RoyaltyStat Blog

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 erudite 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.

Consider two aspects of statistical reliability principles. First, reliability can be measured by the ratio of the selected variable 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 an arm's length profit markup or profit margin of selected comparable companies (enterprises) and of the controlled tested party. For each selected comparable company, Total Costs (Lato) = COGS + XSGA + (DP – AM). In Standard & Poor's Capital IQ (Compustat) mnemonics, COGS is cost of goods sold, XSGA is operating expenses, DP is depreciation of property, plant & equipment (PPENT), and AM is 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 run 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” on these two respects.

Accounting measures of assets are amorphous making them difficult to compare across companies. 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 otherwise comparable companies.

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:

(1)     P(t) = β K(t) + U(t)

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: