DuPont Analysis

DuPont analysis is a method of financial statement analysis that decomposes return on equity into the component ratios that produced it, so a change in the return can be attributed to profit margin, to how hard the asset base works, or to borrowing, instead of being read as one number. It is an identity rather than a measurement: the factors always multiply back to the same return on equity they were taken from, so the analysis explains a figure without ever revising it.

The name comes from the DuPont company. Donaldson Brown developed the expanded return on investment measure now called the DuPont formula in 1914 (Flesher and Previts, Accounting Historians Journal). What he set out was a decomposition of return on investment rather than of return on equity, and the leverage factor arrived later, when the accepted goal of financial management shifted toward the owners’ return (Small Business Institute Journal, Ratio Analysis Featuring the DuPont Method).

The Three-Step Form

The common form splits return on equity into three factors.

ROE  =  (net income / revenue) x (revenue / total assets) x (total assets / equity)

     =    net profit margin    x     asset turnover      x  equity multiplier

Each factor is a ratio with an entry of its own. Net profit margin is net income over revenue for the period. Asset turnover is revenue over the asset base, and the family it belongs to is set out in asset turnover ratios. The equity multiplier is total assets over shareholders’ equity, and it is the only factor that carries the funding mix.

The algebra is what makes it a decomposition rather than a model. Revenue appears once on top and once underneath, and so does total assets, so both cancel.

(net income / revenue) x (revenue / total assets) x (total assets / equity)

    =  net income / equity

Multiply only the first two factors and revenue cancels on its own, leaving net income over total assets, which is why return on assets sits inside this chain as its first two terms.

Every factor here runs on revenue rather than on the narrower net sales caption, a distinction asset turnover ratios works through, and on total assets and total shareholders’ equity read off one balance sheet, which is the convention the chain in equity multiplier uses. An averaged version of both denominators is also in circulation, and the cancellation holds only while every factor uses the same figure, so a factor lifted out of one chain will not reconcile with a ratio computed the other way. Why the averaged convention exists is worked through in return on assets formula.

The Five-Step Form

The extended form opens up the margin term, separating what interest and income tax take from what the operations earned.

ROE  =  (net income / pretax income) x (pretax income / EBIT) x (EBIT / revenue)
          x (revenue / total assets) x (total assets / equity)

     =       tax burden          x     interest burden      x  operating margin
          x    asset turnover        x   equity multiplier

Pretax income, EBIT, revenue and total assets each appear once on top and once underneath, so the chain collapses to net income over equity exactly as the shorter one does. The first three factors multiply out to net income over revenue, so the five-step form is the three-step form with the margin opened up.

Tax burden is net income over pretax income, the share of pretax profit left after income tax expense, which makes it one minus the effective tax rate rather than that rate itself. Interest burden is pretax income over EBIT, earnings before interest and taxes, and it reads as one for a business with no borrowing cost. The third factor, EBIT over revenue, is usually called operating margin, and it is the same idea as the ratio set out in operating margin without being the same figure: that one stops at the income from operations subtotal, while EBIT sits above interest and tax and so carries whatever non-operating income the statement reports.

CFA Institute sets out the same decomposition, noting that many levels of it are possible and describing the five-component version as expressing return on equity as a function of a company’s tax rate, interest burden, operating profitability, efficiency and leverage (CFA Institute, Financial Analysis Techniques). The phrase many levels is doing real work: five-step names no single formula, because the extended model Hawawini and Viallet set out, restated in the Small Business Institute Journal, rebuilds the balance sheet around invested capital instead of total assets and renames the factors to match. The labels are not fixed either, so the same factor travels under more than one name: that restatement calls net income over pretax income the tax effect ratio, and pretax income over EBIT the financial cost ratio. Two five-factor chains can therefore disagree while both are right.

A Worked Example

Say a client’s statements for one closed year carry the figures below.

Revenue                                     5,000,000
EBIT                                          625,000
Interest expense                              125,000
Pretax income                                 500,000
Income tax expense                            150,000
Net income                                    350,000
Total assets                                2,500,000
Total shareholders' equity                  1,000,000

three-step
  net profit margin      350,000 / 5,000,000  =  0.07
  asset turnover       5,000,000 / 2,500,000  =  2.00
  equity multiplier    2,500,000 / 1,000,000  =  2.50
  product                0.07 x 2.00 x 2.50   =  0.35

five-step
  tax burden             350,000 / 500,000    =  0.70
  interest burden        500,000 / 625,000    =  0.80
  operating margin       625,000 / 5,000,000  =  0.125
  asset turnover       5,000,000 / 2,500,000  =  2.00
  equity multiplier    2,500,000 / 1,000,000  =  2.50
  product      0.70 x 0.80 x 0.125 x 2.00 x 2.50  =  0.35

read directly           350,000 / 1,000,000   =  0.35

All three routes land on the same return, because they are the same division written three ways.

Reading the Decomposition in Client Work

The point of the exercise is that the same return can be assembled from very different businesses.

                  margin    turnover   multiplier    ROE
client A            7.0%      2.00        2.50      35.0%
client B           14.0%      1.25        2.00      35.0%

Client A earns little on each dollar of sales and makes it up by turning its asset base over quickly and by carrying more debt. Client B earns twice the margin on a slower asset base and borrows less. A partner looking only at the return sees two identical clients, and the decomposition is what separates a margin story from an asset efficiency story from a funding story.

The same logic reads a move across two years. If the return rises while margin and turnover sit where they were, the multiplier moved, and what improved was the funding mix rather than the trading. That is a useful finding and an uncomfortable one, because leverage lifts the return whether or not the borrowed money earns more than it costs.

One caution belongs with it. Because the identity always balances, a factor can move for reasons that have nothing to do with performance: a change of averaging convention, a reclassification between operating and non-operating captions, or a year end draw on a line of credit will all show up as a shift in one of the terms.

What DuPont Analysis Is Not

Return on Equity

Return on equity is the ratio. DuPont analysis is the decomposition of that ratio, so it revises no return the direct division already produces: the factors are new figures, the return they multiply back to is not. A chain that lands somewhere other than net income over equity has a convention mismatch in it, not a better answer.

A Ratio of Its Own

There is no ratio called the DuPont ratio. Every number the framework yields is either one of the component ratios or the return itself, which is why a request for a client’s DuPont analysis is a request for the whole breakdown rather than for one figure.

Common Questions

Accountably places trained offshore accountants and tax preparers inside US CPA and EA firms, and a trial task lets a firm grade a real block of its own work before a client’s ratio analysis depends on it.