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The Gordon Growth Model, also known as the Dividend Discount Model, is a method used in finance to determine the value of a stock by analyzing the expected dividends in perpetuity, while taking into account a constant growth rate of these dividends. This model assumes the company will continue to pay and increase dividends at a steady rate indefinitely.

The formula is expressed as: \[ P_0 = \frac{D_1}{r - g} \[ where:\( P_0 \) is the current stock price, \( D_1 \) is the expected dividend in the next period, \( r \) is the required rate of return (cost of equity), and \( g \) is the constant dividend growth rate.
Investors find this model attractive for stable and mature companies that have a history of dividend payments. However, if the growth rate exceeds the cost of equity, the model doesn't make sense as it will give a negative stock price, which is practically impossible. Likewise, the model doesn't apply well to non-dividend paying companies or those with erratic dividend growth patterns.

The cost of equity represents the compensation the market demands in exchange for owning the asset and bearing the risk of ownership. In other words, it's the return that investors expect to earn from their investment in the firm's equity. When we talk about the cost of equity, it's all about the opportunity cost of the investors: the return they could have earned by investing in an alternative venture with similar risk.

The cost of equity can be estimated using models like the Capital Asset Pricing Model (CAPM), which accounts for the risk-free rate, the stock's beta, and the market risk premium. It plays a crucial role in the Gordon Growth Model as it is used to determine the proper discount rate for dividend payments. Having a precise estimate of the cost of equity is vital for making informed investment and financial decisions, as it impacts company valuation and capital budgeting.

The dividend growth rate is the annualized percentage rate of growth of a company's dividend payments. It is an important metric because consistent dividend growth can be a signal of a company's financial health and stability. Investors rely on the dividend growth rate to estimate future dividends for the purposes of stock valuation, particularly in models like the Gordon Growth Model.

Calculating the growth rate can be done by looking at historical dividends and observing the pattern of growth over the years. However, many companies aim to maintain a certain target payout ratio, which can also inform estimates of future dividend growth. It can be a challenge to estimate the growth rate for companies with unpredictable earnings or those in rapidly changing industries. It is important to use a reasonable and sustainable dividend growth rate in the valuation models to avoid unrealistic and overly optimistic stock valuations.