## 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 assets is a component of return on equity, both of which can be used to calculate a company's rate of growth.

#### LEARNING OBJECTIVE

• Discuss the different uses of the Return on Assets and Return on Assets ratios

#### KEY POINTS

• Return on equity measures the rate of return on the shareholders' equity of common stockholders.
• Return on assets shows how profitable a company's assets are in generating revenue.
• In other words, return on assets makes up two-thirds of the DuPont equation measuring return on equity.
• Capital intensity is the term for the amount of fixed or real capital present in relation to other factors of production. Rising capital intensity pushes up the productivity of labor.

#### TERMS

• return on common stockholders' equity

a fiscal year's net income (after preferred stock dividends but before common stock dividends) divided by total equity (excluding preferred shares), expressed as a percentage

• quantitatively

With respect to quantity rather than quality.

#### EXAMPLE

• A company has net income of 500,000. It has total assets valued at 3,000,000. Its retention rate is 80%, and its shareholder equity is equal to \$1,500,000. What is the company's ROA and internal growth rate? What is the company's ROE and sustainable growth rate? ROA = 500,000/3,000,000 = 17% Internal growth rate = 17% x 80% = 13% ROE = 17% x (3,000,000/1,500,000) = 34% Sustainable growth rate = 34% x 80% = 27.2%

#### Return On Assets Versus Return On Equity

In review, return on equity measures the rate of return on the ownership interest(shareholders' equity) of common stockholders. Therefore, it shows how well a company uses investment funds to generate earnings growth. Return on assets shows how profitable a company's assets are in generating revenue. Return on assets is equal to net income divided by total assets.

This percentage shows what the company can do with what it has (i.e., how many dollars of earnings they derive from each dollar of assets they control). This is in contrast to return on equity, which measures a firm's efficiency at generating profits from every unit of shareholders' equity. Return on assets is, however, a vital component of return on equity, being an indicator of how profitable a company is before leverage is considered. In other words, return on assets makes up two-thirds of the DuPont equation measuring return on equity.

#### ROA, ROE, and Growth

In terms of growth rates, we use the value known as return on assets to determine a company's internal growth rate. This is the maximum growth rate a firm can achieve without resorting to external financing. We use the value for return on equity, however, in determining a company's sustainable growth rate, which is the maximum growth rate a firm can achieve without issuing new equity or changing its debt-to-equity ratio.

#### Capital Intensity and Growth

Return on assets gives us an indication of the capital intensity of the company. "Capital intensity" is the term for the amount of fixed or real capital present in relation to other factors of production, especially labor. The underlying concept here is how much output can be procured from a given input (assets!). The formula for capital intensity is below:

Capital Intensity=Total Assets Sales

The use of tools and machinery makes labor more effective, so rising capital intensity pushes up the productivity of labor. While companies that require large initial investments will generally have lower return on assets, it is possible that increased productivity will provide a higher growth rate for the company. Capital intensity can be stated quantitatively as the ratio of the total money value of capital equipment to the total potential output. However, when we adjust capital intensity for real market situations, such as the discounting of future cash flows, we find that it is not independent of the distribution of income. In other words, changes in the retention or dividend payout ratios can lead to changes in measured capital intensity.