"During Mark's tenure, Hertz has transformed from a single on-airport car rental brand to a world leading rental car company," said Linda Levinson, who was announced as independent non-executive chairwoman on Monday.
Frissora presided over Hertz's buyout of Dollar Thrifty after a tussle with Avis Budget Group. He also ranked fifth on Business Travel News' list of the 25 most influential executives of 2012.
But some analysts and investors have said Hertz had not been able to raise prices as much as it should have after swallowing up a major competitor. Some are calling for the man who led Dollar Thrifty at the time as a replacement for Frissora.
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"There has been a clamoring for Scott Thompson, who did a fabulous job in taking Dollar Thrifty from close to bankruptcy to an $87.50 per share buyout," said Michael Millman, managing member of independent securities research company Millman Research Associates. Hertz had first offered $2 per share.
To Friday's close, Hertz's stock had fallen 0.6 percent this year compared with a 64 percent jump in the value of Avis, the third-largest U.S. car rental company. Privately held Enterprise Rent-A-Car is the largest player in the $24 billion market.
Hertz's shares were up more than 1 percent in afternoon trading on the New York Stock Exchange on Monday.