With private equity investors of all types flush with cash — from venture capitalists and hedge funds to large leveraged buyout (LBO) firms such as The Blackstone Group and The Carlyle Group — private financing hit record levels in 2006 and is likely to remain strong in the new year, according to Wharton faculty and industry analysts. Nearly a third of the dollar value of all U.S. acquisitions last year involved private equity firms, up from just 3% five years ago, according to U.K.-based Dealogic, which tracks the investment industry. General Electric reportedly has invited private equity firms to bid for its plastic divisions in a deal that could be worth more than $10 billion. The nation’s largest casino operator, Harrah’s Entertainment, is weighing a $15.5 billion bid from a team of private equity players. In November, shareholders of hospital company HCA approved a $33 billion private-equity buyout, topping the prior record of $31.3 billion paid for RJR Nabisco in 1989.…