To determine how many shares of preferred stock Caspian Sea needs to issue to raise $31.00 million, we first need to calculate the price per share of the preferred stock using the dividend and the discount rate.
The formula for calculating the price of preferred stock (P) that pays a constant dividend (D) is given by:
\[ P = \frac{D}{r} \]
Where:
- \( D \) is the annual dividend
- \( r \) is the discount rate (or required rate of return)
Given:
- \( D = 3.41 \)
- \( r = 11.85% = 0.1185 \)
Now, substitute the values into the formula:
\[ P = \frac{3.41}{0.1185} \approx 28.80 \]
Next, we can determine the number of shares needed to raise $31.00 million by dividing the total amount raised by the price per share:
\[ \text{Number of shares} = \frac{\text{Total amount}}{P} \]
Substituting in the known values:
\[ \text{Number of shares} = \frac{31,000,000}{28.80} \approx 1,075,000 \]
Therefore, Caspian Sea will need to issue approximately 1,075,000 shares of preferred stock to raise $31.00 million.
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