To solve the given problem, we'll break down each part step-by-step as follows:
### Part a: Calculate the Earnings per Share (EPS) of Bozo Oil's common stock.
Earnings per Share (EPS) is calculated using the formula:
[tex]\[ \text{EPS} = \frac{\text{After-tax earnings}}{\text{Number of outstanding shares}} \][/tex]
Given:
- After-tax earnings = \[tex]$2,800,000
- Number of outstanding shares = 2,050,000
Substituting the values:
\[ \text{EPS} = \frac{2,800,000}{2,050,000} \approx 1.37 \]
So, the earnings per share (EPS) is \$[/tex]1.37.
### Part b: Calculate the Price-Earnings (P/E) Ratio.
The Price-Earnings Ratio is calculated using the formula:
[tex]\[ \text{P/E Ratio} = \frac{\text{Market value per share}}{\text{Earnings per share}} \][/tex]
Given:
- Market value per share = \[tex]$40
- EPS (from Part a) = \$[/tex]1.37
Substituting the values:
[tex]\[ \text{P/E Ratio} = \frac{40}{1.37} \approx 29 \][/tex]
So, the Price-Earnings Ratio is 29.
### Part c: Calculate the Book Value per Share.
Book Value per Share is calculated using the formula:
[tex]\[ \text{Book Value per Share} = \frac{\text{Assets} - \text{Liabilities}}{\text{Number of outstanding shares}} \][/tex]
Given:
- Assets = \[tex]$15,000,000
- Liabilities = \$[/tex]9,000,000
- Number of outstanding shares = 2,050,000
Substituting the values:
[tex]\[ \text{Book Value per Share} = \frac{15,000,000 - 9,000,000}{2,050,000} = \frac{6,000,000}{2,050,000} \approx 2.93 \][/tex]
So, the book value per share is \[tex]$2.93.
### Summary of Results:
\begin{tabular}{|l|l|}
\hline
a. Earnings per share & \$[/tex]1.37 \\
\hline
b. Price-earnings ratio & 29 \\
\hline
c. Book value per share & \$2.93 \\
\hline
\end{tabular}
