Answer: $49.49.

## Explanation The Gordon growth model formula is: \[ V_0 = \frac{D_1}{r - g} \] Where: - \( V_0 \) = intrinsic value per share - \( D_1 \) = expected dividend next year - \( r \) = required rate of return (15%) - \( g \) = sustainable growth rate **Step 1: Calculate the sustainable growth rate (g)** \[ g = ROE \times (1 - \text{Dividend payout ratio}) \] \[ g = 12\% \times (1 - 40\%) \] \[ g = 12\% \times 60\% \] \[ g = 7.2\% \] **Step 2: Calculate next year's dividend (D₁)** Current year's dividend = $3.60 \[ D_1 = D_0 \times (1 + g) \] \[ D_1 = 3.60 \times (1 + 0.072) \] \[ D_1 = 3.60 \times 1.072 \] \[ D_1 = 3.8592 \] **Step 3: Apply the Gordon growth model** \[ V_0 = \frac{3.8592}{0.15 - 0.072} \] \[ V_0 = \frac{3.8592}{0.078} \] \[ V_0 = 49.4769 \] This rounds to approximately $49.48, which is closest to **$49.49**. **Wait, let me double-check the calculation:** Actually, looking at the options: - A: $36.96 - B: $46.15 - C: $49.49 My calculation gives $49.48, which matches option C. However, I need to verify if there's a common mistake students might make. Some might forget to grow the dividend: \[ V_0 = \frac{3.60}{0.15 - 0.072} = \frac{3.60}{0.078} = 46.15 \] This would give option B. Or they might use the wrong growth rate calculation: \[ g = ROE \times \text{Dividend payout ratio} = 12\% \times 40\% = 4.8\% \] \[ D_1 = 3.60 \times 1.048 = 3.7728 \] \[ V_0 = \frac{3.7728}{0.15 - 0.048} = \frac{3.7728}{0.102} = 36.99 \] This would give option A. The **correct calculation** is: 1. \( g = ROE \times (1 - \text{Payout ratio}) = 12\% \times 60\% = 7.2\% \) 2. \( D_1 = 3.60 \times 1.072 = 3.8592 \) 3. \( V_0 = \frac{3.8592}{0.15 - 0.072} = \frac{3.8592}{0.078} = 49.4769 \approx 49.48 \) Therefore, the correct answer is **C. $49.49**.

Author: LeetQuiz .