The EdgarStat Blog explores issues in transfer pricing and application of the transactional net margin method (TNMM or CPM in the US) and other enterprise profit-based methods. Blog writings reflect the position of the authors and are not the opinion of EdgarStat.
1. Two objects, one name A reader noted that ratio is among the oldest constructions in mathematics, and takes my article to argue that ratios are invalid or biased. My article makes no such claim. My issue focus on the…
Abstract Let for and let denote the ratio indicator. We show that the arithmetic mean of overstates the slope by exactly , where is the harmonic mean of ; that the -th quantile of overstates by exactly , where is…
Adjusted taxable income (ATI) is an IRC §163(j) calculation on the federal corporate return that is filer-specific and not reported in public filings. The equation below, derived using Compustat data fields, is the closest approximation to ATI. The sections that…
Thin capitalization rules ask a single question in two different ways. The older way looks at the balance sheet and asks whether the borrower carries more debt than its equity supports. The newer way looks at the income statement and…
“A trillion here, a trillion there, pretty soon you’re talking real money.” — with apologies to Everett Dirksen On August 17, the Wall Street Journal reported that nine large technology companies have accumulated roughly $3 trillion in off-balance-sheet commitments, most…
For applied transfer-pricing work, I prefer the conventional econometric formulation because every step is visible, reproducible, and open to challenge. Regulatory support for using regression analysis is found in Section 1.482-1(e)(2)(iii)(B), which says that reliability may be increased through application…
Introduction A prior post on this blog recommended HC3 standard errors for the reduced-form markup equation estimated on transfer pricing benchmark sets. It stated the estimator and left two questions unanswered, both of the kind that surface under examination rather…
Introduction Another post traced the ownership of transfer pricing data from Disclosure, Inc. in Bethesda through Primark and Thomson to Ryan in Dallas. That was a history of corporations. This one is a history of a practice, and it is…
A transfer pricing comparables set is small. Thirty independent companies is a generous count; eight to fifteen comparables are common. Each contributes three fiscal years, so the pooled regression runs on fewer than 45 annual observations and often on fewer…
Ordinary least squares (OLS) produce two things: an estimate of the intercept and slope coefficients, and an estimate of their uncertainties. The coefficient estimates are sound, based on matrix algebra inversion. The standard errors rest on an assumption that is…
1. Reliable PLI The interquartile range is not an estimator. A benchmark set of n comparables produces a distribution of ratios : operating margin, markup, return on assets. If the underlying relation is , then and the ratio carries a…
1. The Apparent Contradiction Two positions I have defended appear, at first sight, to pull in opposite directions. First: corporate profits and asset bases are understated because research and development (XRD), advertising (XAD), and software development outlays are expensed as…
1. The System in Three Equations Start from the GDP expenditure identity, collect autonomous expenditure as and decompose it into its mean and its fluctuation, . Close the identity with two behavioral equations, both linear in lagged income: consumption with…
Introduction This article shows that the reported profit level indicator OMAD used in transfer pricing is always lower when intangible-producing expenses such as R&D are expensed rather than capitalized and the firm is growing over time while adopting a constant…
Introduction This article shows that reported profit level indicators (PLIs) used in transfer pricing are distorted when intangible-producing expenses such as R&D are expensed rather than capitalized. For margin-based PLIs the distortion falls on the numerator alone; for asset-based PLIs…
1. The Complaint A commentator objected that stating unit price is proportional — or log-proportional — to unit labor cost (ULC) confuses correlation with causation. The objection deserves a serious answer, because the aphorism it invokes is usually deployed as…
1. The Apparent Contradiction Two positions I have defended appear, at first sight, to pull in opposite directions. First: corporate profits and asset bases are understated because research and development (XRD), advertising (XAD), and software development outlays are expensed as…
1. Two Ratios, One Regime Change Plot two ratios from FRED over 1950-2025. The first is private nonresidential equipment investment as a share of GDP: it has oscillated within a narrow band, roughly 5 to 7 percent, for four decades,…
Discussions of crude oil’s forward curve start the same way — plot , call it contango or backwardation. Contango is , and backwardation is the reverse . This ratio construction is a mistake, and it is the same PLI (profit…
Separate-entity state tax base exposure to international transfer pricing if federal enforcement priorities shift from § 482 to attribution, and why many states already possess the statutory authority to respond without new legislation. “Plurality must never be posited without necessity.”…
Purpose This note derives the combined profit split method when each member of a controlled group has its own profit-per-payroll coefficient. The purpose is to show that variable entity-level coefficients do not defeat a simple payroll-based profit split. They collapse…
1. Introduction The combined profit split method requires an allocation key, and the choice of key determines the reliability of the entire exercise. We propose relative payroll as the allocation key for splitting the combined operating profits of controlled enterprises…
1. Introduction In transfer-pricing analysis and corporate-profit studies, the objective of regression analysis is estimating a meaningful slope coefficient rather than predicting the dependent variable. This distinction has implications for how rival operating profit specifications are selected and evaluated. A…
A controlled party’s reported operating profit is the residual of the intercompany prices under audit examination. Where transfer prices have been set to move income across borders, the reported operating profits are distorted. I’ve developed an internal benchmark for each…
Introduction In certain cases, the data generation process for operating profit (Y) given Net Sales (X) for a company is given by the following equation: This could be the case, for example, when the data is rightly skewed. In this…
1. Introduction A Form 8-K is the filing companies use when an event does not fit the timetable of the next scheduled report. A 10-Q or 10-K follows a reporting cycle. An 8-K follows a trigger. The trigger can be…
Two regressions are implicit in transfer pricing benchmarking: the linear regression of operating profits on revenue, and the double-log regression of the same two variables. Each produces a slope coefficient. The two coefficients have different meanings, different units, and answer…
Ednaldo Silva’s blog post “Measurements and Uncertainties in Transfer Pricing” shows that uncertainty propagates through mathematical operations. This principle is directly relevant for econometric models in which variables are transformed, differenced, and estimated over time. Starting from error propagation, we…
The contrived linear function , with the zero intercept specified in the U.S. and OECD transfer pricing guidelines, is a special case of a much more general structural form: the power function, Two questions arise the moment one fits (1)…
The term prewhitening sounds arcane and likely worse. The word belongs to a long-standing optical metaphor in spectral analysis that predates its econometric usage. This note sets out the etymology, the formal statistical content, and the specific procedure introduced by…
1. Preliminaries The geometric distributed-lag specification for revenue is with Rt revenue, Xt advertising expense, α the intercept (base revenue), γ the impact multiplier, λ the carryover rate, and ut a stochastic disturbance. Two assumptions deserve naming before any algebra.…
Based on Ednaldo Silva’s LinkedIn post “Debt-Driven GDP Growth”, we examine the relationship between government debt and GDP growth. The analysis starts from a simple GDP identity, derives a structural equation for government spending, and transforms it into an empirical…
Inventory markdown disclosure in U.S. public filings runs on two regulatory tracks. GAAP under ASC 330 sets a narrow trigger that applies only to a defined subset of markdown activity. The SEC overlay under Regulation S-K is where the substantive…
1. Introduction Transfer pricing benchmarking under the TNMM (or CPM in the U.S.) depends on a credible comparables set. The standard workflow is familiar: screen a database by SIC code or industry keyword, apply financial filters, and document why each…
Autoregression with Exogenous Variable (ARX) is a time-series regression model that extends OLS by including a lagged value of the dependent variable as an additional regressor. This captures persistence in the dependent variable over time – the tendency of firms’…
1. The Geometric Distributed-Lag Model Like research and development, advertising is a risk-taking investment. The economic rationale is straightforward: a campaign launched in period t builds brand awareness and consumer loyalty that generate revenue and operating profit in the current…
This post builds on my previous one, “Impairment and Amortization: Where Transfer Pricing Analysis Meets GAAP Income Statement Classification,” assuming the Comparable Profits Method (CPM) is chosen under 1.482-1(c) and focusing on building the comparable set. The purpose of this…
Ordinary Least Squares (OLS) assumes the variance of the error term is constant across all observations. In practice, financial data rarely behaves this way. Larger firms, higher-revenue years, or certain industries tend to produce more dispersed residuals than others. When this heteroskedasticity…
1. Introduction Transfer pricing analysis for intangible-intensive corporations requires structural econometric models, not ratio-based profit level indicators (PLIs). The standard operating margin and the Berry ratio are quotients of accounting aggregates. When the underlying structural relationship has a nonzero intercept…
1. Componentes principais As regras de preços de transferência no Brasil que entraram em vigor em 2023 exigem uma mudança de paradigma para os contribuintes. O sistema anterior calcado em margens pré-determinadas na lei para a demonstração de adequação ao…
Laying the Groundwork This post assumes the Comparable Profits Method (CPM) is the best method under 1.482-1(c), with operating margin after depreciation (OMAD) as the profit indicator (PLI). The key question addressed in this post is whether the operating income…
Swanson-Baumol Prior Theoretical Work The Swanson-Baumol 2005 work is a seminal paper in antitrust and patent law. Swanson and Baumol argue that once a technology is adopted into a standard, the patent holder gains immense market power. This is not…
Compared with the Additive and Multiplicative Rivals
The Harmonic Mean Bias in Ratio-Based Profit Level Indicators
Why Induced Heteroscedasticity Compounds the Intercept Bias
This article shows that ratio-based profit level indicators (PLIs)—including return on assets (ROA), Berry ratio, and operating margin—are biased estimators of the structural profit rate when the underlying relationship between...
Abstract The perpetual inventory method (PIM) for estimating capital stock (PPENT) is attributed to Raymond Goldsmith (1951). Goldsmith provided conceptual descriptions without explicit algebraic derivations—a ceremonial citation. However, the extended PIM formula with geometrically declining weights is the standard solution…
1. Introduction Transfer pricing practice relies on ratio analysis. Operating profit divided by revenue, operating profit divided by total cost, operating profit divided by operating assets—these profit level indicators (PLIs) are ratios of the form m(i) = Y(i) / X(i).…
Introduction Extending algebraic developments from Ednaldo Silva, I formalize a truncation of the perpetual‑inventory method (PIM) equation with explicit and tractable error bounds. This treatment of finite‑sample PIM truncation does not appear in standard asset‑valuation cookbooks. Framework Consider the case…
A complete statistical procedure for transfer pricing practitioners. Transfer pricing practice usually determines the arm’s length range using the interquartile range of the chosen profit indicator, defined as a ratio m(i) = Y(i)/X(i) across comparable companies.
Return on Assets and the Harmonic Mean
On May 23, 2017, the OECD released a draft of Action 8 of the Base Erosion and Profit Shifting (BEPS) plan, providing taxpayers and tax administrations with a new transfer pricing approach to measure hard-to-value-intangibles (HTVI):
Transfer pricing industry practice traditionally employs descriptive ratio analysis under 26 CFR 1.482-5(b)(4)(ii) within the Comparable Profits Method (CPM) to determine an arm’s length range.
In this part of the article, I follow closely the exposition of the valuation formulas in the Financial Theory and Corporate Policy textbook by Copeland, Weston and Shastri.
Interest stripping is a tax technique where a company uses high-interest, intercompany debt to shift profits from high-tax jurisdictions to low-tax jurisdictions, by creating significant deductible expenses for the borrowing entity of the MNE.
From Equation Counting to Class Conflict: A Mathematical Reading of Political Economy
Introduction When applying the Comparable Profits Methods (CPM), Return on Assets (ROA) is often used as a Profit Level Indicator (PLI) to establish, in principle, the arm’s length price for a related party transaction. In general, this PLI is given…
Analysts often work with ratios. Whether examining price-to-earnings ratios in finance or profit indicators in transfer pricing, the ratio m(i) = Y(i) / X(i) is often reported. However, this simple ratio masks a systematic bias that affects quartile estimates and other location parameters.
Controlling producer price inflation (PPI) doesn’t require austerity.
Using a less reliable (higher variance) adjusted profit indicator violates the scientific principle of minimizing measurement error. Avoiding error propagation is essential for producing credible and reproducible estimates.
This analysis formalizes the argument presented in Ednaldo Silva's post "U.S. Surplus Growth is Debt-Fueled: Investment Stagnation is the Core Malaise."
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.
The profit rate identity can be estimated as a dynamic framework using an autoregressive distributed lag (ARDL) model.
Some basic rules of differential calculus are useful for understanding economic discourse, such as discussions in business or financial media about U.S. economic performance.
A September 19, 2024 ruling by the Portuguese Administrative Arbitration Center upheld the cost-plus approach used by the taxpayer even though the Portuguese tax authorities objected to the exclusion of employee bonus compensation from the cost base. The cost base included certain pass-through costs, which led to the reported markup for 2019 being less than 4.1%.
This blog presents a basic analytical framework for understanding the relationship between GDP growth and public debt commitments. The Harrod-Domar principle, which posits that increased gross private domestic fixed non-residential investment drives GDP growth, does not apply to the recent GDP growth of many countries.
The Swiss Federal Court ruled in favor of the tax authorities on July 17, 2024 in a litigation that frames a Swiss debate over the role of the annual circular on safe harbor interest rates issued by the Swiss Federal Tax Administration.
A December 15, 2023 ruling by the North Holland District Court involved the transfer of certain distribution rights from British American Tobacco Exports B.V. to British American Tobacco UK Limited. The ruling decided that the value of certain transferred “residual profits” was almost £1.7 billion, which was based on a very elementary application of DCF.
The IRS has recently asserted implicit support in several situations where a foreign based affiliate extended an intercompany loan to a US borrowing affiliate. In this piece, we'll discuss an intercompany loan involving Perrigo, and compare the IRS settlement to the litigation involving GE Capital Canada before we turn to another potential IRS issue.
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.
Quartiles are the most elementary form of univariate (single variable) data summary, because no statistical technique beyond sorting and slicing (tagging) of the data is employed. Distributions of profit indicators have long tails, suggesting that the Median is a good measure for only 50% of the dataset.
Determining arm's length remuneration for a Czech manufacturing affiliate under different transfer pricing models.
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).
Panama’s Administrative Tax Court ruled in favor of the tax authority Dirección General de Ingresos (DGI) in a January 19, 2023 decision involving remuneration for a related-party wholesale distributor of electronics determined using Transactional Net Margin Method (TMMM; CPM in the US). In earlier discussions, we noted how DGI benchmarked the return for a limited-function wholesale distributor of petroleum and the return for a high-function distributor of pharmaceuticals.
This litigation raised an oft-seen issue as to the correct definition of “sales” for transfer pricing approaches that rely on the Comparable Uncontrolled Transaction (Price) method.
On February 20, 2023 Ampol Limited settled its procurement hub transfer pricing dispute with the Australian Tax Office (ATO). Procurement affiliates have been a point of emphasis for the ATO in recent years, and have been gaining the attention of other tax authorities, including the US IRS.
A 2008 restructuring transferred the European rights to the McDonald’s intangibles to McD Europe Franchising Sàrl, a Luxembourg-resident subsidiary with branches in both Switzerland and the U.S. While this migration of intangible assets created substantial controversy in Europe, the real transfer pricing concern would be an IRS issue and not an issue for the French Tax Authority (FTA) if the royalty rate remained at 5%.
EdgarStat® contains an internal regression model to calculate the beta-risk coefficient of an individual enterprise stock price return compared to the return of the S&P 500 stock price (market) index. This stock price return regression model is known as CAPM.
The tax authorities in China and in South Korea have issued different safe harbors with respect to the interest rates on intercompany loans. Safe harbor rates are often in conflict with what would represent an arm’s length rate. Our discussion poses a hypothetical intercompany loan from a South Korean parent corporation to its Chinese manufacturing affiliate to highlight how the arm’s length interest rate depends on the contractual terms of the loans including date, term, and currency and the credit rating of the borrowing affiliate.
The Israel Tax Authority prevailed in Israel vs CA Software Israel Ltd (October 2022, Tel Aviv District Court, Case No 61226-06-17), which involved the valuation of transferred software. While the taxpayer’s experts tried to justify the lower valuation arguing that the economic useful life of the transferred intangibles was very short.
There are several approaches to accounting for ongoing marketing expenses necessary to maintain a brand in a discounted cash flow valuation.
The Dutch tax authority prevailed in its challenge of several British American Tobacco intercompany financing transactions.
Transfer pricing practitioners in the US as well as in other nations often face the dilemma that clients wish to establish intercompany management fees as a percentage of revenues while tax authorities may test the implied cost plus from any intercompany management policy.
Licensees bear significant commercial risk when they use valuable intangible assets owned by another entity. As such, any method that affords them with an expected return to its tangible assets that is only as high as the overall enterprise’s cost of capital is inconsistent with sound economics.
Harold McClure expounds on the issue of currency denomination in intercompany financing, addressing currency adjustments in longer-term fixed interest rates, past controversies, and regulatory guidance.
This discussion presents a simplified illustration of the issues with respect to the unspecified method applied in Medtronic III in contrast to the IRS' extreme CPM approach and a traditional RPSM approach based on sound financial economics.
Italy’s Supreme Court remanded May 17, 2022 a case in which Regional Tax Commission of Lombardy challenged the transfer pricing between Promgas Spa and Gazprom Export, finding alleged deficiency in the tax authority’s application of the Transactional Net Margin Method (TNMM).
In this tutorial, we address comparability adjustments for differences in the currency of the tested loan to that of the comparable transactions.
A discussion of the possible issues in the recently settled transfer pricing dispute between Western Digital Corp. and the United States IRS.
Use of the CPM/TNMM to determine royalty rates for valuable intangibles in transfer pricing is incompatible with basic financial economics.
One of the most challenging transfer pricing issues regarding financial transactions is making a comparability adjustment for differences in country risk between the tested non-US borrower’s country and the comparable US borrower's country in pricing the intercompany loan interest rate.
Regression analysis yields more reliable profit indicators than the linear equation without intercept specified in US and OECD transfer pricing guidelines.
There are often legitimate concerns with using book value versus market value of assets in applying a Return on Assets approach in transfer pricing. While employing a Return on Costs approach may be a reliable alternative, it must also account for comparability differences in asset intensity.
In this tutorial we introduce you to a tool in the EdgarStat CUFT Loan Agreements Database for estimating the implied credit rating of your tested borrower using the Altman Z”-Score Model.
To determine whether the usual financial ratios provide insights into what would represent an arm's length range, any analysis of controlled healthcare distributors must account for the underlying facts surrounding the functions and expenses occurred by the distribution affiliate.
Intercompany financing is a growing area of focus in transfer pricing. CUFT Analytics co-founder and managing director John Hollas provides guidance on using the EdgarStat CUFT Loan Agreements Database to benchmark an arm's length range of interest rates.
Interests fluctuate based on market conditions, and analysts must consider whether the market conditions surrounding their data are comparable to those of the tested intercompany transaction when benchmarking an arm's length interest rate in transfer pricing.