Answer: 6.9%.

The correct answer is **A** (6.9%). To derive the ROE, we use the formula for the forward P/E ratio: \[ \text{P/E}_1 = \frac{p}{r - g} \] where: - \( p \) = dividend payout ratio = \( 1 - \text{retention rate} \) = \( 1 - b \) - \( r \) = required rate of return - \( g \) = dividend growth rate = \( b \times \text{ROE} \) Rearranging the formula to solve for ROE: \[ \text{ROE} = \frac{\left( \frac{1 - b}{\text{P/E}_1} \right) - r}{-b} \] Substituting the given values: \[ \text{ROE} = \frac{\left( \frac{1 - 0.45}{8} \right) - 0.10}{-0.45} \approx 6.9\% \] **Option B (8.0%)** is incorrect because it mistakenly interchanges the retention rate and dividend payout ratio in the calculation. **Option C (9.7%)** is incorrect because it erroneously uses the retention rate instead of the dividend payout ratio in the numerator of the formula.

Author: LeetQuiz Editorial Team