Segue a reliable method to determine the arm's length profit margin of each selected comparable company to benchmark the tested party. For each selected comparable company, we measure Total Costs (*Lato*) = COGS + XSGA + (DP – AM). In Standard & Poor's Global (Compustat) mnemonics, COGS is cost of goods sold, XSGA is operating expenses, DP is the depreciation of property, plant & equipment (PPENT), including AM that is the 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 after depreciation *(EBIT exclusive of amortization or OMBA) are proportional to the company’s net sales during the same period:

*t*) = μ S(

*t*) + U(

*t*)

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

Transfer pricing analysts estimate structural equation (2), which is misconceived. A correct procedure is to substitute (2) into (1) and obtain a reduced-form equation, whose parameters we can estimate using regression analysis:

(3) S(*t*) = λ C(

*t*) + V(

*t*)

where λ = 1 / (1 – μ) > 1 is the *net* *profit markup* and V(*t*) is a 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) using the 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 OMBA ratio can be calculated by using equation (4), which we leave to the reader as an exercise. However, we report the *profit margin* per selected company on the charts below.

Equation (3) was run with the intercept but they are suppressed 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 1983-2019 37 1.0473 282.2 0.9998

Conns’s 156614 2002-2018 17 1.0818 74.2 0.993

Costco 29028 1992-2019 28 1.0322 887.7 0.9999

Home Depot 5680 1980-2019 40 1.1423 72.1 0.9985

Kohl’s 25283 1991-2019 29 1.093 78.1 0.9985

Lowe’s 6929 1978-2019 42 1.0948 238.6 0.9995

Macy’s 4611 1978-2019 42 1.0864 96.7 0.9983

PriceSmart 65343 2001-2019 24 1.0583 201.5 0.9997

Target 3813 1978-2019 42 1.0746 235.8 0.9997

Walmart 11259 1978-2019 42 1.049 243.2 0.9999

All 10 Retailers 1978-2019 658 1.0515 289.7 0.9996

These regression results were computed using RoyaltyStat's online (interactive) scatterplot function.

Home Depot is the only large US retailer in our sample showing double digits net operating profit markup, λ = 14.2% or OMBA = μ = 12.5%.

The OLS regression results are reliable measured by two tests:

First, the Newey-West *t*-statistics are 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 partial regression coefficient measuring the relationship between the dependent variable and the selected independent variable.

We provide a chart of OMBA (EBIT margin, excluding AM) considering all available annual data per company from 1978 to 2019.

For comparison, we provide a chart of OMBD (EBITDA margin), including the profit margin for the top 10 US retailers in our sample. This range of EBITDA margins (6.7% ± 0.5%), which reflects the business operations of the top 10 US retailers, include 658 annual observations. According to the statistical law of large numbers, this large sample produces very reliable results. *E*.*g*., the Newey-West *t*-statistics is 344.3, the OLS (ordinary least squares) *t*-statistics is 1,220.3, and the R^{2} is 0.9996.

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.

In RoyaltyStat, we have integrated scatterplot, multiple regression and other useful statistical functions with our distribution license of Standard & Poor's Global (Compustat) database of listed company financials. RoyaltyStat's built-in (interactive) scatterplot and multiple regression functions include the reporting of Newey-West standard errors of the regression coefficients.

We believe that RoyaltyStat offers for subscription the most effective transfer pricing interactive software as a service (SaaS) 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.