Cerberus, a New York-based private equity firm, would also take an equity stake in Avon, which has a market capitalization of close to $1.6 billion and long-term debt of around $2.2 billion, the people said. Avon also had $587 million in cash as of the end of September. Separately, activist investor Barington Capital Group has built up a 2.8 percent stake in Avon and is launching a campaign to force changes at the company, the people said.