Segue a reliable method to determine an arm's length profit markup or profit margin of selected comparable companies (enterprises) and of the controlled tested party. For each selected comparable company, Total Costs (Lato) = COGS + XSGA + (DP – AM). In Standard & Poor's Capital IQ (Compustat) mnemonics, COGS is cost of goods sold, XSGA is operating expenses, DP is depreciation of property, plant & equipment (PPENT), and AM is amortization of acquired intangibles. Denote C as Total Costs (Lato) and S as Net Sales, which for each selected company is the sum of the unit price of the individual goods and services offered by the enterprise during the fiscal year multiplied by the respective quantity supplied:

(1) S(*t*) = C(*t*) + P(*t*)

for *t* = 1 to T fiscal periods.

Equation (1) represents an accounting identity that in each fiscal period net sales are equal to total costs (*lato sensu*) plus operating profits after depreciation (but excluding the amortization of acquired intangibles because they may not be integral to the business operations under transfer pricing audit) (EBIT).

To simplify exposition, we hide the comparable *i*-th subscript.

Add a behavioral equation that the *net* *profits *(EBIT) are proportional to the company’s net sales during the same period:

*t*) = μ S(

*t*) + U(

*t*)

where the slope μ is the *net* *profit margin* and U(t) is a random error.

In practice, transfer pricing analysts estimate structural equation (2), which is misconceived. Substitute (2) into (1) and obtain a reduced-form equation, which we can subject to regression (least squares) estimation:

(3) S(*t*) = λ C(

*t*) + V(

*t*)

where λ = 1 / (1 – μ) > 1 is the *net* *profit markup* and V(*t*) is the transformed random variable.

The displacement λ ± (2 × SE(λ)), where SE denotes standard error, measures the confidence interval for the slope coefficient of regression equation (3). See Wonnacott & Wonnacott ((1969), pp. 132, 244 and James *et*. *al*. (2013), p. 66.

The *net* *profit margin* is obtained by *indirect least squares* from equation (3) by using the derived formula:

See https://blog.royaltystat.com/profit-margin-in-the-markup-pricing-model

Like John Wallis (1616-1703), “we Test and See it to be so”. See Wallis (1643), pp. 60-61.

**Profit Markup of Major US Retailers**

The net operating profit markup of several major US retailers is estimated using all available data to fit equation (3). The net operating profit margin can be calculated by using equation (4), which we leave as an exercise. Equation (3) was run with the intercept but they are supressed on the table below because they are weak or insignificant. The *t*-statistics are Newey-West estimators that correct for serial correlation among the residuals. See Zeileis (2004) and Green (2018), Section 20.5.2, pp. 998-999 (“The White [1980] and Newey-West [1987] estimators are standard in the econometrics literature.”).

**Company GVKEY Period Count ****λ t-statistics R^{2} **

Best Buy 2184 1983-2018 36 1.0469 277.6 0.9998

Conns’s 156614 2002-2018 17 1.0834 58.7 0.9953

CostCo 29028 1992-2019 28 1.0322 984.9 0.9985

Home Depot 5680 1980-2018 39 1.1379 84.3 0.9985

Kohl’s 25283 1991-2018 28 1.0985 99.8 0.9988

Lowe’s 6929 1978-2018 41 1.0944 192.3 0.9995

Macy’s 4611 1978-2018 41 1.091 108.5 0.9987

PriceSmart 65343 2001-2018 23 1.0615 227.9 0.998

Target 3813 1978-2018 41 1.0776 260.6 0.9997

Walmart 11259 1978-2018 41 1.0504 289.8 0.9999

Home Depot is the only large US retailer in our sample showing double digits net operating profit markup, λ = 13.79% or net profit margin, μ = 12.1%.

The OLS regression results are very reliable measured by two tests. First, the Newey-West *t*-statistics are very high compared to the 1.96 rule-of-thumb. Think of the *t*-statistics as a coefficient of variation defined as the ratio of the regression coefficient (λ) divided by its standard error. The higher the *t*-statistics the more reliable is the estimate of the coefficient measuring the relationship between the dependent and independent variables. Below we provide a chart of the EBIT margin considering all available annual data per company.

Second, the R^{2} of every company assayed is close to one, which is its maximum value. The R^{2} measures the explanatory power of the regression equation, indicating that in our application of equation (3) the residual left to chance is negligible.

The regressions were run in RoyaltyStat® interactive (online) platform that is integrated with our distribution license of Standard & Poor's Capital IQ (Compustat) database of listed company financials. RoyaltyStat's built-in multiple regression function includes the reporting of Newey-West standard errors of the coefficients. We believe that RoyaltyStat has available for subscription (demonstrably) the most effective interactive transfer pricing SaaS application in the industry.

**References**

William Green, *Econometric Analysis* (8th edition), Pearson, 2018.

Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, *An Introdution to Statistical Learning*, Springer, 2013 (corrected at 4th printing 2014).

John Wallis, *Truth Tried*, London, Samuel Gellibrand, 1643, 128 pages. Quote from Amir Alexander, *Infinitesimal*, Scientific American, 2014, p. 327. Wallis was one of the mathematical progenitors of Isaac Newton. For fun, read John Wallis, *The Arithmetic of Infinitesimals* [1656], translated from Latin to English with an Introduction by Jacqueline Stedall, New York, Springer-Verlag, 2004. See also: http://www-history.mcs.st-and.ac.uk/Biographies/Wallis.html

Thomas Wonnacott & Ronald Wonnacott, *Introductory Statistics*, Wiley, 1969.

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

Published on Oct 6, 2019, 4:41:01 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

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.