(Reuters) - KKR & Co KKR.N said on Monday it will buy Envision Healthcare Corp EVHC.N, one of biggest U.S. providers of physicians to hospitals, in a deal valued at $5.57 billion as it builds up its healthcare portfolio.

The private equity firm beat peers Carlyle Group CG.O, TPG Global and others as it sealed the deal for $46 per share - a premium of 5.4 percent to Envision's last close on Friday.

Envision’s shares rose 2.5 percent to $44.76, their highest in nearly eight months. Including debt, the deal is valued at $9.9 billion.

KKR already owns Envision's ambulance unit AMR, which it bought for $2.4 billion last year and merged with its helicopter ambulance service. The firm also took WebMD Health Corp WBMD.O private for about $2.8 billion.

Private equity firms, armed with a record $1 trillion in cash, are investing more in public companies than at any time since the financial crisis.

Take-private deals worldwide reached a decade-high of $109 billion last year, according to data provided to Reuters from industry tracker Preqin.

KKR itself said last month it would buy business software company BMC Software, in a deal that could be worth about $8.5 billion with debt, according to Reuters’ sources.

FILE PHOTO: CEO of Kohlberg Kravis Roberts & Co (KKR) Henry Kravis (C) departs after meeting India's Prime Minister Narendra Modi at a breakfast in the Manhattan borough of New York September 29, 2014. REUTERS/Carlo Allegri/File Photo

As of March 31, KKR had $176 billion in assets under management. It held $1.88 billion in cash and cash equivalents, according to its latest earnings report.

The Envision deal is the latest in a spate of mergers and acquisitions among physician networks, a business that has struggled in recent years to adapt to changes in how U.S. health insurers reimburse providers.

The deal marks an end to Envision’s plan to find strategic options, which the company launched after posting disappointing third-quarter results last year.

The company has been hit by lower patient admissions at hospitals - a trend that has plagued healthcare services providers in the United States.

As part of its strategic review, Envision had reached out to around 25 potential buyers over the last seven months.

UnitedHealth Group Inc's UNH.N OptumCare had also expressed interest in the company, Leerink analyst Ana Gupte wrote in a note.

“We see the arms race for ambulatory care delivery continuing and likely to remain a strategic focus for OptumCare, HCA ... as well as not-for-profit hospital and health systems, and private equity,” Gupte said.

Ryan Daniels, an analyst with William Blair, said the purchase price was a fair multiple for Envision given a number of headwinds facing the industry. Daniels also said there was little to no possibility of other bidders emerging.

Reuters reported the deal on Sunday, citing a source. The deal is expected to close in the fourth quarter.

It was advised by J.P. Morgan, Evercore and Guggenheim Securities.