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The formula for the Sustainable Growth Rate (g) is derived from the relationship between a firm's retention ratio, also known as the plowback ratio, and its return on equity (ROE).

The retention ratio represents the portion of net income that is retained in the business rather than distributed as dividends. This retained earnings are then reinvested to generate future growth. When multiplied by the return on equity, which measures the profitability and efficiency with which a company uses its equity capital, the result gives an estimate of how much a company can grow its earnings (and, subsequently, dividends) sustainably without needing to resort to external financing.

Therefore, the correct formula for the Sustainable Growth Rate is:

Sustainable Growth Rate (g) = Retention Rate * ROE

This correctly encapsulates the core concept that the ability of a company to grow at a sustainable rate is contingent upon how much profit it retains after dividends and how efficiently it can utilize that retained profit to generate returns.

The other formulas do not accurately express the relationship needed to calculate the Sustainable Growth Rate. Dividing the retention rate by ROE or adding them does not reflect their interdependent contributions to sustainable growth, nor does multiplying the retention rate by earnings per share (EPS) capture

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