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*L’un fece il mundo e l’altro l’ha distrutto.*

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**Topics:**Net Profit Indicator- Share

The “return on assets” is an unsatisfactory profit level indicator (PLI) for the “transactional” net margin and comparable profits methods in transfer pricing because (among other major defects) self-developed intangibles are excluded from the assets base denominator. Assets are also composed of *heterogeneous balance sheet accounts* with different depreciation rates.

Operating assets are “solid, massy, hard” and cannot be moved from one company to another within the same industry (horizontal market consolidation) or across companies in different industries (vertical market consolidation), without a time-consuming assets purchase agreement. Moreover, if the intra-company assets transfers are large, anti-trust regulatory impediments may occur.

The idea that “return on assets” is a superior PLI because of its fluent or gravitation properties is not consistent with reality. This dubious return on assets sobriquet is posited as a matter of faith because to our knowledge economics is devoid of rigorous demonstrations of the conditions required for such gravitation to occur in actual industries dominated by oligopoly groups.

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**Topics:**Net Profit Indicator- Share

We take another look that computing profit indicators using restricted data samples can lead to *unreliable measures* of arm’s length taxable income to benchmark controlled inter-group transactions. To produce reliable measures, we must change the pervasive transfer pricing practice of considering three-years of data, and consider as many individual company financial data as available.

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**Topics:**Net Profit Indicator- Share

*In ergodic theory, time and space averages become equal*. Ives Coudène, *Ergodic Theory and Dynamical Systems*, Springer, 2016.

Consider two aspects of statistical reliability principles. First, reliability can be measured by the ratio of the selected parameter *estimate* divided by its *standard error*. We want this reliability ratio to be as high as possible. Second, reliability depends on sample size such that larger samples produce more reliable estimates.

Transfer pricing rules recognize that statistical estimates of the selected profit indicator must consider multiple-year analysis to achieve a reliable measure of arm’s length taxable income. See OECD (2017), ¶¶ 3.75-3.79 and US Treas. Reg. § 1.482-1(f)(2)(iii).

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**Topics:**Net Profit Indicator- Share

Segue a reliable method to determine the arm's length profit margin of each selected comparable company to benchmark the tested party. For each selected comparable company, we measure Total Costs (*Lato*) = COGS + XSGA + (DP – AM). In Standard & Poor's Global (Compustat) mnemonics, COGS is cost of goods sold, XSGA is operating expenses, DP is the depreciation of property, plant & equipment (PPENT), including AM that is the amortization of acquired intangibles. Denote C as Total Costs (Lato) and S as Net Sales, which for each selected company is the sum of the unit price of the individual goods and services offered by the enterprise during the fiscal year multiplied by the respective quantity supplied:

for *t* = 1 to T fiscal periods.

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**Topics:**Net Profit Indicator- Share

*more reliable measures* of arm’s length profits. We hold that markup pricing-based profits are superior to “return on assets” respecting these two conditions.

Assets are heterogeneous making cross-companies comparisons difficult. We may get relief knowing that the specific assets composing the “perpetual inventory” dynamic equation of company growth rates can be restricted to *property, plant & equipment* (PPE); however, different start or acquisition dates (called vintages) and different depreciation rates make PPE also difficult to compare across companies.

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**Topics:**Net Profit Indicator- Share

In transfer pricing, certain analysts prefer using “return on assets” even for businesses such as wholesale or retail trade in which assets are not expected to have a significant impact on operating profits. These analysts postulate a simple linear relationship between operating profits and accounting assets (variously defined) and calculate quartiles without respite. The econometric model underlying the single-variable computation of the quartiles of “return on assets” can be written as:

for *t* = 1 to T years of each selected comparable.

We can test several bivariate (X, Y) regression functions to obtain the most reliable estimate of comparable operating profits. The explanatory variable X can be sales, costs or assets of the selected comparable companies. The dependent variable Y can be sales or operating profits before or after depreciation; and the slope coefficient is an estimate of the comparable operating profit indicator:

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**Topics:**Net Profit Indicator- Share

Selecting a reliable profit indicator is not trivial (reliability is an important metric in transfer pricing). A basic function in algebra represents a straight line, such as the prescribed profit indicator model of the OECD in which the expected value of enterprise profits is a linear function of sales, costs or assets:

where the coefficient β is the slope of the line of the joint pairs X and Y representing a profit indicator.

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**Topics:**Net Profit Indicator- Share

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