RoyaltyStat Blog

"Come to places where opponents give no thought." Sun Tzu, The Art of War, Alfred Knopf (Everyman’s Library), 2018, p. 62.

Applying the comparable profits method (CPM) in the U.S. or the “transactional” net margin method (TNMM) in other OECD countries, many transfer pricing analysts assume that the depreciation rate of property, plant, and equipment is the same among the individual comparables and the tested party.

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

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.

Like other expressions, economic categories reflect reality, and the term royalty isn't an exception.

Michiel de Vaa’s Etymological Dictionary of Latin and the Other Italic Languages (Brill, 2008) has no entry for royalty or its lemma. See his near-neighbor entry (Vaa, pp. 517-518): rego ("to direct, guide, govern"), but the listed cognates don't refer to payments or other economics allusions.

The Oxford English Dictionary, an arbiter of the English language, includes several meanings for royalty (noun (plural royalties)), and attributes its origin from Old French roialté, from roial (regal): 

“The sense ‘royal right (especially over minerals)’ (late 15th century) developed into the sense ‘payment made by a mineral producer to the site owner’ (mid-19th century), which was then transferred to payments for the use of patents, trademarks, and copyrighted materials.”

See the Oxford English Dictionary. Cite: “royalty, n.”

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.

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).

Innovate, innovate, says Schumpeter and his prophets, because innovation is associated with cost reduction and increased profits. However, many controlled (within group) corporate reorganizations lack economic substance because they violate this basic principle of innovation. Ergo, an objective of innovation is to reduce average costs and therefore to increase profits.  We provide a theorem and include an arithmetic proof that cost-reducing innovations (holding the product or service price constant) increase profits.

The comparable uncontrolled price (CUP) method is described in US Treas. Reg. §1.482-3(b).

We hold that the empirical verification of CUP transactions is best measured by regression analysis.

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:

     (1)     S(t) = C(t) + P(t)

for t = 1 to T fiscal periods.

We have well-specified “return on assets” showing that we must estimate reduced-forms (instead of structural) equations and ran away from using this scrappy financial ratio to determine arm’s length profits subject to corporate income taxes. However, criticism is valid if we can provide a better substitute that can satisfy two conditions: First, the new alternative theory (markup pricing) resolves certain knotty issues of the old theory (such as avoid the cloudy base of “return on assets”); and second, the new theory provides 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.