Explanation
The sustainable growth rate (g) is calculated using the formula:
g = ROE × (1 - Dividend payout ratio)
Where:
- g = sustainable growth rate = 6% = 0.06
- Dividend payout ratio = 40% = 0.40
- ROE = Return on Equity (what we need to find)
Rearranging the formula to solve for ROE:
ROE = g / (1 - Dividend payout ratio)
Plugging in the values:
ROE = 0.06 / (1 - 0.40)
ROE = 0.06 / 0.60
ROE = 0.10 = 10.0%
Step-by-step calculation:
- First, calculate the retention ratio: 1 - 0.40 = 0.60 (or 60%)
- Then divide the sustainable growth rate by the retention ratio: 0.06 / 0.60 = 0.10
- Convert to percentage: 0.10 × 100% = 10.0%
Verification:
If ROE = 10.0% and retention ratio = 60%, then sustainable growth rate = 10.0% × 60% = 6.0%, which matches the given information.
Why the other options are incorrect:
- A. 3.6%: This would be too low. If ROE were 3.6% with 60% retention, the sustainable growth rate would be 2.16% (3.6% × 0.60), not 6%.
- C. 15.0%: This would be too high. If ROE were 15.0% with 60% retention, the sustainable growth rate would be 9.0% (15.0% × 0.60), not 6%.
Therefore, the correct answer is B. 10.0%.
