Answer: $4.50

## Detailed Explanation To calculate diluted EPS when convertible preferred shares exist, we need to consider the **if-converted method**. This method assumes the preferred shares were converted at the beginning of the period. ### Step 1: Calculate Basic EPS **Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Common Shares** - Net Income = $1,800,000 - Preferred Dividends = $600,000 - Weighted Average Common Shares = 200,000 **Basic EPS = ($1,800,000 - $600,000) / 200,000 = $1,200,000 / 200,000 = $6.00** ### Step 2: Apply the If-Converted Method for Diluted EPS Under the if-converted method: 1. **Add back preferred dividends** to net income (since if converted, there would be no preferred dividends) 2. **Add the common shares that would be issued upon conversion** to the denominator **Adjusted Net Income = $1,800,000** (no subtraction of preferred dividends) **Additional shares from conversion:** - 50,000 preferred shares × 4 common shares per preferred = 200,000 additional shares **Total shares if converted = 200,000 + 200,000 = 400,000 shares** **Diluted EPS = $1,800,000 / 400,000 = $4.50** ### Step 3: Check for Dilution We must check if the conversion is dilutive (reduces EPS): - Basic EPS = $6.00 - Diluted EPS = $4.50 - Since $4.50 < $6.00, the conversion is dilutive and should be included ### Step 4: Alternative Calculation Method We can also calculate the incremental EPS effect of the conversion: **Incremental EPS = Preferred Dividends / Additional Shares from Conversion** **= $600,000 / 200,000 = $3.00** Since $3.00 < $6.00 (basic EPS), the conversion is dilutive. **Final Diluted EPS = $4.50** **Answer: B. $4.50**

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