# RoyaltyStat Blog

## Ednaldo Silva

Ph.D. Economics from U.C. Berkeley. Founder & Director of RoyaltyStat. Developer of the TNMM = CPM.

### Recent Posts

Innovate, innovate, says Schumpeter and his prophets, because innovation is associated with cost reduction and increased profits. However, many controlled (within group) corporate reorganizations lack economic substance because they violate this basic principle of innovation. Ergo, an objective of innovation is to reduce average costs and therefore to increase profits.  We provide a theorem and include an arithmetic proof that cost-reducing innovations (holding the product or service price constant) increase profits.

The comparable uncontrolled price (CUP) method is described in US Treas. Reg. §1.482-3(b).

We hold that the empirical verification of CUP transactions is best measured by regression analysis.

Segue a reliable method to determine the arm's length profit margin of each selected comparable company to benchmark the tested party. For each selected comparable company, we measure Total Costs (Lato) = COGS + XSGA + (DP – AM). In Standard & Poor's Global (Compustat) mnemonics, COGS is cost of goods sold, XSGA is operating expenses, DP is the depreciation of property, plant & equipment (PPENT), including AM that is the amortization of acquired intangibles. Denote C as Total Costs (Lato) and S as Net Sales, which for each selected company is the sum of the unit price of the individual goods and services offered by the enterprise during the fiscal year multiplied by the respective quantity supplied:

(1)     S(t) = C(t) + P(t)

for t = 1 to T fiscal periods.

We have well-specified “return on assets” showing that we must estimate reduced-forms (instead of structural) equations and ran away from using this scrappy financial ratio to determine arm’s length profits subject to corporate income taxes. However, criticism is valid if we can provide a better substitute that can satisfy two conditions: First, the new alternative theory (markup pricing) resolves certain knotty issues of the old theory (such as avoid the cloudy base of “return on assets”); and second, the new theory provides more reliable measures of arm’s length profits. We hold that markup pricing-based profits are superior to “return on assets” respecting these two conditions.

Assets are heterogeneous making cross-companies comparisons difficult. We may get relief knowing that the specific assets composing the “perpetual inventory” dynamic equation of company growth rates can be restricted to property, plant & equipment (PPE); however, different start or acquisition dates (called vintages) and different depreciation rates make PPE also difficult to compare across companies.

In transfer pricing, certain analysts prefer using “return on assets” even for businesses such as wholesale or retail trade in which assets are not expected to have a significant impact on operating profits. These analysts postulate a simple linear relationship between operating profits and accounting assets (variously defined) and calculate quartiles without respite. The econometric model underlying the single-variable computation of the quartiles of “return on assets” can be written as:

(1)     P(t) = β K(t) + U(t)

for t = 1 to T years of each selected comparable.

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 sales or 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 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: