In the mergers and acquisitions world, they are called “takeunders,” acquisitions at a price that is less than the target company’s stock market value. Now, a number of recent deals for companies that have gone public in recent years offer a variation on the theme: takeovers for less than the initial offering price.

The car-sharing company Zipcar, which announced on Wednesday that it would be acquired by Avis Budget Group, is one such instance.

Zipcar went public in April 2011 at $ 18 a share and rose as high as $ 29.27. Wednesday’s offer of $ 12.25 a share – while amounting to a 49 percent premium over Zipcar’s stock price on Dec. 31 – represents a discount of 32 percent from its I.P.O. price.

Zipcar is only the latest example, according to data from Standard & Poor’s Capital IQ. Take an offering from an exuberant market, when Kohlberg Kravis Roberts & Company took Sealy public in April 2006 for $ 16 a share. In September last year, the company was acquired by a rival, Tempur-Pedic, for $ 2.20 a share.

Other recent deals represent much less of a comedown from such buoyant market debuts. Starbucks acquired Teavana, which went public for $ 17 a share in July 2011, for $ 15.50 a share. That deal closed on Wednesday.

Duff & Phelps, meanwhile, agreed this week to be sold to a consortium including the Carlyle Group for $ 15.55 a share. The financial advisory firm went public in October 2007 at $ 16 a share.

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