Why would a company buy back its own shares?

A stock buyback, also known as a "share repurchase", is a company's buying back its shares from the marketplace. ... The idea is simple: because a company can't act as its own shareholder, repurchased shares are absorbed by the company, and the number of outstanding shares on the market is reduced

Companies routinely elect buyback options to convert classes of stock.  This happens at development stages in a company's growth.  During an initial offerings phase, one class of stock can be offered to the public and then after milestones in that phase are reached, the company fulfills options contracts and exercises those options to convert (usually like Class A) stock into a different class (subdivide a company potentially) with a different set of options.  These types of actions are intended to maintain value; allow the company to free-up raised cash for re-investment and continued development; and offer dividends to investors.  

When a company buybacks its own shares is called purchase of Treasury stock which will decrease the number of shares

the purpose:

1-Increase EPS [earnings per share]

2-use the shares as stock dividends

3-meet the stock needs for a potential merger.