms, one can solve directly for \(r\), which helps in evaluating the potential profitability of investing in the stock.

The required rate of return is the minimum annual percentage return an investor expects to earn by investing in a stock. This rate is critical because it reflects the level of risk an investor is willing to take for a particular investment.When determining the required rate of return using the Gordon Growth Model, the formula can be adjusted to:\[r = \text{Dividend Yield} + g\]In this setup:

• The dividend yield represents the annual dividend expressed as a percentage of the stock price.
• The growth rate \(g\) represents the expected increase in dividends per year.

In the original exercise, after calculating using wrong inputs, an error led to a finding of a negative required rate of return, which is practically unusual and could indicate potential miscalculations or assumptions. Correct application involves adding the dividend yield and growth rate rather than subtracting. Understanding how this rate fits into broader stock valuation aids investors in comparing expected returns against other market alternatives, ensuring they meet personal financial goals.