Explanation:

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

$\text{Diluted EPS} = \frac{€2,500,000}{2,000,000 + (2 \times 1,000,000)} = \frac{€2,500,000}{4,000,000} = €0.625 \approx €0.63$

However, diluted EPS, by definition, must always be equal to or less than basic EPS. The basic EPS is calculated as:

$\text{Basic EPS} = \frac{\text{Net income} - \text{Preferred dividends}}{\text{Weighted average number of shares outstanding}} = \frac{€2,500,000 - (1,000,000 \times €1)}{2,000,000} = \frac{€1,500,000}{2,000,000} = €0.75$

Since the diluted EPS (€0.63) is less than the basic EPS (€0.75), the convertible preferred shares are dilutive, and the correct diluted EPS is €0.63.