American Homes 4 Rent announced Wednesday that Chairman B. Wayne Hughes will purchase $50 million of the company’s common shares in a private offering. The Agoura Hills landlord of single-family homes also plans a public offering of 11 million shares. The proceeds from both the public offering and the Hughes transaction will pay back a $456 million outstanding debt on a credit facility. The company has told the lender it plans to pay off the entire debt on April 7, the next date a regular payment is due. Both the investors in the public offering and Hughes will pay the same price for shares. The company announced the offerings after market close Wednesday. Shares closed up 32 cents, or 1.4 percent, at $23.23 on the New York Stock Exchange.