Discuss the concept of earnings per share $($EPS$)$ and its importance in financial analysis. Explain the calculation of basic and diluted EPS, and how stock splits, stock dividends, and convertible securities affect EPS.

Earnings per share $($EPS$)$ measures the portion of a company$$s profit allocated to each outstanding share of common stock. Explain the calculation of basic EPS, which is derived by dividing net income by the weighted average number of shares outstanding. Discuss diluted EPS, which accounts for potential dilution from convertible securities$,$ stock options, and other instruments. Explain how stock splits and stock dividends affect the number of shares outstanding and the calculation of EPS. Analyze the importance of EPS in evaluating company performance and comparing profitability with other companies.