Billionaire Kirk Kerkorian is making another run at building a significant investment in a U.S.-based automotive company, announcing Monday that it plans to offer $8.50 per share in cash for up to 20 million additional shares of Ford Motor Co.

The offered price represents a 13.3 percent premium over Ford’s closing price on Friday, and Ford shares rose more than 7 percent in premarket trading.

Kerkorian’s Tracinda Corp. already owns 100 million Ford shares, or 4.7 percent of the outstanding stock. If his latest offer is accepted, that stake will increase to 5.6 percent.

California-based Tracinda said Ford’s first-quarter results reinforced that the company is having success in its turnaround efforts, despite the difficult U.S. economy. Tracinda said it believes the Dearborn-based company will continue to “show significant improvements.”

A message seeking comment was left for Ford spokesman Mark Truby before business hours on Monday.

A year ago, Tracinda Corp. made an unsuccessful $4.5 billion cash offer for Chrysler, and in 2006 it dumped the last block of what once was a nearly 10 percent share of General Motors Corp.

Ford shares rose 55 cents, or 7.3 percent, to $8.05 in premarket trading.