The term private equity refers to shares that are held by companies or investors in other companies whose shares are not available for trade on the stock market. A private equity firm is one which exists solely to make a profit on investments made in other companies. One example of such an investment is where a private equity firms invests in a private company with the aim of making that company more profitable and later making a return on the investment when the shares in the company are offered for sale to the public for the first time on a stock exchange through an initial public offering (IPO), or by selling the shares to another company. Another example is where a private equity firm buys out a company listed on a stock exchange that appears to be undervalued.
A common feature of a public equity buyout is that it is financed partly through debt (eg a loan taken out from a bank). The private equity firm will also contribute its own capital (=money).
One of the largest private equity deals occurred in 2005, when three private equity firms acquired Hertz (the car rental company) for $15 billion. Shortly after the buyout, the firms made a return on their investment by selling their shares through an IPO.