Step-by-step calculation:

1. Calculate the growth rate (g):

   • ROE = 12%
   • Dividend payout ratio = 40%
   • Retention ratio (b) = 1 - Dividend payout ratio = 1 - 0.40 = 0.60 or 60%
   • g = ROE × Retention ratio = 0.12 × 0.60 = 0.072 or 7.2%

2. Calculate next year's dividend (D₁):

   • Current year's dividend (D₀) = $3.60
   • D₁ = D₀ × (1 + g) = $3.60 × (1 + 0.072) = $3.60 × 1.072 = $3.8592

3. Apply the Gordon growth model formula:

   • V₀ = D₁ / (r - g)
   • Where: r = required rate of return = 15% = 0.15
   • V₀ = $3.8592 / (0.15 - 0.072) = $3.8592 / 0.078 = $49.4769 ≈ $49.48

Wait, this gives approximately $49.48, which is closest to option C ($49.49). Let me double-check:

Actually, looking at the options:

• A: $36.96
• B: $46.15
• C: $49.49

My calculation gives $49.48, which is closest to option C. However, let me verify if there's a different interpretation:

Alternative calculation (using D₀ instead of D₁): Some might incorrectly use: V₀ = D₀ × (1 + g) / (r - g) = $3.60 × 1.072 / 0.078 = $3.8592 / 0.078 = $49.48

Another common mistake: Using D₀/(r-g) = $3.60/0.078 = $46.15 (option B)

Correct approach: The Gordon growth model uses next year's dividend (D₁), not current dividend (D₀). So: D₁ = D₀ × (1 + g) = $3.60 × 1.072 = $3.8592 V₀ = D₁/(r-g) = $3.8592/0.078 = $49.4769 ≈ $49.48

Therefore, the correct answer is C ($49.49).

Why others might choose wrong options:

• Option A ($36.96): Might have used wrong growth rate or calculation error
• Option B ($46.15): Used current dividend D₀ instead of next year's dividend D₁: $3.60/0.078 = $46.15

Final answer: C