About the Author

In this tutorial, I address a recent question by an EdgarStat subscriber:

I’ve been working with the EdgarStat database and using the Operating Assets Return (ROA) profit indicator. The issue is that [when] using this indicator... we can’t see the working capital adjustment option; there is only unadjusted ROA.

For my response, define Operating Assets = Accounts Receivable + Inventory + Net PPE, a composite (balance sheet) account. Net PPE denotes Property, Plant, and Equipment, net of Depreciation. In transfer pricing, operating assets (hereafter assets) can also be defined as “Working Capital,” which is the composite of Accounts Receivable + Inventory – Accounts Payable.

The sensible economic definition of assets = Net PPE because assets are accumulated (and depreciated) according to the perpetual inventory equation, and not according to the arbitrary (inconsistent) definitions of assets practiced in transfer pricing.

First, consider the assets adjusted operating profit margin (OPM) expressed as a percentage of the comparable companies’ revenue:

(1) P(*t*) = β R(*t*) + φ A(*t*) + U(*t*), β > 0 and φ ≥ 0,

where P is operating profit, R is revenue, A is operating assets, and U is the random uncertainty. The fiscal year index is *t* = 1 to T. Different authors use different definitions of operating assets.

The parameters β and φ are estimated using the online regression analysis from comparable companies’ data found in EdgarStat.

Equation (1) may show multicollinearity between R(*t*) and A(*t*), and the EdgarStat regression analysis function contains the VIF (variance inflation factor) to test the independence of the explanatory factors R(*t*) and A(*t*).

See: https://besjournals.onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2009.00001.x.

If the coefficient φ is insignificant (i.e., φ ≈ 0), the assets adjustment [φ A(*t*)] factor has no statistical support and must be abandoned because the true profit relationship is simpler:

(2) P(*t*) = β R(*t*) + U(*t*), β > 0

Also, the adjusted R^{2} of equation (1) should be higher than the unadjusted R^{2} of equation (2); otherwise, adding the second factor φ A(*t*) does not improve the profit indicator’s explanatory power (reliability).

Second, consider the ROA (return on assets) regression equation:

(3) P(*t*) = φ A(*t*) + V(*t*), φ > 0,

where V(*t*) is the random uncertainty.

The principle of parsimony (Occam's razor) can help decide between models (1), (2) or (3), and economic theory can postulate the apriori model to be tested. In turn, economic theory can represent the dominant or competing paradigms. See Thomas Kuhn, *The Structure of Scientific Revolutions* (4th edition), University of Chicago Press, 2012 [1962].

Substitute A = (Accounts Receivable + Inventory + Net PPE) into equation (3), and obtain:

(4) P(*t*) = φ (Accounts Receivable(*t*) + Inventory(*t*) + Net PPE(t)) + V(*t*),

which must be expressed with three separate regression coefficients:

(5) P(*t*) = φ_{1} Accounts Receivable(*t*) + φ_{2} Inventory(*t*) + φ_{3} Net PPE(*t*) + V(*t*),

The substitution above reveals that the ROA equation (5) includes the separate balance sheet items Accounts Receivable, Inventory, and Net PPE. The partial regression coefficients (φ_{1}, φ_{2}, φ_{3}) measure the reliability of the individual asset adjustment. Therefore, making an extra adjustment for the individual (disaggregated) balance sheet accounts in the ROA equation is redundant (inconsistent, unviable, algebraic nonsense).

See also: https://www.edgarstat.com/blog/tutorial-reliability-of-return-on-assets-as-a-profit-indicator/.

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