## Roe

Sales Net income

Assets

Sales Assets Total equity If we rearrange things a bit, ROE is:

Assets

Sales

Assets Total equity

Return on assets Profit margin X Total asset turnover X Equity multiplier

What we have now done is to partition ROA into its two component parts, profit margin and total asset turnover. The last expression of the preceding equation is called the Du Pont identity, after the Du Pont Corporation, which popularized its use.

We can check this relationship for Prufrock by noting that the profit margin was 15.7 percent and the total asset turnover was .64. ROE should thus be:

ROE = Profit margin X Total asset turnover X Equity multiplier = 15.7% X .64 X1.39

This 14 percent ROE is exactly what we had before.

The Du Pont identity tells us that ROE is affected by three things:

1. Operating efficiency (as measured by profit margin)

2. Asset use efficiency (as measured by total asset turnover)

3. Financial leverage (as measured by the equity multiplier)

Weakness in either operating or asset use efficiency (or both) will show up in a diminished return on assets, which will translate into a lower ROE.

Considering the Du Pont identity, it appears that the ROE could be leveraged up by increasing the amount of debt in the firm. It turns out this will only happen if the firm's ROA exceeds the interest rate on the debt. More important, the use of debt financing has a number of other effects, and, as we discuss at some length in Part 6, the amount of leverage a firm uses is governed by its capital structure policy.

The decomposition of ROE we've discussed in this section is a convenient way of systematically approaching financial statement analysis. If ROE is unsatisfactory by some measure, then the Du Pont identity tells you where to start looking for the reasons.

General Motors provides a good example of how Du Pont analysis can be very useful and also illustrates why care must be taken in interpreting ROE values. In 1989, GM had an ROE of 12.1 percent. By 1993, its ROE had improved to 44.1 percent, a dramatic

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

II. Financial Statements and Long-Term Financial Planning

3. Working with Financial Statements

CHAPTER 3 Working with Financial Statements improvement. On closer inspection, however, we find that, over the same period, GM's profit margin had declined from 3.4 to 1.8 percent, and ROA had declined from 2.4 to 1.3 percent. The decline in ROA was moderated only slightly by an increase in total asset turnover from .71 to .73 over the period.

Given this information, how is it possible for GM's ROE to have climbed so sharply? From our understanding of the Du Pont identity, it must be the case that GM's equity multiplier increased substantially. In fact, what happened was that GM's book equity value was almost wiped out overnight in 1992 by changes in the accounting treatment of pension liabilities. If a company's equity value declines sharply, its equity multiplier rises. In GM's case, the multiplier went from 4.95 in 1989 to 33.62 in 1993. In sum, the dramatic "improvement" in GM's ROE was almost entirely due to an accounting change that affected the equity multiplier and doesn't really represent an improvement in financial performance at all.

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### Responses

• ines
Has an equity multiplier of , total asset turnover of , and a profit margin of percent, then its ROE?
8 years ago