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Unformatted text preview: tements Analysis and LongTerm Planning 55 ros82361_ch03.indd 55 5/27/08 10:15:00 AM Confirming Pages
T ABLE 3.5 (continued ) IV. Profitability ratios Profit margin Net income __________ Sales Net income __________ Total assets Return on equity (ROE) ROE Net income __________ Sales Net income __________ Total equity Assets ______ Equity Return on assets (ROA) V. Market value ratios Priceearnings ratio _Sales _____ Assets Price per share ________________ Earnings per share Markettobook ratio Market value per share ___________________ Book value per share 3.3 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. A Closer Look at ROE
To begin, let’s recall the definition of ROE:
Return on equity Net income _____________ Total equity If we were so inclined, we could multiply this ratio by Assets/Assets without changing anything:
Return on equity Net income _____________ Total equity Net income _____________ Assets Net income _____________ Total equity Assets _____________ Total equity Assets ________ Assets Notice that we have expressed the ROE as the product of two other ratios—ROA and the equity multiplier:
ROE ROA Equity multiplier ROA (1 Debtequity ratio) Looking back at Prufrock, for example, we see that the debtequity ratio was .39 and ROA was 10.12 percent. Our work here implies that Prufrock’s ROE, as we previously calculated, is:
ROE 10.12% 1.39 14% The difference between ROE and ROA can be substantial, particularly for certain businesses. For example, BankAmerica has an ROA of only 1.32 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 14.80 percent, implying an equity multiplier of 11.21. We can further decompose ROE by multiplying the top and bottom by total sales:
ROE Sales ______ Sales Net income _____________ Assets Assets _____________ Total equity If we rearrange things a bit, ROE is:
ROE Net income _____________ Sales _Sales _______ Assets Assets _____________ Total equity Return on assets Profit margin Total asset turnover [3.20]
Equity multiplier 56 PART 1 Overview ros82361_ch03.indd 56 5/27/08 10:15:01 AM Confirming Pages
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 15.7% 14% Total asset turnover .64 Equity multiplier 1.39 This 14 percent ROE is exactly what we had before. The Du Pont identity tells...
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This note was uploaded on 10/28/2009 for the course FINA 505 taught by Professor Deborahcernauskas during the Summer '09 term at Northern Illinois University.
 Summer '09
 DeborahCernauskas
 Finance

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