Accounting measures of assets are amorphous making them difficult to compare across companies. 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 otherwise comparable companies.

In transfer pricing, problems of comparing amorphous assets are exacerbated because regulatory misguidance includes inventory, accounts receivable, and accounts payable in the definition of operating assets. But such inclusions are not warranted. First, for a “tested party” (controlled entity) importing goods and services from affiliates both inventory and accounts payable are contaminated with related-party transactions; thus, they cannot compose the assets base to determine arm’s length profits. Second, for a tested party exporting goods and services to affiliates accounts receivable are not free of related party transactions; thus, accounts receivable cannot compose the assets base to determine arm’s length profits. Also, these short-term assets (inventory, accounts receivable) and liabilities (accounts payable) are not subject to depreciation as PPE, and thus aggregating them with PPE may produce bias.

Including long-term liabilities in operating assets is also misconceived because liabilities are not subject to depreciation and their interest payments are reported *after* operating profits. Therefore, we can get more traction in theory and empirical measurements when operating assets become restricted to PPE. In this regard, the accounting concept of investment = CAPX is misspecified because investments must include compensation of employees, an important account that is not disclosed to the US Securities & Exchange Commission (SEC).

Assume, *arguendo*, that gross investments ≡ CAPX ≡ G (*i*.*e*., excluding compensation of employees), and define PPE (net of depreciation of tangible assets, excluding amortization of acquired intangibles or intangible impairment charges) ≡ K, we posit the *growth rate* of gross investment:

(0) g(*t*) ≡ G(*t*) / K(*t* – 1)

If, despite our alarm that accounting assets are unreliable, a transfer pricing analyst insists in using assets as the base to determine comparable operating profits, we offer another look at ROA (“return on assets”).

Defining P(*t*) ≡ EBIT (operating profits after depreciation; again, excluding amortization of acquired intangibles or excluding depletion) and U(*t*) ≡ random error, we posit:

(1) P(*t*) = β K(*t*) + U(*t*) is the operating profit equation;

(2) K(t) ≡ G(*t*) + (1 – δ) K(*t* – 1) is the perpetual inventory equation considering *t* = 1 to T years of data for each comparable company. See e.g. Kuh (1963), equation 2.3, p. 9, and Maddala (1977), pp. 142-146.

We can’t estimate the structural (behavioral) equation (1) because K(*t*) is *endogenous* and we must consider structural equation (2) to obtain a reduced-form equation:

*t*) = β G(

*t*) + β (1 – δ) K(

*t*– 1) + U(

*t*)

We obtain ROA by dividing reduced-form equation (3) by K(*t* – 1):

*t*) / K(

*t*– 1) = β g(

*t*) + β (1 – δ) + V(

*t*)

where the intercept = β (1 – δ), the denominator K(*t* – 1) is lagged one period, and V(*t*) is the new random error.

Equation (4) means that the ROA (“return on assets,” where assets are restricted to PPE) of a selected comparable company is *proportional* to the rate of its “capital accumulation” g(*t*) plus an intercept. The denominator of ROA is K(*t*) in structural equation (1), and it's K(*t* – 1) using the proper reduced-form equation (3). However, model (3) has the disadvantage of not being intuitive.

It’s a tall order to assume that in cross-sections of comparable companies g(*t*) are constant such that ROA become uniform among them. In fact, it’s difficult to hold that the assumed depreciation rate (δ) is the same among the selected comparables, and so it’s likely that both g(*t*) and the intercept differ between selected comparables and that the expected “invisible hand” of gravitation (tendency towards a single ROA among the comparables) is not achieved.

In sum, the selection of ROA in transfer pricing is clogged with avoidable problems and, perhaps for this same reason, it’s an open grotto for game playing. The Hermes’ thread out of this labyrinth is to produce profit indicators based on more reliable data than accounting measures of assets. We prefer to calculate more reliable profit margins for controlled importers and profit markups for controlled exporters both based on the reduced-form of the price plus profit markup equation.

**Reference**

Edwin Kuh, *Capital Stock Growth* (A Micro-Econometric Approach), North-Holland, 1963.

G. Maddala, *Econometrics*, McGraw-Hill, 1977.

**Ednaldo Silva**(Ph.D.) is founder and managing director of RoyaltyStat. He helped draft the US transfer pricing regulations and developed the comparable profits method called TNNM by the OECD. He can be contacted at: esilva@royaltystat.com

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