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

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

We consider transfer pricing methods based on *operating profits* (profit level indicator) under the comparable profits method (CPM) and “transactional” net margin method (TNMM).

The CPM was divulged in the 1994 US transfer pricing regulations under Treas. Reg. § 1.482-5. The TNMM was released in the 1995 OECD transfer pricing guidelines.

*Operating profits versus gross profits*

We distinguish between transfer pricing methods that use *operating profits* contra *gross profits *indicators (aka financial ratios).

Gross profits are defined as net sales minus cost of goods sold (COGS); 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 book (GAAP or IFRS) accounts between COGS and XSGA schedules. See USA Treas. Reg. § 1.482-5(c)(3) (Data and assumptions).

Since the 1994 and 1995 release of the CPM and TNMM, gross profits methods (mistakenly called “transactional” methods) are debunked.

*Operating profits methods are the mode*

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

In the RoyaltyStat 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 Costs (*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:

(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.

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 ratios 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 Costs (*Lato*) = XOPR + (DP − AM), where XOPR = COGS + XSGA.

We call P(*t*) = OIBAM = Net Sales − (XOPR + (DP − AM)) = Net Sales − (XOPR + DFXA), where DFXA is Compustat's mnemonic for the depreciation of tangible fixed assets.

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*., 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 profit markup or profit margin, to determine a range of operating profit indicators to bound the controlled tested party.

To illustrate equations (3) and (4), we consider 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 = 256.8 (the uncorrected *t*-statistics = 611.1) and R^{2 }= 0.9999.

The estimated intercept is not different from zero, so we disregard it from equation (3).

From the estimated profit markup λ = 1.0494, we 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*) = 1.0484 ∆C(

*t*) + ∆V(

*t*),

which produces strong Newey-West *t*-statistics = 202.6 (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 ratios P(*t*) / S(*t*). For 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 has become 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 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

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.

Published on Mar 17, 2020 6:05:01 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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