Avis Budget Group, the rental car firm, announced this morning that it is buying Zipcar for $500 million in cash, a 49% premium over the stock’s closing price at the end of 2012.

The Cambridge-based company was founded in 2000, went public in 2011 and still plans to move its headquarters to Boston’s Innovation District this year.

“We see car sharing as highly complementary to traditional car rental, with rapid growth potential and representing a scalable opportunity for us as a combined company,” said Ronald L. Nelson, Avis Budget Group chairman and CEO, in a release. “We expect to apply Avis Budget’s experience and efficiencies of fleet management with Zipcar’s proven, customer-friendly technology to accelerate the growth of the Zipcar brand and to provide more options for Zipsters in more places. We also expect to leverage Zipcar’s technology to expand mobility solutions under the Avis and Budget brands.”

The companies claim the deal will produce synergies in the range of $50 to $70 million annually, based on the strategic alignments mentioned above.

Car-sharing is estimated to be a $400 million business globally, and with a presence in 20 cities so far, Zipcar was projected to finish 2012 profitable for the first time.

For Avis, the move helps to counter competitors Hertz and Enterprise, both of which have launched their own Zipcar competitors.