## The DuPont Equation, ROE, ROA, and Growth

As you read this section, you will learn about special ratios that address dividend growth, return on assets, and equity. You will be exposed to their formulas, how to compute them, and which financial statements contain the information needed to calculate the ratios. You will read about the DuPont Equation (also known as the strategic profit model), which comprises multiple financial ratios. You will also learn how to interpret the ratios and apply those interpretations to understanding the firm's activities.

Return on equity measures the rate of return on the ownership interest of a business and is irrelevant if earnings are not reinvested or distributed.

#### LEARNING OBJECTIVE

• Calculate a company's return on equity

#### KEY POINTS

• Return on equity is an indication of how well a company uses investment funds to generate earnings growth.
• Returns on equity between 15% and 20% are generally considered to be acceptable.
• Return on equity is equal to net income (after preferred stock dividends but before common stock dividends) divided by total shareholder equity (excluding preferred shares).
• Stock prices are most strongly determined by earnings per share (EPS) as opposed to return on equity.

#### TERM

• fundamental analysis

An analysis of a business with the goal of financial projections in terms of income statement, financial statements and health, management and competitive advantages, and competitors and markets.

#### EXAMPLE

• A small business' net income after taxes is $10,000. The total shareholder equity in the business is$50,000. What is the return on equity? ROE = 10,000/50,000 ROE = 20%

#### Return On Equity

Return on equity (ROE) measures the rate of return on the ownership interest or shareholders' equity of the common stock owners. It is a measure of a company's efficiency at generating profits using the shareholders' stake of equity in the business. In other words, return on equity is an indication of how well a company uses investment funds to generate earnings growth. It is also commonly used as a target for executive compensation, since ratios such as ROE tend to give management an incentive to perform better. Returns on equity between 15% and 20% are generally considered to be acceptable.

#### The Formula

Return on equity is equal to net income, after preferred stock dividends but before common stock dividends, divided by total shareholder equity and excluding preferred shares.

$\mathrm{ROE}=\frac{\text { Net Income(After Tax) }}{\text { Shareholder Equity }}$

Return On Equity: ROE is equal to after-tax net income divided by total shareholder equity.

Expressed as a percentage, return on equity is best used to compare companies in the same industry. The decomposition of return on equity into its various factors presents various ratios useful to companies in fundamental analysis.

$\mathrm{ROE}=\frac{\text { Net profit }}{\text { Equity }}=\frac{\text { Net profit }}{\text { Pretax profit }} \times \frac{\text { Pretax profit }}{\text { EBIT }} \times \frac{\text { EBIT }}{\text { Sales }} \times \frac{\text { Sales }}{\text { Assets }} \times \frac{\text { Assets }}{\text { Equity }}$

ROE Broken Down: This is an expression of return on equity decomposed into its various factors.

The practice of decomposing return on equity is sometimes referred to as the "DuPont System".

#### Potential Limitations of ROE

Just because a high return on equity is calculated does not mean that a company will see immediate benefits. Stock prices are most strongly determined by earnings per share (EPS) as opposed to return on equity. Earnings per share is the amount of earnings per each outstanding share of a company's stock. EPS is equal to profit divided by the weighted average of common shares.

$Earnings\;Per\;Share = \frac{\text { Profit }}{\text { Weighted Average Common Shares }}$

Earnings Per Share: EPS is equal to profit divided by the weighted average of common shares.

The true benefit of a high return on equity comes from a company's earnings being reinvested into the business or distributed as a dividend. In fact, return on equity is presumably irrelevant if earnings are not reinvested or distributed.