Jan 10 (Reuters) - Healthcare revenue management firm R1 RCM Inc (RCM.O) said on Monday it would buy peer Cloudmed in an all-stock deal worth about $4.1 billion, including debt. Upon the deal"s closing, R1 shareholders will own about 70% of the combined company on a fully diluted basis and Cloudmed equity holders will own the rest. Shares of R1 fell 7% to 21.72 in early trading. Atlanta, Georgia-based Cloudmed, backed by private equity firm New Mountain Capital, partners with over 3,100 healthcare providers in the United States and recovers over $1.5 billion of underpaid or unidentified revenue for its clients annually. "This transaction accelerates our strategy to build the most scalable, flexible, and integrated platform for the revenue cycle and consumer engagement in healthcare," Joe Flanagan, chief executive officer of R1 RCM said. The deal is expected to close in the second quarter of 2022, after which it would be accretive to earnings per share in the first full year, R1 said.