Sustainable Growth Rate: State the Equity and Financing Assumptions

Start with a reconciled equity roll-forward

Synthetic example, in millions: beginning common equity is 500, annual common income 100 and common dividends 40. Assume no issuance, repurchases, other comprehensive income or other equity movements. Retention is (100 − 40) / 100 = 60%, retained income 60 and ending equity 560. Equity growth is 60 / 500 = 12%.

Why the denominator changes the equation

These identities follow from ending equity = beginning equity + retained income. If x measures retained income divided by ending equity, then x = g / (1 + g), so g = x / (1 − x). If x uses the simple opening/closing average, then x = g / (1 + g / 2). Do not place an average-equity ROE into the ending-equity formula or treat all reported ROE fields as interchangeable. The identities assume the stated equity roll-forward, not an arbitrary collection of accounting adjustments.

SGR can involve new borrowing

Continue the hypothetical example with opening debt 250, so debt/equity is 0.50. To retain that ratio when equity reaches 560, debt becomes 280: an increase of 30. Assets financed by debt and equity rise from 750 to 840, or 12%, under the simplified balance sheet. Retained earnings fund 60 of the 90 increase and new debt funds 30. This is not growth financed entirely from internal cash.

• Keeping leverage constant does not mean debt stays constant or that additional loans are automatically available.
• For assets, sales and earnings to grow together, assume stable asset-to-sales requirements, profit margins, retention and financing policy.
• Retained earnings are an accounting equity movement, not a cash account. A cash forecast must separately include collections, payments and capital spending.
• Changing leverage alters the model assumptions and can change interest cost and risk. A higher equity multiplier does not guarantee better outcomes.

Use DuPont as a consistent decomposition

With matching definitions, ROE = (net income / revenue) × (revenue / assets) × (assets / equity). Multiplying by retention adds the payout assumption. Use the same asset and equity bases in the canceling terms. For a separate hypothetical case, a 10% net margin, asset turnover 1.5 and equity multiplier 2 give ROE 30%; retention 60% gives the product 18%. Whether that product directly represents period growth depends on the equity timing convention.

• Margins can change without immediate matching cash collections.
• Higher turnover can lower required assets, but may also reflect an unrepresentative denominator.
• Future investment returns may differ from historical ROE. A high past return is not evidence that all retained income can earn the same return.

Distinguish sustainable from internal growth

An internal-growth model excludes new external financing, while the SGR model permits borrowing that maintains its chosen leverage ratio. Under matching positive-input assumptions, borrowing capacity can raise modeled growth; the rates can coincide for an unlevered firm. IGR is a financing constraint, not a guaranteed minimum growth rate.

• With beginning total assets, the simplified internal equity-funded asset-growth term is ROA × b; with ending total assets, the matching conversion is x / (1 − x), where x = ROA × b. State the no-new-financing assumptions and asset definition.
• Do not assert SGR is always higher for losses, negative equity or incompatible return definitions.
• For zero income, the payout fraction is undefined. Losses, payouts above income, repurchases and other equity movements need an explicit forecast rather than an ordinary positive-growth interpretation.

Actual sales above the model are not proof of overtrading

A company can sell more using spare capacity, better turnover or existing cash. Conversely, growth below a computed SGR can still create a cash shortage if customers pay late or investment occurs before revenue. Review capacity, working capital, debt maturities and financing access. The model is a set of assumptions to test, not a diagnosis based only on two growth percentages.