Press Ganey Holdings Inc. (NYSE: PGND), which helps health-care providers survey patients, agreed to be acquired by private equity firm EQT in a deal valued at about $2.35 billion. EQT will pay $40.50 a share in cash, according to a statement. The offer means a very small premium to Monday’s closing price of $40.33 for Press Ganey, which is majority-owned by private-equity firm Vestar Capital Partners. Still, the price is 62 percent higher than Press Ganey’s initial public offering price of $25 a share in May 2015. New York-based Vestar has been active recently. The PE firm announced plans to sell Snuggle maker Sun Products to Henkel AG and acquire mobile tech provider MTI. Press Ganey helps hospitals and doctors measure patient satisfaction and the quality of the care they provide, and offers consulting to help health-care providers improve. Since the 2010 passage of the Affordable Care Act, known as Obamacare, the U.S. has been increasingly pushing health-care providers to improve care quality. “A takeout at this level is surprising given the company’s strong execution and the stock’s 28 percent run,” David Larsen, an analyst at Leerink Partners, said in a note to investors. Press Ganey “is a high-quality company that has executed well since going public.” As of June 30, Vestar Capital owned 30.34 million Press Ganey shares, or about 57 percent, according to SEC filings. The private-equity firm bought a majority interest in Press Ganey in January 2008. The deal is subject to shareholder approval and other conditions, and the companies said they expect it to be completed in the fourth quarter of this year. Barclays Plc and Goldman Sachs Group Inc. (NYSE: GS) were Press Ganey’s financial advisers, while Latham & Watkins LLP and Richards, Layton & Finger PA provided legal counsel. Bank of America Corp.’s Merrill Lynch and Simpson Thacher & Bartlett LLP advised EQT. EQT’s offer gives Press Ganey an enterprise value of $2.35 billion, according to the statement. The deal has an equity value of about $2.25 billion, including restricted stock, and includes about $100 million of net debt.