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.