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 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.
Transfer pricing practitioners fell in love with the concept of a “limited risk distribution” (LRD) on the hope that they could convince tax authorities in high tax jurisdictions to accept the premise that the local distribution affiliate should be happy with a low operating margin. This pandemic, however, has generated a lot of new transfer pricing advice that appears to contradict the original LRD argument.
“We shall renounce . . . the subterfuges.”
We estimated the equilibrium OMAD [operating (profit) margin after depreciation] of certain U.S. retailers using an autoregressive (AR(1)) model built-in RoyaltyStat®. We use the Gauss run-time engine, so the regression estimates are reliable.
In statistics, we consider a random variable in terms of a reliable estimate of its central value (center) and spread from the center. The center is measured by the mean, and the spread by the standard deviation from the mean. In practice, data samples (such as the usual judgement selection of comparables in transfer pricing practice) contain outliers that distort the estimates of mean and standard deviation. As a result, statistical (confidence or tolerance) intervals based on the mean and standard deviation may not be reliable. See Gerald Hahn & William Meeker, Statistical Intervals (John Wiley, 1991) for a detailed coverage of tolerance and confidence intervals.
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