The fundamental difference between commercial profitability (ROS) and economic profitability (ROCE) lies in what they measure: the former evaluates the efficiency of sales (income statement), while the latter evaluates the efficiency of investments (balance sheet).

Here is a detailed explanation of their distinctions as well as the mathematical relationship between them:

1. Return on Sales (ROS)

The ROS measures the operating margin generated by the company on each currency unit sold. It is an indicator of price/cost competitiveness.

• Definition: This is the ratio between operating income (EBIT) and turnover (Revenue).
• Formula:
  $\mathrm{ROS}={\frac{\mathrm{EBIT}}{\mathrm{Revenues}}}_{}$
• Interpretation: It indicates how much the company earns for each euro of sales made, before paying its creditors (financial expenses) and the State (taxes). For example, a ROS of 12% means that for 100 of sales, the company retains 12 of operating income.

2. Economic profitability (ROCE – Return On Capital Employed)

The ROCE measures the performance of industrial investment. It indicates whether the capital raised (equity + net debt) is being used efficiently to generate profit.

• Definition: This is the ratio between operating income (EBIT) and Capital Employed (CE). Capital Employed includes net fixed assets and Working Capital Requirements (WCR).
• Formula:
  $\mathrm{ROCE}=\frac{\mathrm{EBIT}}{Capital Employed}$
• Interpretation: This is the intrinsic profitability of the economic asset. To find out if the company is creating value, this rate must be compared with the Weighted Average Cost of Capital (WACC). If ROCE after tax > WACC, the company is performing well.

3. The link between ROS and ROCE: The productivity of capital

There is a direct mathematical link between these two indicators. ROCE is the product of commercial profitability through asset turnover (Asset Turn-Over or ATO).

$\mathbf{ROCE}=\mathbf{ROS}\times \mathbf{ATO}$

That is:

$\mathrm{ROCE}=\frac{\mathrm{EBIT}}{\mathrm{Revenues}}\times \frac{\mathrm{Revenues}}{\mathrm{Capital} \mathrm{Employed}}$

This relationship is called the Dupont-de-Nemours formula, from the name of the firm whose management controller Franck D. Brown was the designer and first user. The objective was to make operational managers understand that it is necessary to generate a high commercial profitability in a capital-intensive business (telecommunications, automotive, chemicals), therefore with low capital turnover. Conversely, sectors with low capital intensity, such as retail, can achieve a significant ROCE from a modest commercial profitability, because capital turnover is high.

What this means for management: to improve its economic profitability (ROCE), a company has two levers:

1. Increase its commercial profitability (ROS): Sell at a higher price or reduce its operational costs.
2. Improve the productivity of its assets (ATO): Generate more revenue with the same amount of capital invested, or reduce capital employed (for example by reducing inventories or by outsourcing production via the “Make-or-Buy”).

4. Numerical example

The following example illustrates the difference:

• Revenue (Sales): 300
• Capital Employed (CE): 150
• Operating profit (EBIT): 36
• Calculation of the ROS: 36 / 300 = 12%. (Out of 100 sales, I earn 12).
• Calculation of the ROCE: 36 / 150 = 24% (Out of 100 invested, I earn 24).

In this example, the economic profitability (24%) is double the commercial profitability (12%) because the company generates 2 euros of revenue for each euro invested (Capital Turnover = 2).