DETROIT ? Investors in troubled General Motors Corp. were betting Wednesday that 87-year-old billionaire Kirk Kerkorian’s surprise proposal to acquire a large stake in the company could be a catalyst for better times at the world’s largest automaker.

GM shares soared more than 18 percent Wednesday after Kerkorian’s Tracinda Corp. offered to pay almost $870 million for a nearly 5 percent stake. That would boost Tracinda’s holdings to about 9 percent and make Kerkorian one of GM’s largest shareholders.

GM shares fell to a 10-year low in April after the company reported a $1.1 billion loss for the first quarter. Its sales have slumped in recent months.

Tracinda officials said Kerkorian would have no comment beyond the statement released early in the day saying the proposed purchase was for investment purposes only. But his motives prompted speculation on a variety of scenarios, including that he might desire a controlling stake in the automaker.

“His history is that he’s never been a passive investor in any of the companies he’s gotten involved with,” said David Healy, Burnham Securities analyst.

Beverly Hills, Calif.-based Tracinda is the majority owner of casino and hotel operator MGM Mirage Inc. It was the largest shareholder in Chrysler Corp. when the automaker merged with DaimlerBenz in 1998.

Kerkorian, whose net worth is estimated at $8.9 billion by Forbes, is Tracinda’s sole shareholder.

Tracinda said it was willing to buy up to 28 million GM shares for $31 apiece in cash, an 11.6 percent premium over GM’s closing stock price Tuesday. But Wednesday’s runup pushed GM’s share price above that level. The shares jumped $5.03 to close at $32.80 Wednesday on the New York Stock Exchange.