RoyaltyStat Blog

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.

U.S. transfer pricing regulations about the “rate of return on capital employed” (ROA) are misconceived because they rely on untested assumptions. For example, 26 CFR 1.482-5(b)(4)(ii), states:

As a transfer pricing practitioner with many years' experience across many industries and transactions, I’ve heard many reasons for making working capital adjustments (WCA). I’ve seen it described as ‘standard’ or ‘automatic’, as well as ‘unreliable’ and ‘rarely to be performed’. I’ve also heard some describe it as an adjustment they ‘believe in’, or an economic factor that an arm’s length party would ‘always’ take into account in their pricing. To untangle this knot, I’ve set out below some of the issues that I would consider before undertaking a WCA.

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.

To grasp the legalese of my initial encounters with the 1968 US transfer pricing regulations (under section 482 published in the Federal Register (33 FR 5848), April 16, 1968), I translated the three specified transfer pricing methods (CUP, resale price and cost plus) into algebra and found a multiplier formula tying them together.

I created a two equation system including an accounting equation and a stochastic equation, and obtained the reduced-form equation to estimate the price (CUP) or the selected gross profit indicator. Using the same multiplier procedure, I developed the CPM/TNMM in 1989.

Le secret d’ennuyer est celui de tout dire. Voltaire (1694-1778)

The Berry ratio is vulnerable to the flexible accounting allocation of costs and expenses among the tested party and its comparables.