Calculation Process

Step 1: Calculate initial total book value

• Book value per share = $20
• Shares outstanding = 9,000,000
• Total book value = $20 × 9,000,000 = $180,000,000

Step 2: Calculate cash used for repurchase

• Shares repurchased = 400,000
• Market price = $25
• Cash used = 400,000 × $25 = $10,000,000

Step 3: Calculate new total book value after repurchase

• New total book value = Initial total book value - Cash used
• New total book value = $180,000,000 - $10,000,000 = $170,000,000

Step 4: Calculate new shares outstanding

• New shares outstanding = 9,000,000 - 400,000 = 8,600,000

Step 5: Calculate new book value per share

• New book value per share = $170,000,000 ÷ 8,600,000 = $19.767 ≈ $19.77

Explanation

When a company repurchases shares at a price higher than the current book value per share ($25 > $20), the book value per share decreases. This occurs because the company is paying more than the accounting value of the shares, effectively reducing the overall equity per remaining share. The calculation shows the new book value per share is $19.77, which matches option B.