To determine how many shares of stock Caspian Sea Drinks (CSD) must sell to raise $59.00 million, we first need to find the price per share using the Gordon Growth Model (also known as the Dividend Discount Model), which is given by the formula:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) = price per share
- \( D_1 \) = expected dividend next year
- \( r \) = cost of equity
- \( g \) = growth rate of dividends
Given:
- \( D_1 = 2.54 \) (expected dividend next year)
- \( r = 11.95% = 0.1195 \) (cost of equity)
- \( g = 4.01% = 0.0401 \) (growth rate)
Now we can plug in the values into the formula:
\[ P_0 = \frac{2.54}{0.1195 - 0.0401} \]
Calculating the denominator:
\[ 0.1195 - 0.0401 = 0.0794 \]
Now, we can calculate the price per share \( P_0 \):
\[ P_0 = \frac{2.54}{0.0794} \approx 32.0 \]
Now, to find the number of shares CSD must sell to raise $59.00 million, we will use the following formula:
\[ \text{Number of shares} = \frac{\text{Total amount to raise}}{P_0} \]
Substituting the values:
\[ \text{Number of shares} = \frac{59,000,000}{32.00} \approx 1,843,750 \]
Therefore, Caspian Sea Drinks needs to sell approximately 1,843,750 shares of stock to raise $59.00 million.
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