Answer: $25.31.

## Explanation To solve this problem using Gordon's constant growth dividend discount model, we need to calculate: 1. **Calculate the average compounded annual dividend growth rate (Year 1 to Year 6)** - Year 1 dividend: $1.25 - Year 6 dividend: $1.92 - Number of years: 5 (from Year 1 to Year 6) Using the compound growth formula: \[ g = \left(\frac{D_6}{D_1}\right)^{\frac{1}{5}} - 1 \] \[ g = \left(\frac{1.92}{1.25}\right)^{0.2} - 1 \] \[ g = (1.536)^{0.2} - 1 \] \[ g = 1.0896 - 1 = 0.0896 \text{ or } 8.96\% \] 2. **Calculate the dividend payout ratio for Year 6** \[ \text{Payout ratio} = \frac{D_6}{EPS_6} = \frac{1.92}{3.20} = 0.60 \text{ or } 60\% \] 3. **Calculate the average growth rate** The problem states to use the average of: 1. The average compounded annual dividend growth rate (8.96%) 2. The dividend payout ratio for Year 6 (60%) \[ \text{Average growth rate} = \frac{8.96\% + 60\%}{2} = \frac{68.96\%}{2} = 34.48\% \] **Note:** This seems unusually high, but we must follow the problem's instructions. 4. **Apply Gordon's constant growth model** \[ V_0 = \frac{D_0 \times (1 + g)}{r - g} \] Where: - \(D_0 = D_6 = \$1.92\) (most recent dividend) - \(g = 34.48\% = 0.3448\) - \(r = 15\% = 0.15\) \[ V_0 = \frac{1.92 \times (1 + 0.3448)}{0.15 - 0.3448} \] \[ V_0 = \frac{1.92 \times 1.3448}{-0.1948} \] \[ V_0 = \frac{2.582}{-0.1948} = -13.26 \] This gives a negative value, which doesn't make sense. Let me re-examine. **Wait:** The growth rate (34.48%) is higher than the required return (15%), which violates the Gordon growth model assumption. However, the problem states to use this average method. Let me check if I should use retention ratio instead: - Retention ratio = 1 - Payout ratio = 1 - 0.60 = 0.40 - ROE = 12% (Year 6) - Sustainable growth = Retention ratio × ROE = 0.40 × 0.12 = 0.048 or 4.8% But the problem specifically says to use the average of the dividend growth rate and payout ratio. Actually, looking at the options, let me try a different interpretation: The average should be: (8.96% + 60%)/2 = 34.48% But this seems too high. Maybe they mean: Growth estimate = Average of: 1. Historical dividend growth rate = 8.96% 2. Sustainable growth rate = Retention ratio × ROE = (1 - 0.60) × 0.12 = 4.8% Average = (8.96% + 4.8%)/2 = 6.88% Then: \[ V_0 = \frac{1.92 \times (1 + 0.0688)}{0.15 - 0.0688} \] \[ V_0 = \frac{1.92 \times 1.0688}{0.0812} \] \[ V_0 = \frac{2.052}{0.0812} = 25.27 \] This is closest to $25.31 (Option A). Given the options, the correct approach appears to be: 1. Calculate historical dividend growth rate = 8.96% 2. Calculate sustainable growth rate = Retention ratio × ROE = (1 - 0.60) × 0.12 = 4.8% 3. Average = (8.96% + 4.8%)/2 = 6.88% 4. Apply Gordon model: \(V_0 = \frac{1.92 \times 1.0688}{0.15 - 0.0688} = 25.27\) The closest answer is **$25.31**.