# Principles of Finance/Section 1/Chapter 6/Corp/ROE

## Return On Equity

Return on Equity is an important financial ratio used to compare companies. It is also commonly used as a target for executive compensation. For example, a CEO might have to earn a 15% ROE for the year in order to get his bonus. Targets like these are designed to help shareholders by giving management an incentive to perform better.

ROE is defined as Net Income divided by Shareholder's Equity. However, there are other ways to calculate it. One common way is by using Return on Assets (ROA = Net Income/Assets), which may be easier to calculate, and the debt to equity ratio, in addition to information about tax and interest rates.

${\displaystyle ROE=(1-T)\left[ROA+(ROA-I){\frac {D}{E}}\right]}$

## DuPont Identity

The DuPont Identity is a financial tool that can be used to see how three main factors affect ROE:

• Profit Margin - Net Profit/Sales
• Asset Turnover - Sales/Assets
• Leverage Ratio - Assets/Equity

${\displaystyle ROE={\frac {NetProfits}{Sales}}*{\frac {Sales}{Assets}}*{\frac {Assets}{Equity}}}$

Suppose XYZ Corp. has a profit margin of 20%, asset turnover of 300%, and a leverage ratio of 50%. What would their return on equity be?

We can see that this relatively simple calculation is:

${\displaystyle ROE=.2*3*.5=30\%}$

The DuPont Identity allows us to see that ROE is a complex measure. A company with a low profit margin may have a strong ROE if it is not levered up very much. The equation can be rearranged to solve for missing values, as in the following example:

Suppose ABC Corp. has a 10% profit margin, an ROE of 30%, sales of $2000, and equity of$1000. What is the value of its assets?

By plugging in the values given, we can solve for assets = \$500

${\displaystyle .3=.15*{\frac {2000}{x}}*{\frac {x}{1000}}}$

${\displaystyle x=500}$