Can you walk through the retention rate and ROE relationship to sustainable growth with a detailed example?

The sustainable growth rate (g = b x ROE) tells you how fast a company can grow earnings and dividends without issuing new equity or changing its capital structure. Let's connect it to DuPont decomposition.

DuPont Breakdown of ROE:

ROE = Net Profit Margin x Asset Turnover x Equity Multiplier

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

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

Detailed Example — Thornbury Industries:

What Happened? Thornbury increased leverage (equity multiplier from 2.0 to 2.5), which boosted ROE from 24% to 30% and sustainable growth from 14.4% to 18.0%.

The Leverage Trap:

While higher leverage mathematically increases ROE and sustainable growth, it also:

• Increases financial risk and probability of distress
• Raises the required return on equity (cost of equity increases)
• May not actually increase firm value if the higher growth is fully offset by higher risk

When Sustainable Growth Breaks Down:

1. Company issues new equity: g = b x ROE no longer applies because equity base changed externally
2. ROE is temporarily inflated by one-time gains
3. Company is at maximum debt capacity (cannot increase leverage further)

CFA Exam Application: If a vignette shows ROE increasing solely due to leverage, recognize that the sustainable growth rate increase may be illusory — the higher required return could offset it entirely.

Practice DuPont-linked growth problems in our CFA question bank.