## The Du Pont Identity

As we mentioned in discussing ROA and ROE, the difference between these two profitability measures is a reflection of the use of debt financing, or financial leverage. We illustrate the relationship between these measures in this section by investigating a famous way of decomposing ROE into its component parts. To begin, let's recall the definition of ROE:

Net income

Return on equity =-

Total equity

If we were so inclined, we could multiply this ratio by Assets/Assets without changing anything:

Net income Net income Assets

Total equity Total equity Assets

Net income Assets X

Assets Total equity

Notice that we have expressed the ROE as the product of two other ratios—ROA and the equity multiplier:

ROE = ROA X Equity multiplier = ROA X (1 + Debt-equity ratio)

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

II. Financial Statements and Long-Term Financial Planning

3. Working with Financial Statements

© The McGraw-Hill Companies, 2002

PART TWO Financial Statements and Long-Term Financial Planning

Du Pont identity

Popular expression breaking ROE into three parts: operating efficiency, asset use efficiency, and financial leverage.

Looking back at Prufrock, for example, we see that the debt-equity ratio was .39 and ROA was 10.12 percent. Our work here implies that Prufrock's ROE, as we previously calculated, is:

The difference between ROE and ROA can be substantial, particularly for certain businesses. For example, BankAmerica has an ROA of only 1.23 percent, which is actually fairly typical for a bank. However, banks tend to borrow a lot of money, and, as a result, have relatively large equity multipliers. For BankAmerica, ROE is about 16 percent, implying an equity multiplier of 13.

We can further decompose ROE by multiplying the top and bottom by total sales:

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