Explanation:

When a company has convertible preferred stock outstanding, diluted EPS is calculated using the if-converted method. The formula for diluted EPS in this scenario is:

$\text{Diluted EPS} = \frac{\text{Net income}}{\text{Weighted average number of shares outstanding} + \text{New common shares that would have been issued at conversion}}$

Plugging in the numbers:

$\text{Diluted EPS} = \frac{€5,000,000}{2,000,000 + (6 \times 400,000)} = \frac{€5,000,000}{4,400,000} = €1.14$

Key Points:

1. Option A (€0.95) is incorrect because it subtracts the preferred dividends from net income in the diluted EPS calculation, which is not required under the if-converted method.
2. Option B (€1.02) is incorrect because it subtracts the common dividends from net income, which is also not part of the if-converted method.
3. Basic EPS is calculated as:

$\text{Basic EPS} = \frac{\text{Net income} - \text{Preferred dividends}}{\text{Weighted average number of shares outstanding}} = \frac{€5,000,000 - (400,000 \times €2)}{2,000,000} = €2.10$

Since diluted EPS (€1.14) is less than basic EPS (€2.10), the convertible preferred shares are dilutive, and the correct answer is C (€1.14).