Which equation calculates the sustainable growth rate?

The sustainable growth rate (g) is a measure of how quickly a company can grow its sales, earnings, and dividends while maintaining its current capital structure and without needing additional external financing. The correct equation that calculates the sustainable growth rate is derived from the relationship between the return on equity (ROE), the retention ratio (b), which is the proportion of earnings retained in the business rather than paid out as dividends, and the overall growth rate of the company.

The formula expressed as g = ROE * b reflects that the growth rate is a product of how efficiently a company generates profit (ROE) and how much of that profit it reinvests back into the business (b). This approach shows that a higher ROE or a higher retention ratio will lead to a higher sustainable growth rate. Thus, by multiplying these two factors, the equation provides a clear method for determining the company's growth potential.

In contrast, other options do not appropriately relate both profitability and the reinvestment of earnings to sustainable growth. For example, the equation in option C (g = NI - Dividends) does not factor in how retained earnings contribute to growth since it only considers net income and dividends. Similarly, options involving COGS and inventory are related