# RoyaltyStat Blog

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Determining an arm’s length profit indicator (aka 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).

Operating profit indicators such as the operating profit margin (μ), defined as the quotient of operating profits to net sales revenue, can vary between enterprises in the same industry:

The U.S. transfer pricing regulations prescribe under 26 CFR 1.482-1(e)(2)(iii)(B): “The interquartile range [IQR] ordinarily provides an acceptable measure of this [arm’s length] range; however[,] a different statistical method may be applied if it provides a more reliable measure.”

The U.S. transfer pricing regulations refer to “most reliable” or “more reliable” -- which means (following the statistical principle of minimum variance) the narrowest range computed from the dataset. See Wonnacott (1969), Chapter 7-2 (Desirable properties of estimators), pp. 134-139.

"The true theorist in economics has to become at the same time a statistician."

– Ragnar Frisch (1930), p. 30.

Many transfer pricing reports (against Ragnar Frisch’s advice) are devoid of economics or statistics principles. Here, I show that the usual transfer pricing application of "return on assets" (ROA) is disreputable.

The company-level operating profit markup can be estimated as a power function or a linear function between Net Sales (SALE) and Total Cost = XOPR = COGS + XSGA. The difference between Net Sales and Total Cost (measured by XOPR) is OIBDP (operating income [profit] before depreciation and amortization, or EBITDA). Some analysts include DP (depreciation and amortization) in total cost; however, DP is subject to substantial accounting discretion (such as including acquisition related impairment charges), which can prejudice cross-section comparisons.

The OECD Transfer Pricing Guidelines (2017, ¶ 6.192) makes a perfunctory reference to multi-year data analysis covering intangibles. The guidance about using multi-year analysis of profit indicators is described on ¶ 3.75 to ¶ 3.79 (“examining multiple year data is often useful in a comparability analysis, but it is not a systematic requirement.”). One expects more competence in economics and statistical principles from the OECD Guidelines, instead of the misleading quote. Unsystematic requirement is nonsense.

Here, I show that the return on operating assets (ROA) can be specified as the return on investment (ROI).

Economic time series may have one-period autoregressive errors (AR(1)).

Before Newey-West, the Cochrane-Orcutt or the Prais-Winsten AR(1) error correction was pervasive in applied research. Estimating time-dependent economic variables, such as the individual company’s (tested party and comparables) return on operating assets, without the AR(1) error correction will result in inefficient parameter estimates, and the standard errors will be inconsistent. Hence, the unaware reader can begrime the arm’s length range of comparable return on operating assets.

The return on assets (ROA) is misused to determine the tested party’s operating profits in transfer pricing. ROA is unreliable because multiple (ill-defined) denominators are employed. Only the composite asset property, plant & equipment (PPENT) is consistent with well-received economic theory. If book (accounting) PPENT is the denominator (explanatory variable), ROA is still unreliable because of varied accumulated depreciation practices.

You better stop the things you do. Jay Hawkins (1929-2000), “I Put a Spell on You.”

US-listed retailers data show that a simple formula can be used to provide reliable estimates of a controlled retailer’s operating profits for transfer pricing purposes.

To enhance tax certainty, I recommend that US state tax authorities allow retailers to use the profit margin based on this formula as a transfer pricing safe harbor.

The regression method proposed here can be applied to any industry, including to provide safe harbors for inbound controlled wholesale distributors or to provide safe harbors for outbound controlled suppliers or for outbound controlled service providers.

Quem mostrá esse caminho longe? Sung by Cesária Évora (1941-2011).

Corporate profits should concern policymakers, including tax legislators and tax administrators.

In economic theory, high profits converge toward an entrepreneurial average because of the expected inter-industry flow of investments. According to Stigler’s (1963, p. 54) hyperbole: “There is no more important proposition in economic theory than that, under competition, the rate of return on investment tends toward equality in all industries.”