Week 4 The Du Pont Equation

Week 4: Lecture

Summary—The Du Pont Equation (so called because the Du Pont company first used it)

The Du Pont equation allows you to analyze the components of return on equity (ROE), which can give you additional insight about why the ROE ratio is what it is.

Note: The equation presented here is called the “modified” version of the Du Pont equation because it is an expanded version of the Du Pont equation presented in the M: Finance textbook on pages 62-66.  There are many versions of the Du Pont equation, but the one here is the one we like best.

The modified Du Pont Equation:

ROE = Net Profit Margin x Tot Asset Turnover x Equity Multiplier*
This is the same as:        
Net Income
Common Equity		 = Net Income
Sales		 x Sales
Tot Assets		 x Tot Assets
         Common Equity        

      *Sidenote;  The equity multiplier (EM) is the inverse of the equity-capital ratio we calculated before.  It is just the same ratio 'upside-down!' 

Using this equation you can “take apart” a company’s ROE ratio to see what components make up its value.

For example, for Amalgamated Hat Rack in 2016:
ROE, which is .194 = 347,500
3,200,000		 x 3,200,000
3,461,000		 x 3,461,000
1,785,00
.194, or 19.4% = .1086, or 10.86% x .9246 x 1.93


Examining the terms on the right-hand side of the equation, we make the following observations:

  • Net profit margin, at just under 11%, accounts for about a bit over half of Amalgamated’s ROE
  • Asset Turnover, at .9246, or $0.9246 for each dollar of assets deployed, is pushing ROE down slightly (10.86% profit margin x .9246 asset turnover = 10.05% ROE)
  • If Amalgamated Hat Rack had no debt (debt would make the last term in the equation 1.0) then Amalgamated’s ROE would be only 10.86% x .9246 = 10.05%. However, ROE is actually 19.4%. Therefore, ROE is getting a huge boost from something and that something is the equity multiplier term (92.46% x 20.98 = 19.4%). This is called the leverage effect.
  • The leverage effect explains why firms that use a lot of debt financing (and, therefore, risk) tend to have higher ROE’s than firm’s that stay with equity financing.

Summary
Can you see how our use of the Du Pont equation allowed us to analyze the sources of Amalgamated Hat Rack’s ROE? We knew the company’s ROE was 19.4%, which looks pretty good. Upon further analysis, however, we found that a little over half of the 19.4% came from the profits the firm earned on sales of its products, and that would have been a little higher but for the fact that Amalgamated’s assets don’t quite produce enough in profits for each dollar of assets employed. Finally, whatever return the firm’s operations produced was nearly doubled by the fact that those operations were financed with debt – In other words, Amalgamated is making a lot of money by using other people’s money.