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