market cap = book value + discounted future cash flows = share price * number of outstanding shares
When you do a buyback, the book value drops (company loses cash), but the discounted future cash flows remains unchanged. The number of outstanding shares also drops.
The net result is the stock price increases as a company accumulates cash and uses it for buybacks because the number of outstanding shares drops.
Another way of thinking about it is that it's the same as dividends, but the dividend only goes to the sellers of the stock during a buyback.
Market cap = whatever the market decided at that time, and is determined by offer and demand.
The whole book value + discounted future cash flow does not reflect the real stock exchange at all. If that was the case no investor would want share buybacks because as you say it would only reward the ones who sell...
When taking into account offer and demand stock buybacks make more sense: the buyback increase the demand for the stock. The offer will increase a bit (a few might sell) but not in the same proportion because the offer is not very elastic (most of your investors are in for a long ride and are not going to sell), so the price goes up, you get rid of some short term investors, and the long term investors see their share increasing in value. Everybody's happy and the dividend ratios do not mean anything anymore.
When you do a buyback, the book value drops (company loses cash), but the discounted future cash flows remains unchanged. The number of outstanding shares also drops.
The net result is the stock price increases as a company accumulates cash and uses it for buybacks because the number of outstanding shares drops.
Another way of thinking about it is that it's the same as dividends, but the dividend only goes to the sellers of the stock during a buyback.