# Reverse Engineering Return On Equity

Financial ratios can be used to gauge the effectiveness of a management team, or to evaluate the value of the company's stock for purchase or sale. Ratios are generally accepted across many disciplines and provide an efficient way to organize large amounts of information into readable and analyzable output. While return on equity (ROE) has outstanding evaluation and predictive qualities, return on net operating assets (RNOA) complements ROE, filling in the gaps and assisting in the analysis of management's ability to run a company. In this article we'll explain how interpreting the numbers provides an in-depth evaluation of management's success in creating profitability and provides insight into long-term future growth rates.

## Return on Equity (ROE)

ROE is one of the most commonly used and recognized ratios to analyze the profitability of a business. To the common stockholder, it is an indication of how effective management has been with shareholders' capital after excluding payments to all other net capital contributors.

To derive and differentiate ROE from return on total equity:

﻿ \begin{aligned} &\text{Return on Total Equity} = \frac { \text{Net Income} }{ \text{Average Total Equity} } \\ \end{aligned}﻿

Then to make an accurate measure of the common shareholders measure:

﻿ \begin{aligned} &\text{ROE} = \frac { \text{Net Income} }{ \text{Average Common Equity} } \\ \end{aligned}﻿

Since ROE is an important indicator of performance, it is necessary to break the ratio into several components to provide an explanation of a firm's ROE. The DuPont model, created in 1919 by an executive at E.I. du Pont de Nemours & Co., breaks ROE into two ratios:

﻿ \begin{aligned} \text{ROE} &= \frac { \text{Net Income} }{ \text{Common Equity} } \\ &= \frac { \text{Net Income} }{ \text{Net Sales} } \times \frac { \text{Net Sales} }{ \text{Common Equity} } \\ \end{aligned}﻿

This reveals that ROE equals net profit margin times the equity turnover. The basic premise of the model implies that management has two options to increase its ROE and thus increase value to its shareholders:

• Increase the company's equity turnover and use equity more efficiently
• Become more profitable and subsequently increase the company's net profit margin

One of the most common ways to increase the efficiency of assets is to leverage them. Breaking down ROE even more reveals:

﻿ \begin{aligned} \text{ROE} &= \frac { \text{Net Income} }{ \text{Common Equity} } \\ &= \frac { \text{Net Income} }{ \text{Sales} } \times \frac { \text{Sales} }{ \text{Total Assets} } \times \frac { \text{Total Assets} }{ \text{Common Equity} } \\ \end{aligned}﻿

## Flaws in ROE

While the DuPont formula has proved useful for many years, it is flawed in its inability to separate the decisions regarding both operating and financing changes. For example, an analyst noting a decline in return on assets (ROA) might conclude that the company is experiencing lower operating performance when ROE increased through the use of leverage.

## Return on Net Operating Assets (RNOA)

RNOA, on the other hand, successfully separates financing and operating decisions and measures their effectiveness.

﻿ \begin{aligned} &\text{RNOA} = \frac { \text{OI} }{ \text{NOA} } \\ &\textbf{where:} \\ &\text{OI} = \text{operating income, after tax} \\ &\text{NOA} = \text{net operating assets} \\ \end{aligned}﻿

By isolating the NOA, no incorrect conclusions can be drawn from the ratio analysis, thus repairing the missing link form the original DuPont model. Isolating the components also means that changing debt levels do not change operating assets (OA), the profit before interest expense, and the RNOA.

﻿ \begin{aligned} &\text{ROE} = \text{RNOA} + ( \text{FLEV} \times \text{Spread} ) \\ &\textbf{where:} \\ &\text{FLEV} = \text{financial leverage} \\ \end{aligned}﻿

OR

﻿ \begin{aligned} \text{ROE} = &\ \text{Return From Operating Activities} \ + \\ &\ \text{Return From Non-Operating Activities } \\ \end{aligned}﻿

## Comparing Companies

The best way to understand RNOA and ROE is to compare historical periods across many companies: Between 1963 and 1999, the median ROE achieved by all publicly traded U.S. companies was 12.2%. This ROE is driven by RNOA as illustrated in the following median values:﻿﻿

*Numbers in the table are medians (50th percentile) and quartiles (25th or 75th percentile); thus, the equation does not exactly equal ROE.

The data shows that companies in general are financed rather conservatively as expressed with FLEV< 1.0 and have greater portions of equity in their capital structures. On average, companies are rewarded with a positive spread on money borrowed at 3.9%but this is not always the case, as seen in the lowest 25% of companies. The most important conclusion from the output is that RNOA averages approximately 82% of ROE (10% / 12.2%).

## Bottom Line

ROE is a widely used financial ratio used to evaluate management's ability to run a company. Unfortunately, comparing the ratios between two companies or year-over-year might lead to the wrong conclusion based solely on those results. The DuPont formula does not separate the operating and non-operating performance and it allows the use of leverage to misrepresent the results.

Taking the model one step farther by analyzing RNOA provides a much clearer picture of performance by focusing on operational functions. Once ROE is broken down into RNOA, FLEV and Spread, one can make more accurate predictions of long-term future growth rates using the formula's output.

Article Sources
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1. Review of Accounting Studies. "Ratio Analysis and Equity Valuation: From Research to Practice," Page 129.

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