A:

Sometimes, shares of stock offered by a company are not regular, market-driven common shares. Instead, they may be preferred shares, which are considered fixed income securities and are issued with a par value. When that par value is paid back to the purchaser of the preferred share, this is considered a redemption. Redemption can also occur when issued bonds are called or matured and the principal, or par value, is paid back.
When a company issues shares of common stock for the public to buy and later decides to buy some of those shares back, that's considered a repurchase rather than a redemption. The major difference between the two is that the shares bought back in a redemption are considered a fixed-income security that is expected to be bought back by the issuer. A repurchase of shares, however, reduces the number of outstanding shares that a company has, and can increase the company's holdings so that it remains or regains majority shareholder status. It can also increase the stock's earnings per share, since it reduces the outstanding number of shares. A repurchase may even allow the company to profit off of the resale of its own shares at a later time.

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