Questions: Sustainable Growth Rate and Retention Policy

Question 1

Firm A has ROE = 15% and a 40% dividend payout ratio. Firm B has ROE = 20% and an 80% dividend payout ratio. Which firm has the higher sustainable growth rate?

• A. Firm B — it has the higher ROE regardless of payout policy
• B. Firm A — SGR = 15% × 60% = 9% versus Firm B's 20% × 20% = 4%
• C. Firm B — SGR = 20% × 80% = 16% versus Firm A's 15% × 40% = 6%
• D. They are equal since both can issue equity to supplement internal growth

Answer: (B)

SGR = ROE × retention ratio = ROE × (1 − payout ratio). Firm A: 15% × 0.60 = 9%. Firm B: 20% × 0.20 = 4%. Despite Firm B's higher ROE, it retains only 20% of earnings, severely limiting self-financed growth. The common trap is focusing only on ROE — the interaction between ROE and retention determines SGR, and a high payout can overwhelm a high ROE.

Question 2

A technology firm has ROE = 25% and retains all earnings (payout ratio = 0). Its actual revenue is growing at 40% annually. What must be true?

• A. The firm's SGR is 40%, matching actual growth — high-growth firms automatically expand their SGR
• B. The firm's SGR = 25%; since actual growth exceeds this, it must be increasing debt or issuing new equity
• C. The firm is unsustainable and must immediately cut growth to 25%
• D. SGR does not apply to firms with zero dividend payout

Answer: (B)

SGR = ROE × retention ratio = 25% × 1.0 = 25%. This is the maximum growth rate achievable using only retained earnings while keeping financial ratios constant. Actual growth of 40% exceeds this, meaning internal equity generation is insufficient. The gap must be funded by external equity (new share issuance) or additional debt — the firm's capital structure is changing, whether intentionally or not.

Question 3

A firm that raises its dividend payout ratio will typically increase its sustainable growth rate, because investors respond positively to higher dividends.

• T. True
• F. False

Answer: False

Raising the payout ratio lowers the retention ratio, which directly reduces SGR = ROE × retention ratio. More dividends mean less retained earnings available to fund future growth internally. The claim confuses investor signaling effects (possible stock price reactions) with the mechanical relationship between retention and growth capacity. SGR purely reflects how much equity the firm accumulates through retained earnings — higher payout unambiguously reduces it.

Question 4

A firm consistently growing faster than its sustainable growth rate without issuing new equity will see its debt-to-equity ratio rise over time.

• T. True
• F. False

Answer: True

SGR is defined as the growth rate at which all financial ratios — including leverage — remain constant. Growth faster than SGR means retained earnings alone cannot fund all new assets. The shortfall must come from debt, which grows the liability side faster than equity. Each year, debt-to-equity rises. If unchecked, this rising leverage can become financially unsustainable — making SGR a useful warning signal for credit analysis, not just equity valuation.

Question 5

A mature utility company and a high-growth technology startup both have ROE = 18%. Explain why it might make financial sense for them to have very different dividend payout ratios.

Model answer: The key is the return available on reinvested earnings relative to shareholders' opportunity cost. The utility has limited high-return reinvestment opportunities — retaining earnings to fund mediocre projects destroys value compared to distributing them. A high payout is appropriate. The tech startup likely has abundant projects earning well above its cost of capital; retaining earnings to fund those creates value. A low payout (high retention) maximizes SGR and compounds value internally. Payout policy should match the firm's investment opportunity set.

SGR = ROE × retention ratio. Same ROE × different retention = different SGR. The utility's high payout yields low SGR, which is fine since it doesn't need rapid growth. The startup's low payout yields high SGR, funding the growth that generates its value. Forcing the startup to pay dividends would require it to reissue equity at a cost to fund projects it should have funded with retained earnings — value destruction. This is why dividend policy cannot be evaluated independently of investment opportunities.