*Después de tanto soportar la pena de sentir tu olvido.*

*Cenizas *sung by Toña La Negra. Bolero lyrics by Wello Rivas (1913-1990).

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

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

Dodgy because the proposed asset adjustments are not supported by economic principles, 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 corporate taxpayers, tax authority scrutiny can be sophisticated.

#### Safe harbors

Treas. Reg. § 1.482-1(h)(1) (Special rules) is reserved for safe harbors.

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

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

Second, by the issuance of information requests (IDR) at the beginning of the audit, the tax administration must ascertain if comparable uncontrolled transactions (CUP) exist or if comparables exist to apply a 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 the development of the comparable profits method (CPM or TNMM in the OECD guidelines).

I propose 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 are integrated into the RoyaltyStat® transfer pricing interactive software:

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

I obtained 57 U.S. retailers to calculate 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, I 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(*t*) + XSGA(*t*).

This independent variable is called Total Cost (Stricto) because the depreciation and amortization are excluded from the total cost base.

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

The *t*-Statistics of the regression coefficients are corrected for heterogeneous variances and for 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*).

Fig. 2 shows the strong regression results written above from which I propose 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, the reporting of an OMBD ≥ 6.8% is expected.

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

#### Structural vs. reduced form regression equations

In related blogs, I suggested that the comparable profit margins should be measured by using the reduced-form and not the structural profit equations in regression analysis.

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. Inconsistent estimates are obtained by using ordinary least squares (OLS) when the independent variables and the errors are correlated. Several solutions can be proposed, including using instrumental variables, two-stage least squares (2SLS), and indirect least squares (ILS, pp. 161-163), which is my simpler 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 called 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.”

Again on 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].”

I suggested that the selected profit indicator should measurebefore 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

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

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