Sustainable Growth Rate

How fast can a company grow without raising new equity or piling on debt? Only as fast as it grows its own capital base. Each year the equity grows by the profits kept back — retained earnings — and if the business keeps earning the same return on that bigger base, everything (equity, earnings, dividends) compounds at the same rate.

That rate is retention times return: keep fraction $b$ of an $ROE$ return, and equity grows by $b \times ROE$. A firm earning 15% and paying out a third can self-fund 10% growth — grow faster than that and the money must come from somewhere: new shares, more leverage, or a fatter ROE.

Equity next year is this year's equity plus retained earnings:

So equity growth is:

With a stable ROE and payout, earnings and dividends ride the equity base and grow at the same $g$ — which is exactly the $g$ the Gordon growth model asks for, closing the loop between statement analysis and valuation.

Estimating how fast a firm can grow without external financing, or deriving the growth input for a dividend discount / Gordon model from fundamentals.

Everything is assumed constant — ROE, payout, leverage — and in reality incremental ROE fades as companies scale past their best opportunities, making $b \times ROE$ an optimistic long-run ceiling. It also treats accounting ROE as the reinvestment return, inheriting every book-value distortion, and says nothing about whether retaining earnings is wise: a low-ROE firm retaining everything sustains growth in a business that may not deserve it.

The formula was popularized by Robert Higgins (1977), who asked the corporate treasurer's question — "how much growth can we afford?" — and by the Boston Consulting Group's growth-share planning of the same era. Bankers use it to spot companies growing faster than they can self-fund (a borrowing forecast in disguise), and equity analysts use $g = b \times ROE$ as the disciplined way to feed a growth rate into dividend discount models rather than guessing one.