I got that when we have a buyback, the book value per share after the buyback can either go up or down based on what is the stock price of the company.
However, I dont get the logic behind this.
For example, why do we say that when the stock price is greater than the book value per share (prior to buyback) will decrease the book value per share after the buyback and the same with the stock price being lower than the book value per share ( before buyback) will lead to an increase to the book value per share after the buyback?
Scenario 1: Repurchase of 10 shares at a price per share of $20
shares outstanding: 100 - 10 = 90
BV: $1,000 - $20 * 10 = $800
BVPS: $800 / 90 = $8,89 (-1.11 cts.)
Scenario 2: Repurchase of 10 shares at a price per share of $5
shares outstanding: 100 - 10 = 90
BV: $1,000 - $5 * 10 = $950
BVPS: $950 / 90 = $10.56 (+0.56 cts.)
You see that in scenario 1 (BVPS < share price) the decrease in BV (nominator) is always bigger than the decrease in shares (denominator), so that the new BVPS will decrease. In scenario 2 (BVPS > share price) always the opposite will be the case.