Blackstone Group LP and Carlyle Group are part of buyout groups making rival takeover bids for Hertz Corp, the rental car unit of Ford Motor Co., which also includes Hertz Equipment Rental Corp.

The Wall Street Journal reported last week that Hertz the buying price for Hertz could be as much as $10 billion including debt.

Hertz’ second quarter net income rose 3 percent to $97 million, while Ford’s earnings dropped 19 percent. Selling Hertz is part of Ford’s plan to raise money as it loses market share to Asian automobile makers.

Ford has owned all of Hertz since 2001 when it spent $707 million to buy back an 18.5 percent share it had sold to the public in 1997. Hertz’ net income more than doubled last year. Hertz has been in the car rental business since 1918 and the equipment rental business for more than 40 years.

Based in Park Ridge, N.J., HERC is No. 3 on the RER 100.