*L’un fece il mundo e l’altro l’ha distrutto.*

*Meditaciones del Quijote*(1914), by José Ortega y Gasset)

We discuss transfer pricing methods based on *operating profits* (“net profit indicators”) under the U.S. comparable profits method (CPM) and the OECD “transactional” net margin method (TNMM).

The CPM was divulged in the 1994 U.S. transfer pricing regulations under Treas. Reg. § 1.482-5. The TNMM was released in the 1995 OECD transfer pricing guidelines (TPG). See OECD 2017 TPG, ¶ 2.62 *et*. *seg*.

#### Operating profits versus gross profits

We distinguish between transfer pricing methods based on *gross profits and **operating profits*.

Gross profits are defined as net sales minus cost of goods sold (COGS), and operating profits are gross profits minus operating expenses (XSGA).

Gross profits methods in transfer pricing include the *gross margin* *method,* expressed in terms of net sales; the *gross markup method, *expressed in terms of COGS; and the *Berry ratio,* expressed in terms of XSGA.

These “traditional” transfer pricing methods based on gross profits are unreliable because of inconsistent allocations of (GAAP or IFRS) “book” accounts between COGS and XSGA schedules. See U.S. Treas. Reg. § 1.482-5(c)(3) (Data and assumptions).

Since the 1994 and 1995 release of the CPM and TNMM, gross profits methods (as a solecism they are called “transactional” methods) are debunked. See OECD 2017 TPG, ¶ 2.68: “In some countries the lack of clarity in the public data with respect to the classification of expenses in the gross or operating profits may make it difficult to evaluate the comparability of gross margins, while the use of net profit indicators may avoid the problem.”

#### Operating profits methods are the mode

Now, we discuss transfer pricing methods based on operating profits.

In the RoyaltyStat® online (interactive) company financials database, with data sourced from Standard & Poor’s Global (Compustat®), we can add the depreciation of property, plant, and equipment (DP), excluding the amortization of acquired intangibles (AM), to XSGA, and call Total Cost (*lato **sensu*) = (COGS + XSGA + (DP – AM)). We call Total Costs (*stricto sensu*) = (COGS + XSGA), without the capricious depreciation (DP – AM) allowance.

In practice, transfer pricing analysts estimate the structural equation prescribed by the U.S. regulations and the OECD TPG:

##### (1) P(*t*) = μ S(*t*) + U(*t*)

where P(*t*) denotes operating profits of an individual (comparable) company in fiscal year *t* = 1 to T, and S(*t*) denotes net sales (revenue) during the same period.

Other analysts define Total Cost = COGS + XSGA + DP, so our concept of operating profits is different because we exclude AM from total costs. As Mueller (1986, p. 244) has suggested, we exclude acquired intangibles because they represent capitalized monopoly excess profits.

The slope coefficient (μ) denotes the *operating* *profit margin* (“profit margin”), and the error term U(*t*) denotes a random displacement with assumed constant variance.

Transfer pricing misguidance sets T = 3 years; however, we are against this ill-fated *Meek’s Cutoff* and consider it more reliable to use as many years of data as available, *i*.*e*., we set T ≥ 3 years.

A major problem estimating the slope coefficient (profit margin) by using equation (1) or worse, using quartiles of the selected comparable profit ratios M(*t*) = P(*t*) / S(*t*), is that this *structural* equation is misspecified.

We can complete this two-equations system by adding the matching accounting identity:

##### (2) S(*t*) = C(*t*) + P(*t*)

where C(*t*) denotes Total Cost (*Lato*) = XOPR + (DP − AM) and XOPR = COGS + XSGA.

We call P(*t*) = OIBAM = Net Sales − (XOPR + (DP − AM)) = Net Sales − (XOPR + DFXA), where DFXA = (DP – AM) is Compustat’s mnemonic of the depreciation of tangible fixed assets, *i*.*e*., property, plant and equipment.

We substitute (1) into (2) and write the *reduced-form* equation that is amenable to regression analysis:

S(*t*) = C(*t*) + μ S(*t*) + U(*t*), or collecting net sales (revenue) on one-side of the equation:

S(*t*) − μ S(*t*) = C(*t*) + U(*t*)

##### (1 – μ) S(*t*) = C(*t*) + U(*t*)

##### (3) S(*t*) = λ C(*t*) + V(*t*)

where λ = 1 / (1 – μ) is the *operating profit markup* (“profit markup”) and V(*t*) = U(*t*) / (1 – μ) is the transformed error component.

We can estimate the slope coefficient of the regression equation (3) using the interactive Scatterplot or Regression function in the RoyaltyStat company financials database. Each online statistical function produces Newey-West corrected standard errors of the regression coefficients. See Zeileis (2004).

From the slope coefficient estimate by using equation (3), we can obtain the *profit margin* of each selected (comparable) company by indirect least squares (ILS):

λ = 1 / (1 – μ), after solving for the slope coefficient (μ), we obtain

λ (1 – μ) = 1, or

##### (4) μ = (λ – 1) / λ

which produces a positive profit margin if λ > 1 (*i*.*e*., μ > 0 if the profit markup of the selected company is greater than unity).

#### Regression analysis of operating profits

Using the reduced-form regression equation (3), we can obtain both the *profit markup* for cases when the “tested party” has *controlled net sales* and uncontrolled COGS or XSGA (such as outbound manufacturers and service providers); and we can estimate the *profit margin* when the tested party has *uncontrolled net sales* (such as inbound wholesale or retail entities) and controlled COGS or XSGA.

In either case, we can estimate the regression equation (3) and apply the appropriate profit indicator, either the profit markup or profit margin, and determine a reliable range of operating profit indicators used to benchmark the controlled tested party.

To illustrate equations (3) and (4), we consider annual data from Walmart Inc. (Compustat GVKEY 11259).

Walmart (SIC Code 5331) is engaged in global retail, wholesale and eCommerce, and conducts business in the U.S., Africa, Argentina, Canada, Central America, Chile, China, India, Japan, Mexico, and the U.K.

We consider 42 years of data from 1978 to 2019, and obtain these strong regression results:

##### (3) S(*t*) = 1.0494 C(*t*) + V(*t*)

where λ = 1.0494, the Newey-West *t*-statistics of the slope coefficient = 243.2 (the uncorrected *t*-statistics = 580.8) and R^{2 }= 0.9999. The estimated intercept is not different from zero, so we disregard it from equation (3).

We computed Total Cost (*Lato*) = (COGS + XSGA + (DP – AM)). From the estimated profit markup λ = 1.0494, we can use equation (4) to obtain the *profit margin* μ = 0.04707 or μ = 4.7%.

To stabilize the regression residuals, we take first-differences of equation (3) and obtain a similar profit markup:

##### (4) ∆S(*t*) = 1.0467 ∆C(*t*) + ∆V(*t*),

which produces strong Newey-West *t*-statistics = 175.4 (ordinary *t*-statistics = 114.1) and Count = 41 annual data points.

In sum, we can obtain *more reliable estimates* of λ and μ using equations (3) and (4) than using the quartiles of the individual company profit ratios M(*t*) = P(*t*) / S(*t*). For more robust audit defense, we should use this simple regression approach to determine arm’s length profit indicators instead of using quartiles.

#### References

Developed to solve parameter estimation in astronomy and physics (Laplace, Legendre, Gauss), regression analysis based on least-squares algorithms is today the work-horse of applied economics. We can access many econometrics textbooks, which have become thick tomes. We prefer those written by Wonnacott, Maddala or Kmenta (increasing order of analytical sophistication). Elementary statistics textbooks (*e*.*g*., Hoel) also cover regression analysis (but they don’t appear as perturbed to correct residual errors from the malignant effects of heterogenous variance or serial correlation as those textbooks written by economists).

The econometrics authors cited wrote books prior to the development of Newey-West (1987) corrected standard errors. See Zeileis (2004).

The reference to Meek’s Cutoff is an homage to Kelly Reinhardt’s film (2010) in which the inept frontier guide Stephen Meek misled a wagon train to ruin in the Oregon desert in 1845.

Christian Kleiber and Achim Zeileis, *Applied Econometrics with R*, Springer-Verlag, 2008. https://cran.r-project.org/package=AER

Paul Hoel, *Introduction to Mathematical Statistics* (5^{th} edition; 1^{st} edition in 1947), John Wiley & Sons, 1984. Chapter 7 (Empirical methods for correlation and regression).

Jan Kmenta, *Elements of Econometrics* (2^{nd} edition; 1^{st} edition in 1971), Macmillan, 1986.

Maddala, Econometrics, McGraw-Hill, 1977.

Dennis Mueller, *The Modern Corporation*, University of Nebraska Press, 1986.

Ronald Wonnacott & Thomas Wonnacott, *Econometrics*, John Wiley & Sons, 1970. This book is excellent, written by two gifted (economics and mathematics) writers.

Achim Zeileis, “Econometric Computing with HC and HAC Covariance Matrix Estimators,” *Journal of Statistical Software*, Vol. 11, Issue 10, November 2004. Accessed: https://www.jstatsoft.org/article/view/v011i10/v11i10.pdf

**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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