RoyaltyStat Blog

Selection of the appropriate “net” profit indicator (NPI)

Posted by Ednaldo Silva

We discuss three contending transfer pricing models. Let P = “Net” profits, S = Sales, and A = Assets: For simplicity, we don’t consider profit markup on total costs, and exclude random errors:

Coefficient of Variation of Return on Assets

Posted by Ednaldo Silva

In DuPont’s profit identity, “return on assets” (profit rate) is equal to profit margin multiplied by asset turnover. Using DuPont’s profit formula, combined with an assumption that profit margin and asset turnover (measures of economic performance and adopted technology) are independent, we showed on a prior blog that the coefficient of variation of return on assets is greater than of the profit margin. It follows that profit margin is more reliable (has a lower coefficient of variation) than return on assets. In science, coefficient of variation is an accepted method of determining the reliability of a selected variable.

Most Reliable Profit Indicator Based on Coefficient of Variation

Posted by Ednaldo Silva

Transfer pricing tax compliance is devoid of external CUP (comparable uncontrolled prices). Therefore, we must select (under the TNMM and under the Profit Split Method) the most appropriate “net” profit indicator (NPI) from comparable uncontrolled enterprises. Most appropriate is the most reliable among competing profit indicators. In economics and statistics, reliability is measured by the coefficient of variation (standard deviation / mean) of the selected variable.

Using a distributed lag model to determine arm’s length profits in transfer pricing

Posted by Ednaldo Silva

Transfer pricing reports often lack valid economic principles, relying instead on ad hoc specification. This faulty practice is permitted by misconceived transfer pricing regulations based on the OECD model.

US and OECD method for computing arm’s length profit margin is flawed

Posted by Ednaldo Silva

We analyzed the statistical relation between operating profits and net sales for a large group of US listed companies using RoyaltyStat®’s online database of company financials. The results of this study have led us to conclude that the OECD and US transfer pricing guidance on the comparable profits method (TNMM) does not produce the most reliable measure of an arm’s length operating profit margin and that other more informed measures should be considered. Instead of simple regulatory prescription, we apply economics and statistics to reach these conclusions.

Equilibrium Arm’s Length Profit Ratios

Posted by Ednaldo Silva

An autoregressive (AR) model can produce more reliable measures of comparable company profit ratios (operating margin or profit rate) 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 a fixed-point equilibrium and variance of an AR(1) model allowing the computation of a comparable profit ratio interval to benchmark related party transfers of goods and services. This AR(1) model can be used also to benchmark routine functions (manufacturing, distribution, retail) under the residual profit split method.

Enterprise Profits in Transfer Pricing

Posted by Ednaldo Silva

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

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

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

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.