RoyaltyStat Blog

Equilibrium Arm’s Length Profit Ratios

Posted by Ednaldo Silva on Mar 31, 2017 5:53:43 PM

In several blogs, we postulated that an autoregressive (AR) model can produce more reliable measures of comparable company profit ratios (operating margin over revenue or profit rate over assets) than the naive profit model prescribed by the OECD transfer pricing guidelines. We prefer to work with profit margins because they are pure numbers, unlike profit rates over assets of different vintages. Here, we show the fixed-point equilibrium and the variance of an AR(1) model allowing the computation of a comparable profit ratio interval to benchmark related party transfers of goods and services.

Company Profits in Transfer Pricing

Posted by Ednaldo Silva on Mar 24, 2017 5:09:38 PM

It's useful to model company profits using a first-order autoregressive AR(1) process. However, “duality” (invertibility) between an AR(1) model and a weighted sum of random errors tempers theoretical or long-term ambitions. Duality is a metamorphosis from one dynamic process to another such that an AR(1) model can be converted into a moving average of random errors model. Moving average models lack X-factors explanation.

Operating Profit Margins Don't Obey the Normal Distribution

Posted by Ednaldo Silva on Oct 21, 2016 7:13:23 AM

The operating profit margin (measured after depreciation and amortization (OMAD)) of 23,151 companies listed in many countries, reflecting fiscal year-end 2015 accounting results, departs from the usually presumed normal distribution. In this sample, OMAD gets a better fit using the Gamma distribution.

Profit Margin with Heterogeneous Variance

Posted by Ednaldo Silva on Jun 23, 2016 8:24:25 AM

In transfer pricing, we may encounter a situation in which the statistical residuals among the selected comparables do not have a common variance. This phenomenon is called heteroskedascity. To correct this problem, we can transform or deflate the relevant variables and measure them as ratios. E.g., suppose that we have comparable company coordinated pairs of data on sales (S) and “net” (operating) profits (P), and their bivariate scatter diagram suggests a linear relationship:

Profit Margin Using a Power Function

Posted by Ednaldo Silva on May 24, 2016 5:18:06 AM

Zero Intercept Linear Profit Function

The typical OECD TNMM (CPM in the U.S.) prescribes a linear statistical function to test the arm's length character of “net” profits (Y) in terms of the net sales (X):

      (1)     Yi = α Xi considering i = 1, 2, …, N comparables

where α is the estimated “net” profit margin. For simplification, we set aside a random error term that is added to equation (1). The controlled taxpayer ("tested party") is the case N + 1.

Non-Linear Profit Function 

Instead of equation (1), "net" profits and sales may be represented by a power function:

     (2)     Yi = α Xiβ

Power functions are pervasive in economic estimates. Equation (2) states that Yi is proportional to Xiβ . In this case, the profit margin is the slope coefficient of equation (2), which below we show is different from α. A power function is appropriate e.g. when the selection of comparables to the tested party includes small and large companies or when the residual variance is not constant.

Profit Margin of Corporate Innovators & Imitators

Posted by Ednaldo Silva on May 15, 2016 7:41:56 PM

Consider the profit margin of selected comparables in the general case when the industry includes two types of uncontrolled (or consolidated) enterprises: (i) innovators that can earn a temporary or persistent excess profit margin, and (ii) imitators that are attracted by the excess profit but whose entry in the industry have the effect of eroding the excess profit margin. As a result, the industry of the controlled taxpayer may exhibit over an audit cycle both a common (or equilibrium) and disequilibrium profit margins earned by innovators and their predators. Here is a schema of this competitive technological and marketing treadmill:

Selection of the PLI - Profit Margin

Posted by Ednaldo Silva on May 2, 2016 12:30:35 PM

Quartiles of the profit margin are much abused in transfer pricing. Typically, the profit margin (expressed as profits divided by sales) is computed without information about its logical underpinnings. A source of the problem is equivocal regulatory guidance. Another source is the prevailing use of “best practice” sans cogito. In the OECD Transfer Pricing Guidelines, ¶ 2.90, “A net profit indicator of net profit divided by sales, or net profit margin, is frequently used to determine the arm’s length price of purchases from an associated enterprise for resale to independent customers.” A similar postulate is found in the U.S. Treas. Reg. § 1.482-5(b)(4)(ii)(A)(Profit level indicators) in which the profit margin is defined as the “ratio of operating profit to sales”.

It's time to examine the logical foundations of the selected PLI (profit level indicator) because the profit margin defined as a simple ratio of (gross, operating or net) profits to sales may be valid only under special circumstances. Although this same malady applies to other profit indicators that are defined as a fixed proportion to costs or assets, here we concentrate of the profit margin under the OECD TNMM, which is equivalent to the U.S. CPM (comparable profits method).

Risk-Adjusted Asset Return

Posted by Ednaldo Silva on Mar 25, 2016 1:22:59 PM

According to the OECD Transfer Pricing Guidelines (2010), ¶ 1.36, the “comparability factors” that “may be important” when determining comparability include: 

  • the characteristics of the property or services transferred,
  • the functions performed by the parties (taking into account assets used and risks assumed),
  • the contractual terms,
  • the economic circumstances of the parties, and
  • the business strategies pursued by the parties. 

These comparability factors are discussed in more detail at the OECD’s Section D.1.2. 

Return on Assets - Correct Measure

Posted by Ednaldo Silva on Mar 14, 2016 11:54:36 AM

We must be careful when the profit rate (“return on assets” in the OECD lingo) is selected as the appropriate “profit indicator” to measure the arm’s length behavior of related-party transactions in which the “tested party” (or taxpayer) employs significant identifiable assets (e.g., “capital-intensive activities”) in controlled business. See OECD, Transfer Pricing Guidelines (2010), ¶¶ 2.62, 2.76, 297-298. We have serious misgivings about this choice of profit indicator (called PLI (profit level indicator) in the U.S. Treas. Reg. § 1.482-5(b)(4)(i)(Return on capital employed)) because the usual equation used is misspecified.