Diluted EPS Calculation Explanation

Step 1: Calculate Basic EPS

First, we need to calculate the weighted average number of shares outstanding:

• From Jan 1 to Mar 31 (3 months): 6,000,000 shares
• From Apr 1 to Dec 31 (9 months): 10,000,000 shares

Weighted average shares = (6,000,000 × 3/12) + (10,000,000 × 9/12) = (1,500,000) + (7,500,000) = 9,000,000 shares

Basic EPS = Net Income / Weighted Average Shares = €9,200,000 / 9,000,000 = €1.0222

Step 2: Calculate Diluted EPS using the If-Converted Method

For convertible debt, we need to:

1. Add back the after-tax interest expense to net income
2. Add the potential shares from conversion to the denominator

After-tax interest expense = Interest expense × (1 - Tax rate) = €1,600,000 × (1 - 0.35) = €1,600,000 × 0.65 = €1,040,000

Adjusted net income for diluted EPS = Net income + After-tax interest expense = €9,200,000 + €1,040,000 = €10,240,000

Adjusted weighted average shares = Weighted average shares + Potential shares from conversion = 9,000,000 + 2,000,000 = 11,000,000

Diluted EPS = Adjusted net income / Adjusted weighted average shares = €10,240,000 / 11,000,000 = €0.9309 ≈ €0.93

Step 3: Anti-dilution Test

We need to check if the convertible debt is dilutive:

• Basic EPS = €1.0222
• Diluted EPS with conversion = €0.9309

Since €0.9309 < €1.0222, the convertible debt is dilutive and should be included in diluted EPS calculation.

Final Answer: €0.93 (Option A)

Key Points:

1. The if-converted method assumes conversion at the beginning of the period
2. Interest expense is added back after-tax because if converted, there would be no interest expense
3. The anti-dilution test confirms that including the convertible debt reduces EPS
4. The weighted average shares calculation accounts for the timing of the share issuance