Expanding Two Factor ModelsDuPont Decomposition Example

Ted Mitchell

Two Factor Model of Hours as an input in Biz Cafe

• You are the Owner of the Biz-Café and are very interested in your Return on Equity, ROE

• Output = Conversion Rate x Input• Net Profit = Return on Equity x Amount of Equity• Z = ROE x Equity• You have other related models• Revenue = Revenue on Investment x Investment• R = Sales per Investment x Dollars of Investment• Total Investment = Leverage Ratio x Dollars of Equity• L = leverage x dollars of Equity

The amount of equity in the business is an important determinant of Profit

• Net Profit = Return on Equity x Amount of Equity

• Z = ROE x E• Sample Problem• The owner’s earnings, Z was higher in Store A

than in Store B. • Before we can identify and explain how much of

the difference in the net profit was due to a change in the amount of equity or the ROE

Amount of Equity an important determinant of the owner’s earnings

• We would like to have other important variables to be included in the explanation of Net Profit

• A variable such as Sales Revenue, R• A variable such as the total Investment, I

The Basic Two-Factor Model

• Net Profit = Return on Equity x Amount of Equity,

• Z = ROE x E• Z = (Z/E) x E

To include Revenue, R and Total Investment, I

• We use a process called expand, aggregate and decompose.

• Sometimes just called the “Decomposition

Process”• Goal: To Decompose the Two-Factor Model

into a richer Four Factor Model that includes Revenue and Total Investment

To include Revenue, R and Quantity sold, Q• Z = (Z/E) x E• The expansion of Z = (Z/E) x 1 x 1 x E• Changes nothing• the fact that 1 = R/R and 1 = L/L• Z = (Z/E) x (R/R) x (L/L) x E• Changes nothing• Combine The conversion ratios into an Aggregated Conversion Factor• Z = (Z x R x L)/(R x L x E) x E• Decompose the Aggregated Conversion Factor• Z = (Z/R) x (R/L) x (L/E) x E• Interpret the three new conversion factors• Z = Return on Sales x Investment Turnover x Debt leverage x Equity• Net Profit = ROS x Turnover x leverage x Equity• The Classic DuPont Model

Now explain the difference in Two Net Profits

• Net Profit= ROS x Turnover x Leverage x Equity• Any difference in the Net Profit=• any difference in the Return on Sales, ROS, x• any difference in Investment Turnover, x• any difference the Debit Leverage, x• any difference in the amount of Equity

Decomposition Process allows

• The decomposition of simple 2-factor investment model into richer explanations with more factors being made explicit

• Revenue and Leverage are always at work in the conversion of Equity into Net Profits

• But the Expansion, Aggregation and Decomposition made them explicit!

A 100 years ago the DuPont Family

• Was choosing between investing in a small start up called General Motors and another small firm

• Their business analyst decided that the Two factor model that explained profit from an investment was inadequate

Decomposition Process allows

• A move From• Net Profit = Return on Equity x Equity• To a 4-Factor Explanation of investment• Net profit =

ROS x Turnover x Debit Leverage x Equity• The DuPont legend was born

100 years later most have forgotten

• The decision was an investment problem that was to help explain the differences between the Returns on Equity between two investments

• Have forgotten that• Net Profit = Return on Sales x Turnover x Leverage

x Equity• But most finance textbooks show that• Net Profit/Equity = ROE • ROE = ROS x Turnover x Leverage

In Future Lectures

• Show how to measure the causes of the difference in Net Profit, ∆Z, in two locations

• 1) the difference in return on sales, I∆ROS• 2) the difference in the Turnover, I∆Turnover• 3) the difference in the owner’s Leverage, I∆leverage• 4) the difference in the amount equity invested, I∆E• ∆Z = I∆ROS + I∆Turnover + I∆leverage + I∆Equity

• Any Questions