The comparison between the  annual ROCE (Return On Capital Employed) and the IRR (Internal Rate of Return) of a project reveals fundamental discrepancies, both conceptual and mathematical.

Here are the key points to understand their relationship:

1. A difference in nature and temporality

• The IRR is a multi-year, actuarial indicator. It measures the intrinsic profitability of the project over its entire life cycle by taking into account the time value of money (discounting). This is the rate that cancels out the Net Present Value (NPV).
• The ROCE is an annual and accounting indicator. It measures the profitability of a given period by dividing the operating profit (EBIT) by the capital employed (net fixed assets + WCR).

2. The average ROCE is structurally higher than the IRR

It is formally established that the average ROCE is not equal to the IRR. Worse still, the arithmetic mean ROCE is significantly higher than the project’s IRR.

• The mathematical gap: For a long project (e.g. 25 years) with an IRR of 20%, the average ROCE calculated can be around 60%.
• The effect of duration: The divergence between the average ROCE and the IRR increases with the duration of the project. The longer the project, the farther the average ROCE is (upwards) from the IRR. Even for a shorter duration (10 years), the average ROCE remains significantly higher (e.g. 18% average ROCE for 10% IRR).

3. The mechanical cause: Damping

This divergence can be explained by the accounting mechanism. In a conventional project, the capital employed (the denominator of ROCE) decreases year after year thanks to depreciation, while the operating result (the numerator) can remain stable or decline more slowly.

• As a result, ROCE tends to increase mechanically over time, reaching very high levels at the end of the project’s life (e.g. from 35% in year 1 to 88% in year 5).
• The IRR, on the other hand, smooths out this profitability over the entire period via discounting.

4. The Performance Trap: Value Destruction

Confusion between these two rates can lead to serious management errors.

• The danger rule: If a company sets itself the goal of achieving an average ROCE equal to its Weighted Average Cost of Capital (WACC), it will destroy value.
• Demonstration: Converging the average ROCE to the WACC mathematically leads to generating an IRR lower than the WACC. However, if IRR < WACC, the NPV is negative and the project destroys value.

In summary, although the ROCE and the IRR are based on the same principle (ratio between what the farm brings in and what has been invested), they do not give the same figures. The ROCE gives an annual accounting vision that is often optimistic (especially at the end of the project), while the IRR gives the updated economic truth over the total duration.