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.
The OECD is enamored with the present value of intangibles. To check this paramour, suppose that we don’t have historical (past) data and must rely on projections of sales attributed to certain identifiable intangibles that need to be valued. The present value of projected taxable profits expected from identifiable intangibles can be determined using two formulae, depending on available information. For intangible assets, the stream of taxable profits is called royalties.
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 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.
We can determine a present value of identifiable assets, including a present value of specific intangible assets, from knowledge about their (a) initial investment, (b) comparable operating rate of return, and (c) estimated useful lives. For this purpose, CAPM (capital asset pricing model) is inapplicable to determine comparable operating rates of return for intangible assets because CAPM is designed to estimate rates of return of traded equity shares, which reflect a stream of prospective dividends plus share price variation (capital gains or loss) during a certain period, and not a prospective stream of operating profits attributed to specific intangibles. For a given enterprise, streams of dividends and capital gains and their calculated risks (measured during a specified useful period) are unlikely to be discounted or capitalized by an operating rate of return attributed to intangible assets. Inter alia, intangible assets are not frequently traded in ask-bid exchange markets and subject to speculative capital gains.
We started (1988) in transfer pricing oriundo from academia, and the IRS dominant paradigm was forcing single point estimates of gross profit indicators in audit. This IRS practice included gross profit margin (expressed as a percent of net sales) for controlled inbound distributors, and gross profit markup (expressed as a percent of cost of goods sold (COGS)) for controlled outbound manufacturers. The Berry ratio (gross profits/operating expenses (XSGA)), introduced by Charles Berry in Du Pont, was an unspecified “fourth” method applied to service providers (like DISA) because they may not recognize labor costs in COGS. Functions performed are reflected in COGS and XSGA. See United States Court of Claims. E. I. Du Pont de Nemours and Company v. The United States, Nos. 256-66 & 371-66, April 18, 1978. (Cite as: 1978 WL 3449 (Ct. Cl. Trial Div.)).
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.
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.
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:
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.
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