# DuPont Identity

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DuPont Identity
An expression that breaks return on equity (ROE) down into three parts: profit margin, total asset turnover and financial leverage. It is also known as "DuPont Analysis".

DuPont identity tells us that ROE is affected by three things:
- Operating efficiency, which is measured by profit margin
- Asset use efficiency, which is measured by total asset turnover
- Financial leverage, which is measured by the equity multiplier

ROE = Profit Margin (Profit/Sales) * Total Asset Turnover (Sales/Assets) * Equity Multiplier (Assets/Equity)

If ROE is unsatisfactory, the Du Pont identity helps locate the part of the business that is underperforming.

Here is how the DuPont identity is derived:

ROE = NI/TE
Multiply by 1 (TA/TA) and then rearrange
ROE = (NI / TE) (TA / TA)
ROE = (NI / TA) (TA / TE) = ROA * EM
Multiply by 1(S/S) and then rearrange
ROE = (NI / TA) (TA / TE) (S/S)
ROE = (NI / S) (S / TA) (TA / TE)
ROE = PM * TAT * EM
ROE = Profit Margin * Total Asset Turnover * Equity Multiplier

When:
ROE = Return on Equity
NI = Net Income
TE = Total Equity
TA = Assets
ROA = Return on Assets
EM = TA/TE = 1 + D/E = The Equity Multiplier
S = Sales

Investment dictionary. . 2012.

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