Billionaire Kirk Kerkorian’s investment company Tracinda Corp. on Wednesday offered to buy a large minority stake of 8.8 percent in General Motors Corp. at a premium to the automaker’s depressed stock price.

Beverly Hills-based Tracinda offered $868 million for as many as 28 million GM shares at $31 each, raising its holdings in the Detroit-based automaker to 50 million shares. The $31-a-share offer price, including the regular quarterly dividend of 50 cents per share, represents a 13.4 percent premium over GM shares’ closing price Tuesday of $27.77.

Tracinda said it would hold the common stock in GM, which last month reported its biggest quarterly loss since dodging bankruptcy 13 years ago, for investment purposes.

Kerkorian, a Las Vegas casino mogul, was the largest investor in automaker Chrysler before its link-up with Germany’s Daimler-Benz in 1998.

GM shares surged 18.1 percent to finish the day at $32.80.