*Después de tanto soportar la pena de sentir tu olvido … **y si pretendes remover las ruinas **que tú mismo hiciste*

*Cenizas* in the poignant voice of Toña La Negra. Classic bolero lyrics by Wello Rivas (1913-1990).

When advising tax authorities, we frequently face claims that major U.S. retailers considered to be comparables to an inbound “tested party” have transfer pricing operating profit margins that vary from 0.5% to 1.5% of their net sales.

This interquartile range (IQR) from 0.5% to 1.5% does not reflect the *reported* transfer pricing operating profit margins of the purported comparables but is instead obtained by dodgy asset intensity adjustments.

We say dodgy because the proposed asset adjustments are not supported by a theoretical economic basis, and their statistical significance is not ascertained.

Taxpayers’ transfer pricing positions must be more credible if they stand a chance of surviving audit scrutiny. Unlike the naïve presumption of some taxpayers, tax authority scrutiny can be sophisticated.

*Safe harbors*

Treas. Reg. § 1.482-1(h)(1) (Small taxpayer safe harbor) is reserved for safe harbors.

In IRS, we conducted substantial research to compute industry-specific safe harbors; and on August 20, 1990, IRS Special Counsel (International) issued a memorandum supporting safe harbor transfer pricing adjustments for inbound controlled distributors under three conditions:

First, the sample forming the safe harbor must consist of companies that bear “sufficient similarity” to the functions performed by the taxpayer.

Second, by the issuance of information requests at the beginning of each audit, the tax administration must ascertain if comparable uncontrolled transactions (CUP) exist or if comparables exist to apply another specified method.

Third, the tax administration must share the information underlying the safe harbors with the taxpayer.

Industry-specific safe harbors were called the statistical approach to transfer pricing adjustments, and application of this approach became the nursery-school for our development of the comparable profits method.

We base this (unofficial) safe harbor of transfer pricing operating profit margins on a large sample of U.S. retailers that perform “routine” functions.

The sample was determined from certain canonical search criteria using the Standard & Poor’s Compustat® database of company financials, which we have integrated into our RoyaltyStat® transfer pricing interactive software:

- SIC Code: 5200-5999; except for 5812, eating places.
- Country: United States
- Years: 2002-2019
- Operating Profits > 0 in all selected years.

We obtained 57 U.S. retailers from which we calculated the IQR of operating profit margins before the depreciation (OMBD) of property, plant & equipment, and before the amortization of acquired intangibles:

Count = 1026 annual OMBD; Q1 = 5.701%; Median = 9.371%; Trimean = 9.390%; Q3 = 13.117%.

For comparison, we estimated the reduced-form operating profit markup equation:

S(*t*) ≈ 316.1 + 1.0731 C(*t*)

NW *t*-Statistics 4.7 335.8

where S(*t*) denotes the individual company net sales in year *t* = 2002 to 2019 and C(*t*) = COGS + XSGA.

We call this independent variable Total Cost (Stricto) because we exclude depreciation and amortization from the cost base.

The sample count = 1026 paired observations, R^{2} = 0.9995.

We corrected the *t*-Statistics of the regression coefficients for heterogeneous variances and serial correlation by using RoyaltyStat’s built-in Newey-West (NW) algorithm.

The regression slope = 1.0731 is the change in S(*t*) that accompanies a unit [USD million] change in the independent variable C(*t*).

This operating profit markup = 1.0731 is equivalent to a safe harbor OMBD = 0.0681 or 6.8%. See https://blog.royaltystat.com/transfer-pricing-methods-based-on-operating-profits

Fig. 1 of this blog shows that the standard model of the operating *profit margin* does not produce a good statistical fit, so the regression coefficients are unreliable. Operating profit is the difference between S(*t*) and C(*t*).

In contrast, Fig. 2 shows the strong regression results written above from which we obtained the safe harbor minimum U.S. retail OMBD of 6.8%.

*Transfer pricing operating profit margins – the takeaway*

The standard error of the regression slope coefficient is minuscule, *i*.*e*., the Newey-West standard error of the operating profit markup = 0.0032.

Thus, under transfer pricing audit scrutiny, even if the controlled U.S. retailer is stripped of its key purchasing function, we should expect an OMBD ≥ 6.8% (or, perhaps depending on circumstances, equal or greater than Q1 = 5.7%).

As in Rivas’s presage bolero quoted above, some audit pain and ruin are self-inflicted.

**Notes about structural vs. reduced form regression equations**

Elsewhere in related blogs, we suggested that we should measure comparable profit margins by using reduced-form and not structural profit equations.

Arthur Goldberger, *Econometric Theory*, Wiley, 1964, p. 318: “consistent estimates of structural parameters may be obtained from consistent estimates of the reduced-form parameters.” Consistent estimates of structural equations require special methods, such as *two-stage least squares* (2SLS).

Ronald Wonnacott and Thomas Wonnacott, *Econometrics*, Wiley, 1970, pp. 152-153 contains a good explanation of the problem of estimating structural equations. We get inconsistent estimates using ordinary least squares (OLS) when the independent variables and the errors are correlated. We have several solutions, including using instrumental variables, two-stage least squares (2SLS), and indirect least squares (ILS, pp. 161-163), which is our choice.

Lawrence Klein, *Econometrics* (2^{nd} edition), Prentice-Hall, 1974, p. 138: “*reduced form* of a system … is an alternative way of writing a system so that each endogenous variable is expressed as a function of predetermined variables alone.” Exogenous variables and lagged endogenous variables are predetermined (p. 133).

Jan Kmenta, *Elements of Econometrics* (2^{nd} edition), Macmillan, 1986, pp. 651-660. *E*.*g*., p. 653: “Typically, economic theory tells us which relations make up the model, which variables are to be included in each of the relations, and what is the sign of some of the partial derivatives. As a rule, economic theory has very little to say about the functional form of the relations, the time lags involved, and the values of the parameters.”

And p. 656: “The reduced form of the system [of simultaneous equations] is obtained by solving the structural form equations for the values of the endogenous variables, that is, by expressing the *y*’s [endogenous variables] in terms of the *x*’s [exogenous variables] and the *u*’s [uncertainties or random errors].”

We suggested also that we should measure the selected profit indicator before depreciation (EBITDA) and not after depreciation (EBIT) because accounting depreciation rates differ among purported comparables of the tested party. See https://blog.royaltystat.com/transfer-prices-based-on-ebitda-not-ebit

**Reference about the trimean**

The *trimean* is computed using the formula:

TRIM = 0.25 (Q1 + 2 Median + Q3),

where Q1 and Q3 are the lower and upper quartiles.

Tukey’s trimean is superior to the median because it is a weighted average of Q1, median, and Q3.

Independent of data count, the median reflects a single middle value (when the sample is odd) or the average of two middle values (when the sample is even). “[W]e like to use trimeans instead of medians to give a somewhat more useful assessment of location or centering. We can use the trimean almost any place where the median is used.”

John Tukey, *Exploratory Data Analysis,* Reading, Addison-Wesley, 1977, 46-47.

Published on Apr 18, 2020 2:01:07 PM

**Ednaldo Silva**(Ph.D.) is founder and managing director of RoyaltyStat. He helped draft the US transfer pricing regulations and developed the comparable profits method called TNNM by the OECD. He can be contacted at: esilva@royaltystat.com

and

**RoyaltyStat**provides premier online databases of**royalty rates**extracted from unredacted license agreementsand

**normalized company financials**(income statement, balance sheet, cash flow). We provide high-quality data, built-in analytical tools, customer training and attentive technical support.