The correct option for the question regarding the ratio that indicates the efficiency of a firm's sales with respect to the cost of goods sold is B. gross profit margin. Explanation of the Correct Answer Gross Profit Margin is a financial metric that shows the percentage of revenue that exceeds the cost of goods sold (COGS). It is calculated using the following formula: [ \text{Gross Profit Margin} = \left( \frac{\text{Gross Profit}}{\text{Revenue}} \right) \times 100 ] Where: - Gross Profit is calculated as: [ \text{Gross Profit} = \text{Revenue} - \text{Cost of Goods Sold} ] The gross profit margin indicates how efficiently a company is producing and selling its goods. A higher gross profit margin means that a company retains more profit from each dollar of sales after covering the direct costs associated with producing its goods. This ratio is crucial for assessing the operational efficiency of a firm in managing its production costs relative to its sales. Why the Other Options Are Incorrect A. Return on Capital Employed (ROCE): - This ratio measures a company's profitability and the efficiency with which its capital is employed. It is calculated as: [ \text{ROCE} = \left( \frac{\text{Operating Profit}}{\text{Capital Employed}} \right) \times 100 ] - While ROCE is important for understanding how well a company is using its capital, it does not specifically focus on the relationship between sales and the cost of goods sold. Therefore, it is not the best indicator for this question. C. Net Profit Margin: - This ratio measures how much of each dollar of revenue is converted into profit after all expenses (including operating expenses, interest, and taxes) have been deducted. It is calculated as: [ \text{Net Profit Margin} = \left( \frac{\text{Net Profit}}{\text{Revenue}} \right) \times 100 ] - While the net profit margin provides insight into overall profitability, it includes all expenses, not just the cost of goods sold. Thus, it does not specifically indicate efficiency in relation to COGS. D. Return on Equity (ROE): - This ratio measures the profitability of a company in relation to shareholders' equity. It is calculated as: [ \text{ROE} = \left( \frac{\text{Net Income}}{\text{Shareholders' Equity}} \right) \times 100 ] - ROE is focused on the returns generated for shareholders and does not provide information about the efficiency of sales relative to the cost of goods sold. Summary of Key Points

• Gross Profit Margin is the correct answer as it directly relates sales to the cost of goods sold.
• It measures the efficiency of production and sales operations.
• Other options (ROCE, Net Profit Margin, ROE) focus on different aspects of financial performance and do not specifically address the relationship between sales and COGS.
• Understanding these ratios helps in evaluating a company's operational efficiency and profitability.

Revision Summary

• Gross Profit Margin indicates efficiency in sales relative to COGS.
• It is calculated as (Gross Profit / Revenue) × 100.
• Other ratios like ROCE, Net Profit Margin, and ROE focus on different financial aspects.
• Knowing the purpose of each ratio is crucial for effective financial analysis.