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The “return on assets” is an unsatisfactory profit level indicator (PLI) for the “transactional” net margin and comparable profits methods in transfer pricing because (among other major defects) self-developed intangibles are excluded from the assets base denominator. Assets are also composed of heterogeneous balance sheet accounts with different depreciation rates.

Operating assets are “solid, massy, hard” and cannot be moved from one company to another within the same industry (horizontal market consolidation) or across companies in different industries (vertical market consolidation), without a time-consuming assets purchase agreement. Moreover, if the intra-company assets transfers are large, anti-trust regulatory impediments may occur.

The idea that “return on assets” is a superior PLI because of its fluent or gravitation properties is not consistent with reality. This dubious return on assets sobriquet is posited as a matter of faith because to our knowledge economics is devoid of rigorous demonstrations of the conditions required for such gravitation to occur in actual industries dominated by oligopoly groups.

We showed in a prior blog post that operating assets at the beginning of the year, and not assets at the end of the year, are the proper base denominator for return on assets:

     (1)     P(t) = ρ K(t – 1)

where the dependent variable P(t) denotes operating profits in fiscal year t = 1 to T, the “independent” variable K(t – 1) denotes operating assets at the beginning of the year, and the parameter ρ (return on assets) is the estimated regression coefficient (for simplicity of exposition, we don’t write the error term on regression equation (1) above or on (3) below).

One claim (hypothesis) made in transfer pricing is that intangible assets yield a higher expected return than tangible assets (how about the relative standard errors?).

Here, we devise a statistical test of this return on assets inequality hypothesis and describe a major practical difficulty in performing this test. For this purpose, we divide assets into two separate tangible and intangible configuration:

     (2)     K(t) = K_τ(t ) + K_ι(t)

where the Greeks tau denotes tangible and iota denotes intangible assets.

Another contradictory claim made in transfer pricing is that ρ_τ = ρ_ι = ρ, which assumes the same return between tangible and intangible assets. This assumption, which is implied in regression equation (1), is not consistent with the rival claim that ρ_ι is greater than ρ_τ.

We substitute (2) into (1), and write:

     (3)     P(t) = ρ_τ K_τ(t – 1) + ρ_ι K_ι(t – 1)

which allows ρ_ι to diverge from ρ_τ without imposing an untested hypothesis that they are equal.

In practice, we don’t have information about K_ι because (under local GAAP or under IFRS) listed companies are not obligated to disclose self-developed intangibles. The intangible assets recorded on the balance sheet (both amortizable intangibles and goodwill) of listed companies are acquired; they are not intangible assets resulting from the cumulative investments in research & development, software, or advertising.

As a result of this accounting grace, we need to compute K_ι per company using the perpetual inventory method (PIM) because acquired intangibles may have a tenuous (immaterial) relationship with generating operating profits. However, calculating an annual series of aggregate or company-level K_ι (intangible assets) is not trouble-free because the PIM formula depends on ρ.

Thus, return on assets suffers from circularity disorders because assets are not independent variables. For the apparent circularity of the PIM formula, see Lange (1969), pp. 101-102 (equation 1a), Allen (1963), p. 176, Patterson & Schott (1979), pp. 48-49, Garegnani (1990), p. 14 (equation II.5').

Also, the computation of self-developed (organic) intangible assets is intractable because listed companies are not obligated to disclose software or advertising investments, which are treated as undisclosed expenses under current accounting principles.

Thus, even if we can capitalize research & development expenses using PIM, the resulting intangible assets would be under-estimated because of undisclosed information about cumulative advertising expenses creating marketing intangibles. This same problem affects software development expenses, which are not capitalized on the balance sheet of listed companies.

E.g., in 1994 the US Securities and Exchange Commission (SEC) issued Financial Reporting Release No. 44 (FRR No. 44), which no longer required the disclosure of advertising expenses. Research indicates that after 1994 the disclosure of advertising by US listed companies declined, which makes the computation of self-developed marketing intangibles and related tests of comparable DEMPE activity difficult. 

Conclusions

We draw très tristes conclusions discouraging using the return on assets (PLI) in the “transactional” net margin and comparable profits methods.

First, the equalizing gravitation of “solid, massy, hard” heterogeneous assets is an ideal, an apparent myth, which can’t be confused with the complex (balance sheet) reality of the selected comparables.

Second, the claim that the return of intangible assets is higher than the return of tangible assets remains an untested hypothesis (it’s hearsay).

Third, acquired intangible assets cannot be used to test the postulated return on assets inequality (ρ_ι > ρ_τ) because the functional relationship between acquired assets and operating profits requires a factual determination, and cannot be assumed à priori.

This means that it’s improper to include acquired (instead of self-developed) intangibles in the regression equation (1) or (3).

In sum, return on assets is an unsatisfactory PLI because the operating assets base denominator is an ill-defined composite of heterogeneous balance sheet accounts, excluding self-developed (production (trade), marketing and software) intangibles; therefore, it’s difficult to establish assets composition comparability between the tested party and its benchmark peers.

References

Roy Allen, Mathematical Economics (2^nd edition [1^st edition 1956]), Macmillan, 1963.

Roy Allen was known by three initial characters R. (Roy), G. (George), D. (Douglas) Allen (1906-1983), a British predilection for using multiple initials instead of writing a first name. Before the publication of Alpha Chiang’s excellent book, Fundamental Methods of Mathematical Economics, McGraw-Hill, 1967, Allen’s rich in economics content mathematical book was a standard reference. Allen wrote a more elementary mathematical book, Mathematical Analysis for Economists, Macmillan, 1938, which we hold in our library. In the first edition of James Henderson & Richard Quandt, Microeconomic Theory (A Mathematical Approach), McGraw-Hill, 1958, p. viii, the authors cite Allen (1938) as a preliminary reference.

Pierangelo Garegnani, “Quantity of Capital” in John Eatwell, Murray Milgate & Peter Newman (editors), Capital Theory, W. Norton, 1990 (first published in The New Palgrave Dictionary of Economics, Macmillan Press, the same editors, in four volumes, 1987). Garegnani was the most focused economist I’ve met.

Oskar Lange, Theory of Reproduction and Accumulation, Pergamon Press, 1969.

From the PIM (perpetual inventory method) equation, Lange (1969, pp. 101-102) developed the simpler to compute capital stock equation:

     K(t) = φ K(0), where (phi) φ = [(1 + γ)^t  − 1] / γ.

This K(t) formula represents the relationship between the initial value of the capital stock K(0), the growth rate (γ) of additional gross investments (CAPX), and the value of the capital stock in period t.

This same K(t) formula is found (without derivation) in several places, including Garegnani (1990), p. 14, and Allen (1970) (also without derivation), p. 176.

We have indicated that K(t) must be interpreted as the individual company (or aggregate) balance sheet composite account PPENT (property, plant and equipment), and not as total operating assets, which include cash & equivalents, accounts receivable and inventories.

Oskar Lange (1904-1965) and Michael Kalecki (1899-1970), another accomplished Polish economist, influenced my theoretical economics development in favor of indicative planning (plano de metas) against the myth of self-regulated markets. Another influence was Brazilian economist, Celso Furtado (1920-2004), who promoted import substitution industrialization (aka Verdoorn’s “law” in Europe) in developing countries against neo-mercantilist export promotion strategies expounded by a concerted British and American academic armada.

K. Patterson & Kerry Schott (editors), The Measurement of Capital (Theory & Practice), Macmillan, 1979. Papers from a conference at Southampton University (UK) in summer of 1976.

Newton’s expression that matter is “solid, massy, hard” recognizes that particles are moveable. See David Knight, Atoms and Elements, Hutchinson, 1967, pp. 5-6. Like other forms of matter, assets are moveable, and certain “liquid” or “portfolio” assets (such as cash and short-term investments) can move fast. However, “fixed” or depreciable assets (such as property, plant and equipment (PPENT)) are “putty clay”. Once installed, depreciable assets are difficult to move from one company to another.

Depreciable assets transfers can trigger slow-moving tax, anti-trust, and ecological events; as such, the notion that assets (which are stock and not flow variables) can flow by “invisible hands” (competition) from one company to another within and between industries to equilibrate the rate of return to a uniform parameter is an old-fashion analogy distant from company balance sheet reality.

The expression très tristes conclusions is a parody to Cabrera Infante’s novel, Tres Tristes Tigres (Three Trapped Tigers), Obras Completas, Vol. III, Galaxia Gutenberg [1966], 2016.