Final answer:
The growth rate affects the expected future dividends, elevating the stock value in the dividend-discount model. The cost of equity represents investors' required returns, influencing present value - higher growth leads to higher expected returns and vice versa.
Step-by-step explanation:
The relationship between the growth rate and the cost of equity implied in the dividend-discount model is critically important. The dividend-discount model determines the present value of a stock based on the future dividends it is expected to provide, which are discounted back to their present value. When applying this model, the expected growth rate of dividends is a key factor. A higher growth rate will suggest more substantial future dividends, leading to a higher stock value when discounted at the cost of equity. Conversely, the cost of equity represents the return investors require on their investment. The higher the cost of equity, the greater the return required, thus lowering the present value of the future dividends.
Effectively, investors are willing to pay more for stocks that are expected to grow faster. However, this also increases the cost of equity, as the demand for higher returns on these potentially higher-growth investments is greater. The cost of equity could be affected by factors like market volatility, company-specific risks, and the general economic climate, which in turn influence investor expectations and the rate of expected capital gains or dividends.