Ednaldo Silva’s blog dated August 21, 2025, contains three sequential equations about the profit rate. My purpose is to demonstrate the connection between his logarithmic 2nd equation and the 3rd equation, referencing the ECM and ARDL econometric models. I used the same econometric reference he cited and adopted some notations of the textbook by Dimitrios Asteriou and Stephen Hall.
Microeconomics are detached from the reality of corporate profits behavior. Here, I explore the operating profits (before depreciation and amortization) of a major group of U.S. corporations (consolidated entities) that make up a large fraction of U.S. gross domestic product.
The operating profit margin (OMBD or OMAD) can be derived from the profit markup by indirect least squares (ILS). This is the most theoretically defensible and reliable operating profit indicator that can be obtained from comparable data.
U.S. 26 CFR 1.482-5(b)(4)(i-ii) claim that the “return on capital employed” (return on assets) is less sensitive to “functional differences” than the operating profit margin or the operating profit markup. This claim is based on the unrealistic premise that “capital flows” to equalize profit rates (return on assets) among companies in the same (or in different) industries by some "invisible hand."
Data suggest that “big oil” forms an oligopoly industry. Noise about oil and gas prices being determined by supply and demand is suspect.
Determining an arm’s length profit indicator (profit ratio) requires two equations, and not one equation, as prescribed in financial statement analysis textbooks. E.g., Bernstein (1993), Drake & Fabozzi (2012). An accounting critique of univariate profit ratios is found in Whittington (1986).
Regression analysis yields more reliable profit indicators than the linear equation without intercept specified in US and OECD transfer pricing guidelines.
Dr. Ednaldo Silva illustrates why asset intensity adjustments to the Return on Assets profit indicator are redundant and unviable.
Applied properly, the Comparable Profits Method (CPM) can be a useful approach for well-defined transfer pricing issues, such as the appropriate profitability of a sales affiliate. Unfortunately, CPM is often applied mechanically without regard for economic principles and functional comparability.
In February 2021, the Supreme Court of Canada declined to hear the Canadian Revenue Agency's (CRA) appeal in its case against uranium multinational Cameco Corporation. However, this only marked the end of Round 1, as the courts only ruled on 8 of 14 years under review.
Notwithstanding its acceptance in Coca Cola Co. v. Commissioner of the IRS, Return on Assets is a controversial profit indicator to use in transfer pricing. At the very least it must be subject to economic analysis to corroborate a relationship between operating profit and operating assets.
Selecting alleged comparable companies with different functions than the tested party is known to open Pandora's Box in transfer pricing controversy, and is often exacerbated by a failure to adjust for material differences between the tested party and the selected comparables.
Ad hoc adjustments are a risky endeavor in transfer pricing. Using regression analysis, we can test if asset intensity is relevant to explain the behavior of the operating profit markup or profit margin and calculate a reliable adjustment to the profit indicator.
The prevalent use of quartiles to determine profit indicators often results in a wide (unreliable range) and ad hoc assets adjustments. These problems can be solved by using regression analysis, which produces more defensible statistical ranges of the profit indicator resistant to audit scrutiny.
Comparability is a key issue in transfer pricing that is often not fully appreciated. However, comparability issues are hardly uncommon in transfer pricing controversies and can create a trickle-down effect that leads to major taxation issues.