Shares of Lionsgate hit at an all-time high on Tuesday — and have more than doubled their price since the company bought Summit Entertainment less than a year ago.Lionsgate gained 1%, rising 15¢ to $17.46 in trading Tuesday on the New York Stock Exchange. When Lionsgate closed the Summit deal on Jan. 13, the shares were trading at $8.60. Shares have been gaining on Wall Street’s optimism over the next three “Hunger Games” films and development of other franchises, the deleveraging of the balance sheet, the possibility of a small dividend and the FX series “Anger Management.” Wall Street analysts have a consensus price target of $19.20. Summit is prepping another potential young-adult franchise in “Divergent,” with Shailene Woodley starring and a release date of March 14, 2014, set. Thanks largely to “Breaking Dawn — Part 2″ and “The Hunger Games,” Lionsgate crossed the $1 billion mark in 2012 at both the domestic and foreign box office.