Explanation

The Gordon growth model formula is:

$V_0 = \frac{D_0 \times (1 + g)}{r - g}$

Where:

• $V_0$ = intrinsic value per share
• $D_0$ = current dividend per share = $2.00
• $r$ = required return = 8% = 0.08
• $g$ = sustainable growth rate

First, we need to calculate the sustainable growth rate (g):

$g = b \times ROE$

Where:

• $b$ = retention ratio = 1 - dividend payout ratio
• ROE = return on equity = 9% = 0.09

Dividend payout ratio = 55% = 0.55 Retention ratio (b) = 1 - 0.55 = 0.45

$g = 0.45 \times 0.09 = 0.0405 = 4.05\%$

Now, calculate $D_1$: $D_1 = D_0 \times (1 + g) = 2.00 \times (1 + 0.0405) = 2.00 \times 1.0405 = 2.081$

Apply the Gordon growth model: $V_0 = \frac{2.081}{0.08 - 0.0405} = \frac{2.081}{0.0395} = 52.6835$

Rounded to two decimal places: $52.68

Therefore, the intrinsic value per share is closest to $52.68, which corresponds to option B.

Key points:

1. The Gordon growth model requires the dividend in the next period (D₁)
2. The sustainable growth rate is calculated as retention ratio × ROE
3. The model only works when r > g (which is true here: 8% > 4.05%)
4. The result matches option B: $52.68