Private shares of stock are issuances of equity in a company that is not publicly listed on a stock exchange. Anyone can own private shares, although the stock must be purchased directly from the issuing company. In addition, private shares are typically only bought during capital funding ventures and purchased in large quantities. Private stock can typically only be sold back to the issuing company.
A private company may perform a buyback of stock to consolidate who owns the company, reduce the cost of outstanding capital, or capitalize on the belief its stock is undervalued. A major difficulty of selling private stock is valuing the equity as there is no public market that establishes the price per share.