Which formula represents the internal growth rate?

The internal growth rate (IGR) is a measure of how rapidly a firm can grow its sales and earnings using only its retained earnings. To derive this rate, the return on assets (ROA) and the retention ratio (b) — which is the proportion of retained earnings from net income — are crucial.

The formula that represents the internal growth rate can be understood as follows:

• ROA reflects how efficiently a company generates earnings from its assets.

• The retention ratio (b) indicates how much of net income is reinvested into the business rather than paid out as dividends.

The internal growth rate formula combines these two components, which is why the formula you selected, ( (ROA \times b) / ((1 - ROA) \times b) ), captures the essence of how productive the retained earnings are in generating further growth.

The denominator, ( (1 - ROA) \times b ), works to balance the overall growth with the constraints imposed by asset returns and retained earnings. This formula illustrates that the internal growth rate depends directly on how profitably a company uses its resources and how much of that profit is reinvested in the firm.

Other formulas do not appropriately express this relationship between retention and return