Return on equity (ROE) and return on assets (ROA) are two of the most important measures for evaluating how effectively a company’s management team is doing its job of managing the capital entrusted to it. The primary differentiator between ROE and ROA is financial leverage or debt. Although ROE and ROA are different measures of management effectiveness, the DuPont Identity formula shows how closely related they are.

## The Formula for ROE:

﻿\begin{aligned} &\text{ROE} = \frac{ \text{Net Income} }{ \text{Shareholder Equity} } \\ &\textbf{where:}\\ &\text{Shareholder Equity} = \text{Assets} - \text{Liabilities} \\ \end{aligned}﻿

## The Formula for ROA:

﻿\begin{aligned} &\text{ROA} = \frac{ \text{Net Income} }{ \text{Total Assets} } \\ &\textbf{where:}\\ &\text{Total Assets} = \text{Shareholder Equity} + \text{Liabilities} \\ \end{aligned}﻿

## Main Differences

The way that a company's debt is taken into account is the main difference between ROE and ROA. In the absence of debt, shareholder equity and the company's total assets will be equal. Logically, their ROE and ROA would also be the same.

But if that company takes on financial leverage, its ROE would rise above its ROA. By taking on debt, a company increases its assets thanks to the cash that comes in. But since shareholder equity equals assets minus total debt, a company decreases its equity by increasing debt.

In other words, when debt increases, equity shrinks, and since shareholder equity is the ROE's denominator, its ROE, in turn, gets a boost.

## ROE and The DuPont Identity

The DuPont identity explains the relationship between both ROE and ROA as measures of management effectiveness. It's a popular formula that's another way of looking at ROE. The DuPont Identity divides ROE into three core components:

﻿\begin{aligned} &\text{ROE} = \text{Profit Margin} \times \text{Asset Turnover} \times \text{SE} \\ &\textbf{where:}\\ &\text{SE} = \text{Shareholder equity} \\ &\text{Profit Margin} = \frac{ \text{Net Income} }{ \text{Total Assets} } \\ &\text{Asset Turnover} = \frac{ \text{Revenue} }{ \text{Total Assets} } \\ &\text{Financial Leverage} = \frac{ \text{Total Assets} }{ \text{SE} } \\ \end{aligned}﻿

The first half of the equation, (net income divided by total assets) is actually the definition of ROA, which measures how efficiently management is using its total assets (as reported on the balance sheet) to generate profits (as measured by net income on the income statement).

The second half of the equation is called financial leverage, which is also known as the equity multiplier. A higher proportion of assets compared to shareholder equity demonstrates the extent to which debt (leverage) is used in a company’s capital structure.

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## An Example

ROE and ROA are important components in banking for measuring corporate performance. Return on equity (ROE) helps investors gauge how their investments are generating income, while return on assets (ROA) helps investors measure how management is using its assets or resources to generate more income.

In 2013, banking giant Bank of America Corp (BAC) reported a ROA of 0.50%. Its financial leverage was 9.60. Using both equated to a ROE of 4.8 percent, which is a pretty low level. For banks to cover their cost of capital, ROE levels should be closer to 10 percent. Prior to the financial crisis of 2008-09, Bank of America reported ROE levels closer to 13 percent and ROA levels closer to 1 percent.

## The Bottom Line

There are key differences between ROE and ROA that make it necessary for investors and company executives to consider both metrics when evaluating the effectiveness of a company's management and operations. Depending on the company, one may be more relevant than the other—that's why it's important to consider ROE and ROA in context with other financial performance metrics.