Company’s market price is $50/share. There are 10M shares outstanding. The book equity is 200M. Therefore, the book value of each share is $20.
Company announces a $25,000,000 buyback. Since shares are worth 50 dollars each, that’s 500,000 shares bought back.
My analysis was that you now have a book value of (200M - 25M) = 175M and 9,500,000 outstanding shares. Therefore, the book value has decreased from $20.00/share to $18.42 a share
My friend commented that my calculation might have been correct for the purposes of getting the question right, but that the answer was unrealistic because it was strategically unsound. His logic was that by completing the share buyback, all the company did was dilute (lower) the book value and make it look unattractive to investors.
The question whether the transaction is dilutive or not depends of the earnings per share (EPS) or cash flow per share. And both should have increased under a ceteris paribus condition as the same amount of earnings or cash flow is distributed amongst less shareholders.
This should also increase the market price per share from 50$ to a higher number.