RoyaltyStat Blog

Alternative Functional Forms of Comparable Profits

Posted by Ednaldo Silva

We can test several bivariate (X, Y) regression functions to obtain the most reliable estimate of comparable operating profits. The explanatory variable X can be sales, costs or assets of the selected comparable companies. The dependent variable Y can be their operating profits before or after depreciation, and the slope coefficient is an estimate of the comparable operating profit indicator:

     (1)     Linear: Y = α + β X, slope = β

Selecting a Reliable Profit Indicator

Posted by Ednaldo Silva

Selecting a reliable profit indicator is not trivial (reliability is an important metric in transfer pricing). A basic function in algebra represents a straight line, such as the prescribed profit indicator model of the OECD in which the expected value of enterprise profits is a linear function of sales, costs or assets:

     (1)     Y =f(X) = β X

where the coefficient β is the slope of the line of the joint pairs X and Y representing a profit indicator.

Profit Margin Using Koyck Transform

Posted by Ednaldo Silva

We posit that enterprise profits (P(t) = EBITDA(t)) depend on the same period sales (S(t)) and on previous period sales such that the weights of past period sales decline as a power function. This means that enterprise profits depend on a weighted sum of current and past sales whose parameters we can estimate using the Koyck transform equation:

Return on Assets (ROA) is An Unreliable Profit Indicator

Posted by Ednaldo Silva

Return on assets (ROA) is ill-defined and selection of this profit indicator in transfer pricing can lead to intractable controversy between the tax administration and corporate taxpayers. Assets (which combine liabilities and equity) are an accounting quagmire. The nebulous definitions provided by the OECD Transfer Pricing Guidelines (2017), ¶¶ 2.103 and 2.014 create more pain than relief. Likewise, the vague definitions provided by US 26 CRF 1.482-5(b)(4)(i) and (d)(6) are misconceived because they aggregate heterogeneous elements disrespecting short- versus long-term assets vintages (acquisition dates), assets associated and those not associated with interest deductibility, economic cycle dynamics, and different depreciation schedules.

Location Savings Adjustment to Profits

Posted by Ednaldo Silva

The OECD, UN, and United States transfer pricing rules recognize that tax administrations and controlled MNE (multinational enterprise) groups must consider location savings adjustments when uncontrolled comparable enterprises operate in different geographical markets from the tested party. Location savings adjustments are needed when we can measure (in different geographic markets; e.g., UK versus Nigeria or South Africa or US versus Brazil or Mexico) significant differences in wage shares and adopted technology measured by incremental capital/output ratios.

Profit Margin by Indirect Least Squares

Posted by Ednaldo Silva

A practice in transfer pricing is to select a “net profit indicator” (such as operating profit margin or return on assets) and calculate quartiles among i = 1, 2, …, N selected enterprise-level comparables. This practice produces unreliable profit indicators that can’t survive audit scrutiny. A major fallacy of this practice is to estimate structural equations when reduced-forms should be estimated. In this blog, we discuss and solve this fallacy.

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.