How do you derive the sustainable growth rate from the DuPont identity, and how does it connect to valuation?

The sustainable growth rate is the maximum rate a company can grow earnings without issuing new equity or changing its capital structure. It's foundational for any dividend discount model. Let me build the full derivation.

Starting Point

g = b x ROE

Where b = retention ratio = 1 - dividend payout ratio.

DuPont Decomposition of ROE

The 5-factor DuPont breaks ROE into:

ROE = (Net Income / EBT) x (EBT / EBIT) x (EBIT / Revenue) x (Revenue / Assets) x (Assets / Equity)

Or more commonly the 3-factor version:

ROE = Net Profit Margin x Asset Turnover x Equity Multiplier

ROE = (NI/Sales) x (Sales/Assets) x (Assets/Equity)

Therefore:

g = b x (NI/Sales) x (Sales/Assets) x (Assets/Equity)

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Worked Example: Castleton Industries (fictional)

Metric	Value
Net income	$48 million
Sales	$320 million
Total assets	$400 million
Total equity	$200 million
Dividends paid	$12 million

Step 1: Retention ratio = 1 - (12/48) = 1 - 0.25 = 0.75

Step 2: Net profit margin = 48/320 = 15.0%

Step 3: Asset turnover = 320/400 = 0.80x

Step 4: Equity multiplier = 400/200 = 2.00x

Step 5: ROE = 15.0% x 0.80 x 2.00 = 24.0%

Step 6: g = 0.75 x 24.0% = 18.0%

Connection to Valuation

In the Gordon Growth Model: P0 = D1 / (r - g). If Castleton pays D0 = $0.50 per share and the required return is 22%, then:

D1 = $0.50 x 1.18 =$0.59

P0 = $0.59 / (0.22 - 0.18) =$0.59 / 0.04 = $14.75

Critical Insight for Exams: If a company increases leverage (higher equity multiplier), ROE rises and so does the sustainable growth rate -- but this also increases financial risk, which should increase the required return r. Students often forget that changing one DuPont component has ripple effects on valuation through both numerator and denominator.

Practice more DuPont problems in our CFA question bank.