Tutorial: Reliability of Return on Assets as a Profit Indicator

March 08, 2021 by Ednaldo Silva
About the Author
Ednaldo Silva
(Ph.D. Econ.) is a leading economist with over 25 years’ experience in transfer pricing and the valuation of intangibles.
He is founder and managing director of RoyaltyStat, a boutique data, software and consulting firm specializing in transfer pricing and intellectual property solutions. Dr. Silva was first Sr. Economic Advisor at the IRS Office of Chief Counsel, a drafting member of U.S. 26 IRC section 1.482 transfer pricing regulations, and introduced the “comparable profits method” (CPM in the US and TNMM in the OECD), “best method” rule and the concept of arm’s-length represented by a range of results, rather than point estimate.
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The fascination with the return on assets (ROA) profit indicator in transfer pricing is naïve. See Regs. § 1.482-5(b)(4)(i) (Rate of return on capital employed). I agree with Schumpeter (1954), p. 561, that “In every scientific venture, the thing that comes first is vision.


Theories of return on assets are opaque. E.g., Solow (1964) mixes “capital” assets (stock) with investment flow (“the central concept in capital theory should be the rate of return on investment”). Solow (1964), p. 16. See also pp. 53, 73, 76, 86-87.

Stigler (1963, p. 54) uses total assets (stock) but makes a hyperbolic claim about investments: “There is no more important proposition in economic theory than that, under competition, the rate of return on investment tends toward equality in all industries.” Italics added.

The pater of American capital theory is Fisher’s (1930) concept that “capital” (asset value, a “fund”) is the present value of prospective profits, discounted by a predetermined interest rate on sovereign bonds.

According to Fisher, “Capital, in the sense of capital value, is simply future income discounted or, in other words, capitalized. The value of any property, or rights to wealth, is its value as a source of income and is found by discounting that expected income…. The bridge or link between income and capital is the rate of interest…. The value of capital must be computed from the value of its estimated future income, not vice versa.” Italics in original.

The return on assets as a profit indicator has no reliable theoretical support. Assets are ill-defined and there is confusion of “capital” as the book value of property, plant & equipment reported on the company’s balance sheet, the calculated present value of discounted prospective net profits, and the flow capital expenditure (CAPX) reported on the company’s cash flow statement.

Under oligopoly, cross-industry equality of return on investment is not expected because the profit margin (an element of return on investment) is a nonlinear function of the local company’s market share. See Varian (1992), pp. 289-290.

Heterogeneous Assets

In addition, “operating assets” is a nebulous account in transfer pricing. See Regs. § 1.482-5(d)(6) (Operating assets). If only the combined (aggregated) balance sheet “fixed assets”:

(a) Property,

(b) Plant and

(c) Equipment

are the defined operating assets, the three aggregated stock accounts perform different functions, and they exhibit different depreciation rates.

Leased assets further complicate the comparability of the asset composition between the tested party and the comparables.

Despite Regs. § 1.482-5(d)(6) definition that operating assets must include “current assets” (such as cash, cash equivalents, accounts receivable, and inventories), cash and equivalents cannot be added to operating assets because they yield no return. Perhaps cash equivalents can yield the short-term interest rate, but not ROA.

Inventories cannot be added to “operating assets” because inventory changes are incorporated in the cost of goods sold (included in the numerator of return on assets), and the inventory account may be mixed with related party transactions. Imputing the rate of return to accounts receivable is an adjustment fudge.

If the tested party (taxpayer) is the manufacturer purchasing raw materials or purchasing intermediate goods from affiliates, or if the distributor or the retailer purchases finished goods for resale from affiliates, inventories are mixed with related party accounts.

Moreover, inventories are valued using different accounting methods and are not subject to depreciation.

The same related party problem exists with accounts receivable or with accounts payable involving affiliated entities. Thus, these mixed accounts cannot compose “operating assets” because they distort the base of return on assets.

Aggregating heterogeneous balance sheet accounts mixed with related party activities, showing varying depreciations schedules, including assets with zero depreciation rate, is not reliable. See Brief (1986).

Summa Sine Laude

Return on assets is a controversial profit indicator to use in transfer pricing because operating assets are not well-defined in theory, and the regulatory guidance is vague. Accounting measures of operating assets provide no solace.

As a result, the aggregation of heterogeneous assets that compose the return on assets base (denominator) is likely to be contentious.

Despite several application problems (see below), return on assets was asserted by the U.S. Tax Court in Coca-Cola v. Commissioner of IRS, Docket No. 31183-15, 115 T.C. No. 10, released Nov. 18, 2020.

The Court did not disclose the IRS search criteria but stated that the search included worldwide companies in SIC code 2086 (disregarding the geographic location comparability factor of Regs. § 1.482-1(d)(4)(ii) (Different geographic markets)). To check the IRS win, I searched for companies in SIC code 2086 (Bottled and canned soft drinks) in EdgarStat®, dated March 6, 2021.

I used the search criteria:

  1. SIC code 2086
  2. Report date from 2007 to 2009
  3. Revenue > 0 in the selected years
  4. Operating Profit > 0 in the selected years

Only 31 companies were found, including eight companies using the Coca-Cola trade name.

The quartiles of the 92 individual observations of ROA ranges from 6.548% to 18.985%, and the median = 10.755%. The average ROA = 15.165% and the STDEV = 15.148%, so the coefficient of variation is undesirable at about one. The interquartile range (IQR) is very wide, exceeding 10% points difference between the upper and lower quartiles. Several companies have missing data.

Next, I ran three regressions online in EdgarStat. In two regressions, Operating Profit is the dependent variable and Revenue or Operating Assets is the independent variable. In the third, Revenue is the dependent variable and Total Cost is the independent variable:

Hypothesis 1, Operating Profits are determined by Revenue:

(1)   Operating Profit = 0.2045 Revenue – 167.8654
      Newey-West t = 8.481                       −2.1369
      R2 = 0.8755, Count 93 annual observations.

The operating profit margin = 20.45% is the regression coefficient of model (1) multiplied by 100. This profit specification (1) suffers from omitted variable upward bias.

Hypothesis 2, Operating Profits are determined by Operating  Assets:

(2)  Operating Profit = 0.2126 Operating Assets − 232.5386
      Newey-West t = 18.7868                                −3.5254
      R2 = 0.9338, Count 91 annual observations

where Operating Assets = Total Assets – (Short Term Investments + Long Term Investments).

The return on operating assets = 21.26% is the regression coefficient of model (2) multiplied by 100.

Hypothesis 3, Prices are determined by a fixed markup on Total Cost:

(3)  Revenue = 1.2452 Total Cost – 170.4642
      Newey-West t = 36.2737          −1.8799
      R2 = 0.9913, Count 93 annual observations.

where Total Cost = Direct Expense + Indirect Expenses.

The operating profit markup factor = 1.2452 (markup = 24.52%). The operating profit margin = 19.69% of regression (3) is obtained by indirect least squares (ILS), calculated using the formula (regression coefficient – 1) / regression coefficient = (1.2452 – 1) / 1.2452 = 19.69%.

Among the three rival regressions, model (3) is superior in this case because 99.13% of the variation in Revenue can be explained by the variation in Total Cost. The Newey-West residual variance corrected t-Statistics = 36.2737 is the highest (most reliable) of the three regressions.

The IRS applied no economic or statistical analysis to the return on assets in Coca-Cola v. Commissioner (this ROA fascination was contagious because it was not rebutted and influenced the court).

No economic expertise is required (as expressed in the IRS work in Coca-Cola narrated by the court) to (i) select a group of companies located in different countries with different population sizes, different levels of per capita income, and different trade (tariff and foreign exchange control) regimes, and (ii) calculate quartiles of the univariate return on assets—i.e., Operating Profits divided by Operating Assets.

However, the absence of economic and statistical analyses leaves the naïve IRS approach in Coca-Cola vulnerable to protest.



Richard Brief (editor), Estimating the Economic Rate of Return from Accounting Data, Routledge, 1986.

Irving Fisher, The Theory of Interest, Macmillan, 1930. (My Kindle edition has no page numbers.)

Joseph Schumpeter, History of Economic Analysis, Oxford University Press, 1954.

Robert Solow, Capital Theory and the Rate of Return, Rand McNally, 1964.

George Stigler, Capital and Rates of Return in Manufacturing Industries, Princeton University Press, 1963.

Hal Varian, Microeconomics, (3rd edition), Norton, 1992.

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