## Thursday, October 06, 2011

### Return on Equity and the Dupont System

CFA Level 1 - Financial Ratios

DuPont System

A system of analysis has been developed that focuses the attention on all three critical elements of the financial condition of a company: the operating management, management of assets and the capital structure. This analysis technique is called the "DuPont Formula". The DuPont Formula shows the interrelationship between key financial ratios. It can be presented in several ways.

The first is:
Formula 7.41
 Return on equity (ROE) = net income / total equityIf we multiply ROE by sales, we get:Return on equity = (net income / sales) * (sales / total equity)Said differently: ROE = net profit margin * return on equity

The second is:                                                                                      Formula 7.42
 Return on equity (ROE) = net income / total equityIf in a second instance we multiply ROE by assets, we get:ROE = (net income / sales) * (sales / assets) * (assets / equity)Said differently:ROE = net profit margin * asset turnover * equity multiplier

Uses of the DuPont Equation

By using the DuPont equation, an analyst can easily determine what processes the company does well and what processes can be improved. Furthermore, ROE represents the profitability of funds invested by the owners of the firm.
All firms should attempt to make ROE as high as possible over the long term. However, analysts should be aware that ROE can be high for the wrong reasons. For example, when ROE is high because the equity multiplier is high, this means that high returns are really coming from overuse of debt, which can spell trouble.

If two companies have the same ROE, but the first is well managed (high net-profit margin) and managed assets efficiently (high asset turnover) but has a low equity multiplier compared to the other company, then an investor is better off investing in the first company, because the capital structure can be changed easily (increase use of debt), but changing management is difficult.

More Useful Dupont Formula Manipulations

The DuPont formula can be expanded even further, thus giving the analyst more information.

Formula 7.43
 ROE = (net income / sales) * (sales / assets) * (assets / equity)If in a third instance we substituted net income for EBT * (1-tax rate), we get:ROE =(EBT/sales) * (sales / assets) * (assets / equity)* (1-tax rate)

Formula 7.44
 ROE = (net income / sales) * (sales / assets) * (assets / equity)If in a forth instance we substituted EBT for EBIT - interest expense, we get:ROE = [EBIT / sales * sales / total assets - interest / total assets] * total assets / equity * [1 - tax / net before tax]Said differently: ROE = operating profit margin * asset turnover - interest expense rate * equity multiplier * tax retention

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