Sometimes the continuing shareholders benefit from share buybacks; and sometimes they lose. If the shares are bought by the company at a price low relative to their intrinsic value they are going to be value creating for continuing shareholders.

If they are bought at a high price relative to intrinsic value per share then they will reduce value for continuing shareholders.
Here is Warren Buffett’s take on this issue (in latest Letter to Berkshire shareholders):
“At Apple and Amex, repurchases increased Berkshire’s ownership a bit without any cost to us.
The math isn’t complicated: When the share count goes down, your interest in our many businesses goes up.
Every small bit helps if repurchases are made at value-accretive prices.
Just as surely, when a company overpays for repurchases, the continuing shareholders lose. At such times, gains flow only to the selling shareholders and to the friendly, but expensive, investment banker who recommended the foolish purchases.
Gains from value-accretive repurchases, it should be emphasized, benefit all owner…….
…………..Of course, the difficult bit is estimating intrinsic value. As you have seen in my analyses of the companies I’ve bought into there is usually a range of plausible values, even when sticking to conservative assumptions.
Prof Glen Arnold now offers a Managed Portfolio Service at Henry Spain Investment Services under which clients’ portfolios contain the same shares as his (write to Jackie.Tran@henryspain.co.uk)