Our analysis of a large sample of US-listed retailers has revealed that a simple formula can be used to provide reliable estimates of a controlled retailer’s operating profit markup for transfer pricing purposes. To enhance tax certainty, we recommend that US state tax authorities allow retailers to use arm’s length ranges based on this formula as a transfer pricing safe harbor.

The regression method proposed here can be applied to any industry, including to provide safe harbors for inbound controlled distributors or to provide safe harbors for outbound controlled suppliers or service providers.

**Determining profit markup**

In standard microeconomic theory, a difference in transfer prices charged for the same product in different geographic markets is determined by differences in their elasticities of demand, assuming identical or similar average costs of production, and holding the market shares constant.

In practice, elasticity of demand is difficult to compute because of regression model identification and the lack of product-specific data.

Thus, while standard models of price determination are based on elasticity of demand, modern versions add a fixed markup to average costs.

Microeconomics textbooks consider only the standard (elasticity of demand) version. See Henderson & Quandt (1980), pp. 176, 178, 181-182.

A modern version (without appeal to elasticity of demand) of markup pricing is found in Kalecki (1971), pp. 43-47.

As a pedagogical device, we develop the standard version of markup pricing:

(1) R* _{i}* = p

*q*

_{i}

_{i}Accounting equation (1) states that revenue per company product *i* = 1 to N is the individual product price multiplied by the quantity sold.

In a stylized version in which the seller is a price-taker, we assume that p* _{i}* = p = market price. But we reject this parable and assume the existence of oligopoly with the resulting company-level stable profit markups.

We take the total differentiation of revenue equation (1) and obtain the Amoroso-Robinson relation between price and the slope of the demand curve of the *i*-th company or product:

(2) p* _{i}* − q

*∂ p*

_{i}*/ ∂ q*

_{i}*= c*

_{i}

_{i}where c* _{i}* is the average cost of the

*i*-th product in consideration.

The partial derivative ∂ p* _{i}* / ∂ q

*is the slope of the demand function for the company or product*

_{i}*i*. The negative sign stems from the result that ∂ p

*/ ∂ q*

_{i}*< 0, because of the inverse relationship between the quantity of product sold and its price. See Henderson & Quandt (1980), p. 176 and Phlips (1983), pp. 96, 257 (endnote 21).*

_{i}We transpose the partial derivative expression to the right-hand side of (2), and obtain the profit markup price equation:

(3) p* _{i}* = c

*+ κ*

_{i}

_{i}where the profit markup is κ* _{i}* = q

*∂ p*

_{i}*/ ∂ q*

_{i}*> 0.*

_{i}We can show that the profit markup is related to the product market share by multiplying kappa by q / q. See Phlips (1983), pp. 95-98.

We prefer the multiplicative form of the markup price equation because it is amenable to regression analysis:

(4) p* _{i}* = λ

*c*

_{i}*+ random error*

_{i}where the profit markup is λ* _{i}* > 1.

If we test the regression equation (4) by using annual aggregated product data for a large sample of US-listed companies, we find that the estimated profit markup is stable over time.

In practice, we can run the regression price equation with grouped product data per company:

(5) R* _{t}* = λ C

*+ U*

_{t}

_{t}where the aggregate company revenue is R = ∑ R* _{i}* and the aggregate company total costs are C = ∑ C

*.*

_{i}From the estimated operating profit markup, we can obtain the operating profit *margin* using a simple formula:

(6) µ = (λ – 1) / λ

We use Standard & Poor’s Compustat mnemonics and define the selected company revenue as R = REVT and the total company costs as C = XOPR = COGS + XSGA.

We exclude depreciation and the amortization of acquired intangibles (DT) because they are deductible *returns* to the prior acquisitions of property, plant & equipment (PPENT), and external intangible assets (INTAN).

We can use the “tested party” (taxpayer under audit) and the selected comparable company historical data because the disaggregated R* _{i}* = p

*q*

_{i}*datasets are not available. See Maddala (1977), § 10-5 (*

_{i}*Aggregation*), pp. 207-217.

The variable U in equation (5) is the unknown uncertainty (or the random error) because (4) is not an exact relationship.

For example, we obtained the following operating profit (EBITDA) markups before depreciation and amortization (OIBDP) for Best Buy and Walmart using all available data in the interactive RoyaltyStat/Compustat database:

*Example 1: Best Buy Co* Inc. (GVKEY 2184)

(5.1) R* _{t}* = 1.0669 C

*+ U*

_{t}

_{t}We count 37 years of paired company data, the Newey-West corrected *t*-statistics = 298.6, and the correlation coefficient squared = 0.9998.

*Example 2: Walmart* Inc. (GVKEY 11259)

(5.2) R* _{t}* = 1.071 C

*+ U*

_{t}

_{t}We count 50 years of paired company data, the Newey-West corrected *t*-statistics = 311.9, and the correlation coefficient squared = 0.9999.

The high Newey-West corrected *t*-statistics suggest that the standard errors of the regression coefficients are minuscule compared to the central values of the estimated operating profit markup.

The minuscule standard errors of the regression coefficients suggest that the empirical results of price equation (5) are extremely reliable.

*Example 3: Group of Ten Major U.S. Retailers *

(5.3) R* _{t}* = 1.0713 C

*+ U*

_{t}

_{t}We count 434 years of paired company data, the Newey-West corrected *t*-statistics = 344.6 and the correlation coefficient squared = 0.9996.

The ten major US retailers analyzed in this group are: (1) Best Buy Co Inc. (GVKEY 2184), (2) Conn’s Inc. (15614), (3) Costco Wholesalers Corp. (29028), (4) Dillard’s Inc. (3964), (5) Home Depot Inc. (5680), (6) Kohl’s Corp. (25283), (7) Lowe’s Cos Inc. (6829), (8) Macy’s Inc. (4611), (9) Target Corp. (3813), and (10) Walmart Inc. (11259).

The interquartile range of these historical operating profit markups varies from Q1 = 4.824% to Q3 = 8.89%, with median = 7.001%, average = 7.031%, and trimean = 6.929%. The Tukey’s statistical notches of operating profit markups are even more reliable than the quartiles, varying from 6.664% to 7.338%.

**A transfer pricing safe harbor for retailers **

From this exploratory data analysis (EDA), we can conclude that the operating profit markup reported by major US retailers is stable.

The wide operating profit markup variations found among cherry-picked comparables in the US retail industry are a statistical fiction created by the artificial truncation (discretionary clipping) of the available data.

Given the stability of the operating profit markup ratios among major US retailers, state tax authorities can establish arm’s length ranges as safe harbors to enhance tax certainty.

However, any state safe harbor should exclude controlled retailers primarily engaged in lower volume specialty (differentiated) goods and services (because they have elevated market shares) or that create marketing intangibles by deducting substantial advertising expenses. The characterization of the tested party with either of these important attributes as a limited function, limited risks, and limited assets retailers is a legal fiction without empirical support.

Like the proposed Section 1.163(j) regulations that set safe harbor limits for related-party interest deductions, we can use internal data from the consolidated taxpayer (in which related party transactions are eliminated) to estimate equation (5) in transfer pricing cases. This is a reliable test of reasonableness of the proposed transfer pricing adjustments made under the comparable profits (CPM ≈ TNMM) or the profit split method.

**References**

James Henderson & Richard Quandt, *Microeconomic Theory* (A Mathematical Approach), (3^{rd} edition), McGraw-Hill, 1980.

Michal Kalecki, “Costs and Prices” (1943, 1954) in his *Selected Essays on the Dynamics of the Capitalist Economy*, Cambridge University Press, 1971.

This chapter about markup pricing was first published by Michal Kalecki, *Studies in Economic Dynamics*, George Allen & Unwin, 1943, pp. 9-31 (“If technical progress reduces average costs of all firms in the same proportion, it does not affect the markup (unless technical change alters the conditions of market imperfection and oligopoly”)).

In the price equation (4), the profit markup λ is a stable constant, such that ∆p* _{i}* = λ

*∆c*

_{i}*and ∆c*

_{i}*< 0 is regarded as a cost-reducing technical change.*

_{i}Instead of using the Cournot-Amoroso-Robinson elasticity of demand approach, we can obtain the markup price equation *à la* Kalecki by defining an accounting equation in which average price = total costs (XOPR) + operating profits (OIBDP, EBITDA) and positing that operating profits are proportional to total costs:

(1a) p* _{i}* = c

*+ κ*

_{i}

_{i} (2a) κ* _{i}* = φ

*c*

_{i}

_{i} (3a) p* _{i}* = c

*+ φ*

_{i}*c*

_{i}

_{i} (4) p* _{i}* = λ

*c*

_{i}

_{i}where the operating profit markup factor, λ* _{i}* = (1 + φ

*), can be estimated by regression analysis using linear or double-logarithms specifications.*

_{i}Maddala, *Econometrics*, Mc-Graw-Hill, 1977.

Louis Phlips, *The Economics of Price Discrimination*, Cambridge University Press, 1983.

**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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