Question

Caspian Sea Drinks needs to raise $89.00 million by issuing additional shares of stock. If the market estimates CSD will pay a dividend of $1.50 next year, which will grow at 4.31% forever and the cost of equity to be 13.40%, then how many shares of stock must CSD sell?

Answer 1

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.