# What is your ROA? An investigation of the many formulas for calculating return on assets.

INTRODUCTION

A recent study by Mankin and Jewell (2010) of ratios in 77 current business textbooks made several interesting discoveries. The study included accounting, finance, management, marketing, and financial statement analysis textbooks. Two of the most interesting points are as follows. First, textbook authors are in unanimous agreement on how to calculate very few ratios. The current ratio, gross profit margin, and dividend yield are the most notable of these ratios. Second, most ratios, even the most commonly used ones, have several alternate formula versions. Common ratios with substantial disagreement in the formulas are return on assets, quick ratio and inventory turnover.

This research focuses on return on assets (ROA) because it is a popular ratio with many different formula variations. This paper will show the eleven different ratio formulas found in current business textbooks and propose three additional ROA formulas that would be possible based on the sample data.

LITERATURE REVIEW

Financial Ratios

Financial ratios are used for several important purposes. Whittington (1980) summarized two basic uses of financial ratios: normative and positive. Normative uses include measuring a firm's ratios to a standard such as another company or to an industry average. Positive uses include estimation of financial variables such as profit margins, returns, leverage, and stock prices. Positive uses can also include researchers using predictive models for corporate failure, bankruptcy, and credit risk.

Normative uses of financial ratios involve two primary functions: financial analysis and business education. Financial analysis involves evaluating a firm's profitability and riskiness and then comparing them to industry averages. Ratios generally involve a mathematical proportion of X / Y that allows analysts control in two ways (Barnes, 1987). First, ratios control for the size of the financial information. Because of this characteristic, different firms' current ratios can be compared even if the firms' current assets and/or current liabilities are not comparable. Second, ratios control for industry factors. Industries often have unique characteristics that are seen if a firm's financial ratios are compared to the industry average. It is axiomatic that a firm's financial ratios should be compared to industry averages. Both financial researchers (Lev, 1969) and textbook authors (White, Sondhi, & Fried, 2003) recommend that financial analysis should include industry averages. This type of recommendation is a normative use of ratios.

A second normative use of financial ratios includes their use in business education. Financial ratios are an important tool in business education. Students learn to use financial ratios in accounting, finance, marketing, and management classes. Huefner (2002) argued that financial ratio preparation and analysis is an important part of the very first accounting course. Recently, the New York State Society of Certified Public Accountants (NYSSCPA) has issued a white paper of educational goals for CPA candidates (Fierstein, 2008). The preparation and interpretation of financial ratios were included in the NYSSCPA goals for students preparing for careers as CPAs.

Besides normative uses, financial ratios also have positive uses. Positive uses of financial ratios include estimating certain financial variables or predicting future outcomes such as bankruptcy or business failure. Financial ratios are used in many financial research studies to predict certain outcomes. Several studies have tested whether financial ratios are normally distributed. For example, Deakin (1976) concluded that a normal distribution could not be assumed for financial ratios with the possible exception of the debt/assets ratio.

One of the more well-studied positive uses of financial ratios is in the area of business failures. Beaver (1966) used financial ratios of failed firms and non-failed firms to predict business failure. Since each ratio was analyzed separately, this was essentially a univariate technique. He identified financial ratios that were predictive in identifying failed firms. Altman (1968) expanded this into multivariate research by using multiple discriminant analysis (MDA). This research led to the Z-score model that is widely used in business failure analysis (Krantz, 2010). Altman (2000) later expanded the Z-score model into a second-generation predictive model called Zeta[R] analysis.

Return on Assets

Return on Assets (ROA) is one of the most popular and useful of the financial ratios. ROA has been used in industry since at least 1919 when the DuPont Company used it as the top of its ratio triangle system. The ratio was called return on investment and was calculated as Profit / Total Assets. The base of the DuPont triangle was the expanded ROA formula: Profit Margin (Profit / Sales) and Capital Turnover Ratio (Sales / Total Assets) (Horrigan, 1968).

The importance that educators and practitioners place on ROA can be seen in three ways. First, at least one ROA formula is presented in most business textbooks. ROA was the third most frequently presented ratio in a study of business textbooks, appearing in 70 of the 77 textbooks (Mankin & Jewell, 2010). Only the current ratio and inventory turnover ratio occurred more often than ROA.

Second, at least one version of ROA is used often in failure prediction studies. The original Altman (1968) Z-Score included ROA as one of its five factors used to predict business failure using a version defined as Earnings Before Interest and Taxes / Total Assets (EBIT / TA). Beaver (1966) also used ROA as one of the six ratios used to predict business failure. The ROA version in the Beaver study was Net Income / Total Assets (NI / TA). Hossari and Rahman (2005) ranked the popularity of all financial ratios used in studies predicting business failures. Their study included 53 previous studies from 1966 to 2002 and ranked 48 separate ratios. The ROA version Net Income / Total Assets (NI / TA) was the single most common ratio in all the failure prediction studies.

Third, analysts often use ROA in their investigation of a firm's financial position, performance, and future prospects. Gibson (1987) surveyed Chartered Financial Analysts about the importance of many financial ratios. The study included four different versions of ROA, and each version was selected by at least 90% of the CFA respondents as a primary measure of profitability.

Return On Assets In Textbooks

Of all of the ratios presented in business textbooks, authors disagree the most about return on assets. In the Mankin and Jewell (2010) study, 70 of the 77 textbooks included ROA. The study found eleven different versions of ROA in business textbooks. The different versions of ROA are shown in Table 1, along with the frequency with which they appear in the sample.

In the Table 1 data, 28 textbooks, or 40% of the textbooks in the sample, define ROA as Net Income / Total Assets. To simplify the discussion, a version number has been assigned to each ROA formula. So, the most popular formula for ROA has been assigned version 1, the second most popular is version 2, etc.

It is important to understand that Table 1 does not include "semantic" differences in how the ratio is defined or how the formula is displayed. Table 1 has standardized all insignificant differences in terminology, of which there were many. All eleven versions of ROA can be economically and mathematically different in different situations, sometimes by large amounts. Each version should also be defined and interpreted in slightly different ways in an economic or accounting sense. This idea will be expanded on later. It is also important to realize that each of the eleven versions was simply called "Return on Assets" or "Return on Total Assets" or some other synonymous term in the textbook. These naming issues have the potential to cause considerable confusion among students and practitioners who may assume that the version of ROA in a given textbook is the only version of ROA, or the definitive version of ROA.

This is not to say that the ratios above are only known as "Return on Assets." For example, five other textbooks in the sample include the ratio Earnings Before Interest and Taxes / Total Assets (EBIT / TA). However, in those five texts that ratio is known as "Basic Earnings Power." Therefore those five observations are not included in Table 1.

A few basic observations about the various versions of ROA can be made simply by noting the details of Table 1. First, the most widely used version of ROA is also the simplest version, Net Income / Total Assets (NI / TA). Second, the top two versions comprise about 56% of the sample, while the bottom nine versions comprise the other 44%. Third, several versions of ROA have identical numerators but differ in that one version averages total assets in the denominator while the other does not. Version 1 and 2 of ROA fit this pattern, as do versions 3 and 8, 4 and 9, and 6 and 11. So, out of the eleven versions of ROA there are only seven unique numerators. Fourth, the ratios can be categorized not only based on their denominators, but also based on the "size" of their numerators. The versions with Operating Profit, EBIT, or EBT in the numerator will obviously give answers of larger magnitude in most situations than those with after-tax numbers in the numerator.

Table 2 attempts to organize the various versions of ROA in a more logical manner. The ratios are separated based on whether or not the denominator averages total assets; they are also arranged in descending order of typical magnitude. Although the study found only eleven versions of ROA in textbooks, there are three additional valid versions that can be constructed by combining three of the existing numerators with average total assets as the denominator. These new versions are all denoted with a * on the version number. For example, there is no version of ROA in the sample defined as Earnings Available to Common Shareholders / Average Total Assets (EACS / ATA). This version is introduced in Table 2 and given the version number 14*. This new version 14* has the same numerator as ROA version 5. Table 2 also introduces an abbreviated formula for each version.

Since the versions are now organized in a logical way, the differences can be analyzed. The two denominators, total assets and average total assets, can be compared.

Why do some authors average total assets while others do not? It is interesting to note that of the 70 textbooks in the sample that include a formula for ROA, 29 (41.4%) of the texts average the total assets in the denominator while 41 (58.6%) of the textbooks do not. It is even more interesting to note that 24 of 29 (82.8%) of all the texts that use average total assets are accounting textbooks. The accounting texts used average total assets in 24 of the 28 (85.7%) textbooks. Only 4 of the 42 (9.5%) non-accounting texts used average total assets. The reason for this is very simple. ROA compares an income number (a flow measure) to total assets (a stock measure). Whenever comparing flow measures to stock measures accountants like to average the stock measure in order to preserve the matching principle. Apparently, however, the authors of the finance, management and marketing texts in the sample feel no compulsion to preserve the matching principle in their versions of ROA.

Comparing the Denominator

So what is the practical impact of averaging the denominator versus not averaging? A very simple example can answer this question. In this example, consider the two most basic and popular versions of ROA, versions 1 and 2. These two versions have the same numerator, net income, but version 2 averages the denominator while version 1 does not. Holding net income constant, each ratio is calculated for several years and several different levels of total assets. This will isolate the effect of averaging the denominator. Calculations are shown in Table 3.

There are several interesting observations can be made from this example. First, and most obviously, one extra year of ROA can be calculated with version 1. Since averaging the denominator requires two years worth of total assets, analysts must have at least two years of data before they can calculate an ROA with version 2. Second, based on the results for 2007, when total assets are falling, averaging the denominator yields a lower ROA (version 2 < version 1). Third, the reverse is true for 2008. When total assets are rising, averaging the denominator yields a higher ROA (version 2 > version 1). Fourth, focusing on 2007--2010, averaging the denominator may make ROA slower to recognize trends. In this case the firm appears to be adding non-productive assets (assets that do not contribute to income). This makes both ROA's fall, but version 1 begins to fall more quickly than version 2. The reverse would be true as well. If the firm were to shed inefficient assets the positive trend should be detected more quickly by version 1. Of course if variation in total assets were not informative for some reason, analysts would prefer an ROA that was less affected by the "noisy" changes. Assume for the moment that the variation of total assets from 2006--2008 was not meaningful. Version 2 has the advantage of being unaffected by these noisy changes in total assets. A summary of the advantages of each denominator can be found in Table 4.

Comparing the Numerator

Table 5 begins the process of comparing the seven different numerators. Once again simple examples will illustrate the practical differences between the ratios. In order to fully explore the differences between the seven numerators, ROA is calculated for eight different example firms. These example firms have identical operating income and total assets; however, they each differ in one important variable, such as interest expense. In order to simplify the analysis even further only a few firms will be compared at a time. The first comparison, highlighting the effects of non-operating items, appears in Table 5.

Table 5 compares Firm A, the base firm, to Firm B, which has non-operating income, and Firm C, which has non-operating losses. Note that version 7 of ROA is exactly the same for all three firms. Every other version is higher for firm B, due to the presence of non-operating income. Likewise, every other version is lower for firm C, due to the presence of non-operating losses. So, version 7 of ROA has the distinct benefit of being completely unaffected by non-operating items. This makes version 7 particularly useful when comparing different firms that have varying levels of non-operating items.

The second comparison, highlighting the impacts of interest expense, appears in Table 6. Here important differences among the various versions really start to emerge. In this example we are comparing Firm A, the base firm, to Firms D and E. Firm D is a low debt firm with low interest expense, while Firm E is a high debt firm with high interest expense. We can make four interesting observations from Table 6. The first two observations will certainly not be surprising, while the latter two may be.

First, both version 7 and 11 of ROA are completely unaffected by interest expense. Second, higher interest expense leads to lower values of ROA for versions 10, 1, 5. Comparing the results for Firm D and Firm E shows this. Third, higher interest expense leads to higher values of ROA for version 8. This seemingly perverse result actually makes sense if we interpret version 8 as being an "all investors" ROA. In other words, version 8 is measuring the total return on assets generated for both debt and equity holders. To restate, version 8 is measuring the total return on assets available to pay both debt and equity holders of the firm. Fourth, version 9, like versions 7 and 11, is also completely unaffected by debt levels and interest expense. However, since version 9 is based on Net Income it yields a smaller value than versions 7 or 11, which are both based on pretax numbers.

So, if an analyst wanted to compare the ROA's of various firms while eliminating any differences caused by debt policy he could use version 7 or 11 for a pre-tax ROA or version 9 for an after-tax ROA. If the analyst wanted to compare ROA's while considering the differences caused by debt policy, he would use version 10 for a pre-tax ROA or version 1 or 5 for an after-tax ROA. Finally, if an analyst wanted to know an "all investors" ROA she would use version 8.

Table 7 shows the effects of taxes and dividends on ROA. In this example, the base firm is compared to firms with different levels of taxes and dividends. Firm F has tax loss carry forwards that cut its tax expense for the current year in half. Firm G pays a preferred dividend, while firm H pays a common dividend. There are several observations we can draw from Table 7.

First, Firm F's tax situation highlights the fact that we have three pre-tax versions of ROA, versions 7, 11, and 10, and four after-tax versions of ROA, versions 8, 9, 1, and 5. The pre-tax versions of ROA are unaffected by Firm F's tax loss carry-forward. However, the after-tax versions of ROA all benefit from higher values caused by the reduced taxes. Second, Firm G's preferred dividend only affects version 5 of ROA, causing it to be lower than version 5 for the base firm. Since version 5 is the only version to subtract preferred dividends, it can be thought of as a "common shareholders ROA." Finally, it is interesting to note that all of the versions of ROA are identical for Firm A and Firm H. This highlights the fact that none of the versions of ROA are affected by common dividends.

The examples above illustrate that each version of ROA can be useful in the proper context. The various numerators are all measuring something slightly different. Table 8 summarizes the advantages of each numerator.

Earlier in the paper, the issue of "naming confusion" was mentioned. This "naming confusion" potentially arises from calling so many different formulas that all measure slightly different things "return on assets." To help alleviate this problem we propose new names for many of the versions of ROA. The proposed taxonomy serves two different purposes: the proposed names are descriptive of the mathematics involved with the ratio and the proposed names will help differentiate each version of ROA from every other version. The proposed taxonomy is shown in Table 9.

CONCLUSION

Return on assets (ROA) is a popular and well-known ratio. It is used by analysts to measure the profitability of a firm and by researchers to make predictions on financial variables and events. However, the current study shows that there are eleven different versions of ROA in current business textbooks. One of the problems with the existence of so many disparate versions is that it makes comparability between versions more difficult. Imagine analysts, sitting around a boardroom, or students in a study group attempting to discuss the ROA of a firm. Unless they have previously agreed upon the ROA version to be used, there could be considerable confusion. It is possible, even likely, that different participants will have different "correct" answers and draw different conclusions about the profitability of the firm depending on the version of ROA used.

Now imagine a student or a professional researching a firm using Yahoo! Finance, Morningstar, or any other financial data service. Unless she understands the version of ROA used by that site, she is very likely to misuse and misinterpret the data. This problem is compounded when comparing different ROA's from different data sources.

Therefore, based on the analysis above, it is appropriate not to think of ROA as a single ratio but as a "category of ratios." This category includes almost any ratio that compares an earnings related number from the income statement to Total Assets or Average Total Assets. This study shows each of the eleven versions of ROA can have a valid use in the proper context, but that none should be presented as the only or the definitive version of ROA. In the future, it would be beneficial for both students and practitioners if textbook authors would use names that would more accurately reflect the uses and highlight the differences among the various versions of ROA. Perhaps a decade from now, instead of multiple versions of ROA all sharing the same name, there will be a less confusing and more descriptive nomenclature in use.

REFERENCES

Altman, E. I. (1968). Financial Ratios Discriminant Analysis and the Prediction of Corporate Bankruptcy. Journal of Finance, 23(4), 589-609.

Altman, E. I. (2000). Predicting Financial Distress of Companies: Revisiting the Z-Score and Zeta[R] Models. Unpublished manuscript, New York University.

Barnes, P. (1987). The Analysis and Use of Financial Ratios: A Review Article. Journal of Business Finance & Accounting, 14(4), 449-461.

Beaver, W. H. (1966). Financial Ratios as Predictors of Failure. Journal of Accounting Research, 4(3), 71-111.

Deakin, E. B. (1972). A Discriminant Analysis of Predictors of Business Failure. Journal of Accounting Research, 10(1), 167-179.

Fierstein, S. S. (2008). Examination of Pre-Certification Education. The CPA Journal, 78(8), 26-33.

Gibson, C. (1987). How Chartered Financial Analysts View Financial Ratios. Financial Analysts Journal. May-June.

Horrigan, J. (1968). A Short History of Financial Ratio Analysis. Accounting Review, 43(2), 284-294.

Hossari, G., & Rahman, S. (2005). A Comprehensive Formal Ranking of the Popularity of Financial Ratios in Multivariate Modeling of Corporate Collapse. Journal of American Academy of Business, Cambridge, 6(1), 321-327.

Huefner, R. J. (2002). Redesigning the First Accounting Course. The CPA Journal, 72(10), 58-60.

Krantz, M. (2010). The Altman Z-Score: A Tool to Predict Financial Trouble. USA Today, July 13.

Lev, B. (1969). Industry Averages as Targets for Financial Ratios. Journal of Accounting Research, 7(2), 290-299.

Mankin, J. A. & J. J. Jewell (2010). A Sorry State of Affairs: The Problems With Financial Ratio Education. Unpublished working paper.

White, G. I., A. C. Sondhi & D. Fried. (2003). The Analysis and Use of Financial Statements (3rd ed.). Hoboken, NJ: John Wiley & Sons.

Whittington, G. (1980). Some Basic Properties of Accounting Ratios. Journal of Business Finance and Accounting, 7(2), 219.

Jeffrey J. Jewell, Lipscomb University

Jeffrey A. Mankin, Lipscomb University
```Table 1: ROA Formulas and Frequencies
(Mankin & Jewell, 2010)

Version                    Formula                   Number   Percent
in       in
Sample   Sample

1          Net Income / Total Assets                   28     40.00%

2          Net Income / Average Total Assets           11     15.71%

3          (Net Income + Interest Expense) /           8      11.43%
Average Total Assets

4          [Net Income + Interest Expense x            7      10.00%
(1-Tax Rate)] / Average Total Assets

5          Earnings Available to Common                5       7.14%
Shareholders / Total Assets

6          Earnings Before Interest and Taxes /        3       4.29%
Average Total Assets

7          Operating Profit / Total Assets             2       2.86%

8          (Net Income + Interest Expense) /           2       2.86%
Total Assets

9          [Net Income + Interest Expense x            2       2.86%
(1-Tax Rate)] / Total Assets

10         Earnings Before Tax / Total Assets          1       1.43%

11         Earnings Before Interest and Taxes /        1       1.43%
Total Assets

TOTALS                                                 70     100.00%

Table 2: ROA Versions by Size and Denominator

Version   Formula                             Abbreviated Formula

Panel A: Denominator = Total
Assets

7         Operating Profits / Total                 OP / TA
Assets

11        Earnings Before Interest and             EBIT / TA
Taxes / Total Assets

10        Earnings Before Tax / Total                EBT/TA
Assets

8         (Net Income + Interest Expense)      (NI + IntExp) / TA
/ Total Assets

9         [Net Income + Interest Expense    [NI + IntExp(1-T)] / TA
x (1--Tax Rate)] / Total Assets

1         Net Income / Total Assets                 NI / TA

5         Earnings Available to Common              EACS/TA
Shareholders / Total Assets

Panel B: Denominator = Average
Total Assets

12 *      Operating Profits / Average               OP / ATA
Total Assets

6         Earnings Before Interest and             EBIT / ATA
Taxes / Average Total Assets

13 *      Earnings Before Tax / Average            EBT / ATA
Total Assets

3         (Net Income + Interest Expense)     (NI + IntExp) / ATA
/ Average Total Assets

4         [Net Income + Interest Expense    [NI + IntExp(1-T)] / ATA
x (1--Tax Rate)] / Average
Total Assets

2         Net Income / Average Total                NI / ATA
Assets

14 *      Earnings Available to Common              EACS/ATA
Shareholders /Average Total
Assets

Table 3: The Impact of Averaging the Denominator

2006        2007        2008

Net Income       \$12,000     \$12,000     \$12,000
Total Assets    \$100,000     \$90,000    \$100,000

VERSION

1          NI / TA          12.00%      13.33%      12.00%
2          NI / ATA           --        12.63%      12.63%

2009        2010

Net Income       \$12,000     \$12,000
Total Assets    \$110,000    \$120,000

VERSION

1          NI / TA          10.91%      10.00%
2          NI / ATA         11.43%      10.43%

Table 4: Advantages of Each Denominator

Average Total   1. Preserves the matching principle
Assets
2. Less affected by "random" changes in total assets

3. Higher ROA when assets are rising

Total Assets    1. Simplicity

2. Requires less data to calculate ROA

3. Quicker to react to trends

4. Higher ROA when assets are falling

Table 5: The Effects of Non-Operating Items on ROA

FIRM A        FIRM B

Firm Description          Base     Non-Operating
Income

Total Assets                 \$500,000      \$500,000
Tax Rate                       40%           40%

Income from Operations       \$100,000      \$100,000
Plus: Non-Operating Income      0           10,000
EBIT                         100,000       110,000
Less: Interest Expense          0             0
EBT                          100,000       110,000
Less: Tax                     40,000        44,000
Net Income                    60,000        66,000
Less: Preferred Dividends       0             0
EACS                          60,000        66,000

VERSION

7             OP / TA                       20.00%        20.00%
11            EBIT / TA                     20.00%        22.00%
10            EBT / TA                      20.00%        22.00%
8             (NI + IntExp) / TA            12.00%        13.20%
9             [NI + IntExp(1-T)] / TA       12.00%        13.20%
1             NI / TA                       12.00%        13.20%
5             EACS / TA                     12.00%        13.20%

FIRM C

Firm Description        Non-Operating
Loss

Total Assets                    \$500,000
Tax Rate                          40%

Income from Operations          \$100,000
Plus: Non-Operating Income      (10,000)
EBIT                             90,000
Less: Interest Expense             0
EBT                              90,000
Less: Tax                        36,000
Net Income                       54,000
Less: Preferred Dividends          0
EACS                             54,000

VERSION

7             OP / TA                          20.00%
11            EBIT / TA                        18.00%
10            EBT / TA                         18.00%
8             (NI + IntExp) / TA               10.80%
9             [NI + IntExp(1-T)] / TA          10.80%
1             NI / TA                          10.80%
5             EACS / TA                        10.80%

Table 6: The Effects of Interest Expense on ROA

FIRM A     FIRM D     FIRM E

Firm Description               Base     Low Debt   High Debt

Total Assets                 \$500,000   \$500,000   \$500,000
Tax Rate                       40%        40%         40%
Income from Operations       \$100,000   \$100,000   \$100,000
Plus: Non-Operating Income      0          0           0
EBIT                         100,000    100,000     100,000
Less: Interest Expense          0        10,000     30,000
EBT                          100,000     90,000     70,000
Less: Tax                     40,000     36,000     28,000
Net Income                    60,000     54,000     42,000
Less: Preferred Dividends       0          0           0
EACS                          60,000     54,000     42,000

VERSION

7        OP / TA                       20.00%     20.00%     20.00%
11       EBIT / TA                     20.00%     20.00%     20.00%
10       EBT / TA                      20.00%     18.00%     14.00%
8        (NI + IntX) / TA              12.00%     12.80%     14.40%
9        [NI + IntX(1-T)] / TA         12.00%     12.00%     12.00%
1        NI / TA                       12.00%     10.80%      8.40%
5        EACS / TA                     12.00%     10.80%      8.40%

Table 7: The Effects of Taxes and Dividends on ROA

FIRM A           FIRM F

Firm Description                  Base           Tax Loss
Carryforwards

Total Assets                    \$500,000         \$500,000
Tax Rate                          40%              40%
Income from Operations          \$100,000         \$100,000
Plus: Non-Operating Income         0                0
EBIT                            100,000          100,000
Less: Interest Expense             0                0
EBT                             100,000          100,000
Less: Tax                        40,000           20,000
Net Income                       60,000           80,000
Less: Preferred Dividends          0                0
EACS                             60,000           80,000
Less: Common Dividends             0                0

VERSION

7          OP / TA                          20.00%           20.00%
11         EBIT / TA                        20.00%           20.00%
10         EBT/TA                           20.00%           20.00%
8          (NI + IntExp)/ TA                12.00%           16.00%
9          [NI + IntExp(1-T)] / TA          12.00%           16.00%
1          NI / TA                          12.00%           16.00%
5          EACS / TA                        12.00%           16.00%

FIRM G           FIRM H

Firm Description               Preferred          Common
Dividends        Dividends

Total Assets                    \$500000          \$500,000
Tax Rate                          40%              40%
Income from Operations          \$100,000         \$100,000
Plus: Non-Operating Income         0                0
EBIT                            100,000          100,000
Less: Interest Expense             0                0
EBT                             100,000          100,000
Less: Tax                        40,000           40,000
Net Income                       60,000           60,000
Less: Preferred Dividends        10,000             0
EACS                             50,000           60,000
Less: Common Dividends             0              10,000

VERSION

7          OP / TA                          20.00%           20.00%
11         EBIT / TA                        20.00%           20.00%
10         EBT/TA                           20.00%           20.00%
8          (NI + IntExp)/ TA                12.00%           12.00%
9          [NI + IntExp(1-T)] / TA          12.00%           12.00%
1          NI / TA                          12.00%           12.00%
5          EACS / TA                        10.00%           12.00%

Table 8: The Advantages of Each Numerator

Operating Profit     1. Unaffected by non-operating items, debt
levels, taxes, or dividends

2. Useful for comparing firms with different
exposure to non-operating items

EBIT                 1. Unaffected by debt levels, taxes, and
dividends

2. Useful for comparing pre-tax returns of
firms with different capital structures

EBT                  1. Unaffected by taxes and dividends

2. Useful for comparing firms with different
tax situations

(NI + IntExp)        1. Measures "all investors" ROA

2. Shows the total ROA available to "pay"
investors a return

[NI + IntExp(1-T)]   1. Eliminates the effects of different debt
levels and interest expense

2. Useful for comparing after-tax returns of
firms with different debt levels

Net Income           1. Simplicity

2. The "bottom line" ROA for all equity
holders

EACS                 1. The only version that considers preferred
dividends

2. The "bottom line" ROA for common
shareholders

Table 9: Proposed Taxonomy for the Different Versions of ROA

Version            Formula                   Proposed Name

7          OP / TA                    Operating Return on Assets

11         EBIT / TA                  Basic Earning Power (This
for this version)

10         EBT/TA                     Pre-tax Return on Assets

8          (NI + IntExp) / TA         All Investors Return on
Assets

9          [NI + IntExp(1-T)] / TA    Debt Neutral Return on
Assets

1          NI / TA                    Net Return on Assets

5          EACS/TA                    Common Shareholders Return
on Assets

12*        OP/ATA                     Operating Return on Average
Assets

6          EBIT / ATA                 Basic Earning Power of
Average Assets

13*        EBT / ATA                  Pre-tax Return on Average
Assets

3          (NI + IntExp) / ATA        All Investors Return on
Average Assets

4          [NI + IntExp(1-T)] / ATA   Debt Neutral Return on
Average Assets

2          NI / ATA                   Net Return on Average
Assets

14*        EACS/ATA                   Common Shareholders Return
on Average Assets
```
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