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# DuPont analysis

Ratios must be looked at in the context of the industry and ratio from one category must be used to refine/corroborate conclusion reached by other ratios.

DuPont Analysis is one such example of integrated ratio analysis. It decomposes the return on equity into its different sources which helps in understanding the differences between ROE of different companies.

We start with ROE and do some basic algebraic manipulation to derive the DuPont relationship:

$ROE=\frac{Net\ Income}{Average\ Shareholders\ Equity}\times\frac{Average\ Total\ Assets}{Average\ Total\ Assets}\times\frac{Sales}{Sales}$ $ROE=\frac{Net\ Income}{Sales}\times\frac{Average\ Total\ Assets}{Average\ Shareholders\ Equity}\times\frac{Sales}{Average\ Total\ Assets}$ $ROE=Net\ Profit\ Margin\times Financial\ Leverage\ Ratio\times Total\ Assets\ Turnover$

This shows that a company’s return on equity depends on its net profit margin (i.e. profitability), financial leverage (use of debt) and asset turnover (efficiency).

We can also use similar manipulation to shows that:

$ROE=ROA\times Leverage$

We can further breakup the net profit margin to show the effect of interest and taxes as follows:

$ROE=TB\times IB\times EBIT\ Margin\times Total\ Asset\ Turnover\ \times Leverage$

Where TB is the tax burden and it equals the ratio of net income to pretax income, and IB is interest burden which equals pretax income divided by EBIT.

This decomposition shows that a company’s ROE would higher if its taxes are lower, interest expense is lower, operating margin is higher, efficiency (asset turnover) is higher and/or financial leverage is higher.