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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 figure is contaminated. I developed an internal benchmark for each party’s…

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…

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…

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.

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.