American Homes 4 Rent plans to sell 16.3 million shares in a secondary public offering that will raise about $599 million.The Calabasas single-family home rental company will use the money to pay down debt and for general corporate purposes, it said in a release.About 5.5 million shares will be offered directly by the company and another 10.8 million shares will be offered by forward purchasers or their affiliates in connection with forward sales agreements.American Homes will enter into forward sales agreements with JPMorgan Chase Bank and Bank of America. Both banks are expected to borrow from third parties to sell to the underwriters 10.8 million shares of common shares of American Homes, the company said.The pricing announcement was made on Thursday. Shares of American Homes closed down on Friday 83 cents, or just more than 2 percent, to $37.25 on the New York Stock Exchange, on a day when the Dow Jones closed up a fraction of a percent.