Final answer:
The book value per share will increase by approximately €0.1111.
Step-by-step explanation:
The book value per share will increase by the amount of the repurchased shares divided by the remaining shares outstanding. In this case, the company repurchases 2 million shares out of the 20 million shares outstanding, leaving 18 million shares remaining. The increase in book value per share can be calculated as:
Book value per share increase = Repurchased shares / Remaining shares
= 2,000,000 / 18,000,000
= 0.1111
Therefore, the book value per share will increase by approximately €0.1111.