Explanation:

To calculate diluted EPS, the following steps are taken:

1. Net Income Adjustment: Subtract preferred dividends from net income: €3,000,000 - €400,000 = €2,600,000.

2. Weighted Average Common Shares: Calculate the weighted average number of common shares outstanding during the year:

   • Shares outstanding on January 1: 3,500,000
   • Shares issued on April 1 (outstanding for 9 months): 1,000,000 * (9/12) = 750,000
   • Total weighted average shares: 3,500,000 + 750,000 = 4,250,000

3. Convertible Preferred Shares: Each preferred share converts into two common shares, so 400,000 preferred shares become 800,000 common shares.

4. Diluted EPS Calculation:

   • Numerator: €3,000,000 (no adjustment for preferred dividends in diluted EPS)
   • Denominator: 4,250,000 (weighted average shares) + 800,000 (converted shares) = 5,050,000
   • Diluted EPS: €3,000,000 / 5,050,000 ≈ €0.5941, rounded to €0.59.

5. Anti-Dilution Check: Basic EPS is (€3,000,000 - €400,000) / 4,250,000 ≈ €0.6118. Since diluted EPS (€0.59) is less than basic EPS, the convertible preferred shares are dilutive, and the reported diluted EPS is €0.59.