To determine how many shares of preferred stock Caspian Sea will need to issue to raise $31.00 million, we need to calculate the price per share of the preferred stock using the dividend discount model for preferred stock.
The formula for the price of preferred stock is given by:
\[ P = \frac{D}{r} \]
Where:
- \(P\) = Price of the preferred stock
- \(D\) = Dividend per share
- \(r\) = Discount rate (required rate of return)
In this case:
- \(D = 3.39\)
- \(r = 10.04% = 0.1004\)
Now we can calculate the price per share:
\[ P = \frac{3.39}{0.1004} \approx 33.7 \]
Now that we have the price per share, we can determine how many shares need to be issued to raise $31 million:
\[ \text{Number of shares} = \frac{\text{Total amount to be raised}}{P} \]
Calculating the number of shares:
\[ \text{Number of shares} = \frac{31,000,000}{33.7} \approx 918,145.13 \]
Since you cannot issue a fraction of a share, we round up to the next whole number:
\[ \text{Number of shares} = 918,146 \]
Thus, Caspian Sea will need to issue 918,146 shares of preferred stock to raise $31.00 million.