Metro-Goldwyn-Mayer Inc., the movie studio controlled by billionaire Kirk Kerkorian, agreed in principle to be bought by an investor group led by Sony Corp. for $12 per share, or about $2.9 billion, plus assumed debt.

The Sony-led group includes private equity firms Texas Pacific Group, Providence Equity Partners, and DLJ Merchant Banking Partners, MGM said in a statement. MGM said it received a $150 million “security deposit” yesterday, and its management will recommend the sale to the MGM board by September 27.

Sony became the only remaining bidder after Time Warner Inc., the world’s largest broadcasting and publishing company, said yesterday that it was withdrawing its offer for MGM. The purchase will double the size of Tokyo based Sony’s film library to about 8,000 titles, adding MGM movies including the James Bond and Pink Panther series.

The library will help Sony boost sales of digital video discs.

“The combo would be good. It’s the library they want,” said an entertainment analyst at Sanders Morris Harris in Los Angeles, David Miller. “The more films you have, the more you can keep costs low.”

Mr. Miller rates MGM shares as “hold” and made his comment before the agreement was announced.

Sony already owns Sony Pictures Entertainment, the parent of Columbia Pictures and TriStar Pictures. The MGM library includes such Academy Award winners as “Ben Hur” and “Midnight Cowboy” as well as 10,000 hours of TV programming.

Time Warner’s chief executive officer, Richard Parsons, 56, said that his company withdrew its bid because it couldn’t come to terms on a “price that would have represented a prudent use of our growing financial capacity.”

The transaction would represent the third time that Mr. Kerkorian, who owns 74% of MGM and tried unsuccessfully to merge it with Sony in 2001, has sold the studio.

American consumers will spend $14.8 billion to buy DVDs this year, according to Adams Media Research of Carmel, Calif. That is expected to rise to $20.6 billion by 2007. This year’s projected box office total is $9.6 billion, Adams said.

Mr. Kerkorian, the president and chief executive of closely held Tracinda Corp., is ranked as the 65th wealthiest person with $6 billion in net worth, according to Forbes magazine.

The son of an Armenian immigrant rancher in California’s San Joaquin Valley, Mr. Kerkorian first bought the MGM film studio in 1970. Under Mr. Kerkorian, the company built the MGM Grand Hotel in Las Vegas in 1973. The casino unit was spun off into a separate company in 1980.

Mr. Kerkorian sold the studio to Ted Turner in 1986 and then bought it back, leaving the pre-1948 library with Mr. Turner, who used it to create movie-oriented cable networks such as Turner Classic Movies.

Mr. Kerkorian later sold the part of MGM he retained to Italian financier Giancarlo Parretti, who lost it to the French bank Credit Lyonnais after defaulting on loans used to buy the studio.

With veteran studio executive Frank Mancuso, Mr. Kerkorian bought MGM a third time in 1996 for $1.3 billion in cash.

Texas Pacific, started in 1993 by David Bonderman, a former adviser to the billionaire Bass family of Texas, last year raised a $5.3 billion takeover fund, TPG Partners IV LP.

The firm has a history of investing in brand names in need of resuscitation, including Continental Airlines Inc. and fast-food chain Burger King Corp.

Providence Equity, named for the Rhode Island city where it is based, invests in communications and media companies and was started in 1991.The firm is currently investing its $2.8 billion Providence Equity Partners IV.

DLJ Merchant Banking Partners is an affiliate of Credit Suisse First Boston.

A Sony-MGM transaction would represent the third multibillion- dollar purchase of an entertainment company in the past year.

Rupert Murdoch’s News Corp. paid $6.6 billion in December for a controlling interest in DirecTV Group Inc., the largest American satellite television service.

General Electric Co.’s NBC unit in May completed its $14 billion purchase of Vivendi Universal SA’s American entertainment assets, creating NBC Universal. Comcast in February made an unsolicited offer to buy Walt Disney Co. for $54.1 billion. The offer was later withdrawn.

JPMorgan Chase & Co. advised the Sony group on MGM.

Time Warner shares yesterday fell 6 cents to $16.45 at in New York Stock Exchange composite trading. The shares have fallen 8.6% this year. MGM rose 44 cents to $11.55 and has increased 12% this year. Sony’s American depositary receipts, each representing one common share, rose 53 cents to $35.82 and are up 3.3% this year.