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Answer: higher under Scenario 2.
## Explanation The sustainable growth rate (SGR) formula is: **SGR = ROE × (1 - Dividend Payout Ratio)** Where **ROE = ROA × Financial Leverage** Given that ROA is the same for both scenarios, we can analyze: **Scenario 1:** - Dividend payout ratio = 60% (retention ratio = 40%) - Financial leverage = 3.0 - ROE₁ = ROA × 3.0 - SGR₁ = (ROA × 3.0) × (1 - 0.60) = (ROA × 3.0) × 0.40 = ROA × 1.2 **Scenario 2:** - Dividend payout ratio = 40% (retention ratio = 60%) - Financial leverage = 2.5 - ROE₂ = ROA × 2.5 - SGR₂ = (ROA × 2.5) × (1 - 0.40) = (ROA × 2.5) × 0.60 = ROA × 1.5 **Comparison:** - SGR₁ = ROA × 1.2 - SGR₂ = ROA × 1.5 Since ROA is the same positive value for both scenarios, **SGR₂ > SGR₁**. **Key Insights:** 1. **Lower dividend payout ratio** (40% vs 60%) means higher retention of earnings for reinvestment 2. Although **financial leverage is lower** in Scenario 2 (2.5 vs 3.0), the higher retention ratio more than compensates 3. The combined effect of retention ratio and leverage determines SGR Therefore, the sustainable growth rate is **higher under Scenario 2**.
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An analyst gathers the following information to evaluate the effect of dividends and leverage on future growth:
| Scenario 1 | Scenario 2 | |
|---|---|---|
| Dividend payout ratio | 60% | 40% |
| Financial leverage | 3.0 | 2.5 |
If return on assets is the same for each scenario, the sustainable growth rate is:
A
higher under Scenario 1.
B
higher under Scenario 2.
C
the same under both Scenario 1 and Scenario 2.
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