To find out how many shares of stock Caspian Sea Drinks (CSD) must sell to raise $89 million, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model determines the value of a stock based on the expected future dividends that grow at a constant rate.
The formula for the value of a stock according to the Gordon Growth Model is:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \(P_0\) = price of the stock today
- \(D_1\) = expected dividend next year
- \(r\) = cost of equity (required return)
- \(g\) = growth rate of dividends
Given:
- \(D_1 = 1.50\) (next year's dividend)
- \(r = 0.1340\) (cost of equity)
- \(g = 0.0431\) (growth rate)
First, we need to calculate the current price of the stock \(P_0\):
\[ P_0 = \frac{1.50}{0.1340 - 0.0431} \]
Calculating the denominator:
\[ 0.1340 - 0.0431 = 0.0909 \]
Now calculate \(P_0\):
\[ P_0 = \frac{1.50}{0.0909} \approx 16.52 \]
Now that we know the price of each share is approximately $16.52, we can determine how many shares need to be issued to raise $89 million:
\[ \text{Number of shares} = \frac{\text{Total funds required}}{P_0} = \frac{89,000,000}{16.52} \]
Calculating the number of shares:
\[ \text{Number of shares} \approx 5,386,678.77 \]
Since CSD cannot issue a fraction of a share, they would need to issue approximately 5,386,679 shares to raise $89 million.
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