RoyaltyStat Blog

Unlike the debutant affection of the OECD, we discourage using projected profits or cash flows to measure hard-to-value-intangibles (HTVI) for transfer pricing purposes because this method is speculative and based on several impeachable assumptions.

We estimated the equilibrium OMAD [operating (profit) margin after depreciation] of certain U.S. retailers using an autoregressive (AR(1)) model built-in RoyaltyStat®. We use the Gauss run-time engine, so the regression estimates are reliable.

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.

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.

The claim that it is impossible to find comparable royalty rates and that from the start we should use the residual profit split method for high-value intangibles needs revisiting. This claim is made prima facie without regard for the license agreements available in curated databases such as RoyaltyStat, which as of today contains over 17,875 unique and unredacted license agreements. Also, adopting the residual profit split method, when separate tested party methods such as the TNMM could suffice, creates unwarranted costs and audit management challenges for both the taxpayer and the tax administration.

We can consider a first-order autoregressive (AR(1)) model to determine an arm’s length profit margin of a “tested party” subject to transfer pricing audit compliance:

It’s useful to study the mean and variance of the first-order autoregressive model (AR(1)), which is postulated as univariate:

We can determine an arm's length profit margin (expressed as operating profit divided by net sales) of a controlled taxpayer (“tested party”) by using a first-order autoregressive model, which we can show (like any stable first-order difference equation) to be equivalent to a range of comparable “routine” profit margins plus a weighted random error time series.

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.

Naive analysts use the normal (Gauss-Laplace) distribution to compute the mean and standard deviation, or quartiles, without verifying if the data are abiding. Double fault is committed when they propose a “broad and unconvincing” range of data, such as the interquartile range (IQR), which may become useless to determine arm’s length (or reasonable) royalty rates. In practice, the interquartile range of royalty rates is used to help settle licensing disputes in tax or intellectual property valuation.