ARV Assisted Living Inc. posted a loss of $4.1 million for the second quarter, in part because of a $1.2-million payout to founder and former chairman Gary Davidson, who resigned last month. Davidson quit ARV on Oct. 15, one day after the company rejected a $286-million buyout offer from Emeritus Corp., which owned 8% of ARV. That offer followed a $135-million bid for 49% of the company from Lazard Freres & Co., a New York investment firm. The second-quarter loss of $4.1 million, or 37 cents a share, also included $1.3 million in start-up losses from four facilities that have been opened since the beginning of the fiscal year, the company said. Costa Mesa-based ARV, which operates facilities that offer accommodations for elderly residents who need assistance, earned $747,000, or 8 cents a share, for the corresponding period last year. Revenue for the quarter ended Sept. 30 rose 51%, to $28.8 million from $19.1 million. For the six months, the company reported a net loss of $4.9 million, or 47 cents a share, contrasted with profit of $612,000, or 7 cents a share, a year ago. Revenue rose 63%, to $56.2 million from $34.4 million.