How sustainable growth works

Sustainable growth is the rate of sales (and asset) growth a firm can fund from retained earnings without issuing new equity and without changing its payout, its margin, or its equity multiplier:

$$g = \text{ROE} \times b$$

$b$ is the retention ratio, $1$ minus payout. On $45,000 of net income, $18,000 of dividends and $300,000 of book equity, payout is 40 percent, retention is 60 percent, and return on equity is 15 percent. Then $g = 0.15 \times 0.60 = 0.09$, 9 percent.

The payout ratio calculator on this page builds $g$ from the same three lines, so ROE and retention cannot be typed from different years. How the payout ratio works owns the 40 percent. This page owns the 9 percent.

How DuPont analysis works splits that ROE into margin, turnover and the equity multiplier. If those pieces stay put, $g$ is the growth the retained residual can fund.

Net income $60,000, dividends $0, equity $600,000. Payout is 0 percent. Retention is 100 percent. ROE is 10 percent. g is 10 percent.

With $b = 1$, every unit of ROE is kept, so sustainable growth equals ROE. That is the identity, not a claim that the firm should pay nothing. The first sheet kept 60 percent of a 15 percent ROE and printed 9 percent. This sheet keeps all of a 10 percent ROE and prints 10 percent. Ranking on ROE and ranking on g are not the same order.

How the payout ratio works owns the 0 percent split. This page owns the g that equals ROE when nothing is paid.

Net income $80,000, dividends $40,000, equity $400,000. Payout 50 percent, retention 50 percent, ROE 20 percent. g is 10 percent.

ROE rose from 15 percent to 20 percent. Retention fell from 60 percent to 50 percent. g only moved from 9 percent to 10 percent. Ranking on ROE and ranking on g are not the same order.

How the Gordon growth model works uses a $g$ in a price. That $g$ is an assumed perpetual dividend growth rate. This $g$ is an accounting identity on one year's sheet. Mixing them is how a 9 percent book $g$ gets read as next year's coupon growth.

The word sustainable here means internally fundable at the current mix, not guaranteed. If the payout rises, $b$ falls and $g$ falls even if ROE does not move. If the margin compresses, ROE falls and $g$ falls. If the equity multiplier changes, ROE changes and $g$ follows.

Write $g = \text{margin} \times \text{turnover} \times \text{equity multiplier} \times b$ and every piece has to hold for the 9 percent to repeat. That is a teaching condition, not a forecast.

How ROE works is the one division. This page is that rate times retention.

It is not a CAGR. CAGR is a root on two balances over $t$ years. This $g$ is one year's identity.

It is not PEG growth. PEG divides a P/E by expected EPS growth points, often an analyst number. Sustainable $g$ is ROE times retention on this book.

It is not a required return. The Gordon denominator is $k - g$. This page is only $g$.

It is not a sales forecast, not a two-stage DCF, and not a target of 9 percent. The three sheets are 9 percent on $45,000 of profit, $18,000 of dividends and $300,000 of equity (15 percent ROE times 60 percent retained), 10 percent when payout is 0 on $60,000 of profit, and 10 percent on 20 percent ROE times 50 percent retained. This is educational material, not financial advice.