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Cash return on equity (CROE) is a financial metric that measures how efficiently a company generates cash flow from its shareholders' equity. It is specifically calculated by dividing the cash flows from operations (CFO) by the average shareholders' equity over a certain period.

This calculation provides insights into the cash-generating ability of a company relative to the equity invested by shareholders, thereby reflecting the effectiveness of management in utilizing equity capital. A higher ratio indicates more effective use of equity to generate cash flow.

The alternative calculations provided do not accurately assess the performance in relation to equity: one option includes total equity rather than average, which does not account for fluctuations in equity during the period; another involves the debt to equity ratio, which is unrelated to cash generation; and the last option includes average assets, which focuses on asset efficiency instead of equity efficiency. Thus, the correct approach for cash return on equity is to relate CFO directly to average shareholders' equity.