The Walt Disney Co. board has extended the contract of Chief Executive Robert Iger for a year. Iger, 62, originally had been set to retire as head of the Burbank entertainment and media conglomerate in March 2015 and as chairman of the board in June 2016. The extension will have him step down from both positions in June 2016. The board asked Iger to remain as chief executive an additional year based on his track record of producing high-quality content, technological innovation and international expansion that has led to record growth in revenue and income, said Orin C. Smith, independent lead director of the Disney board. “Now, Disney will continue to have the full benefit of Mr. Iger’s leadership as CEO and chairman for the duration of his tenure,” said Smith, in a prepared statement. Iger became chief executive of Disney in September 2005 as the successor to Michael Eisner. Shares closed up 78 cents, or more than 1 percent, to $63.93 on the New York Stock Exchange.