"I feel pretty good right now," Bewkes said in response to a question about whether the company, whose holdings include Warner Bros., HBO and Turner Broadcasting, had a succession plan in place should he step down when his current contract is up.
Without naming names, Bewkes said Time Warner has a "deep bench of potential successors" and has a "very good situation in terms of choice of who should run the company." He also noted that Time Warner is not afraid of succession, having put in new leadership at its key units -- HBO, Turner Broadcasting and Warner Bros. -- in the last few years.
All of Bewkes' top executives were at the meeting, including HBO Chief Executive Richard Plepler, Turner head John Martin and Warner Bros. Chief Executive Kevin Tsujihara. Martin, who took over running Turner earlier this year, is a former chief financial officer of Time Warner and is seen as a potential successor to Bewkes.
Asked by a shareholder about extending his contract to stay beyond 2017, Bewkes said that would be up to the board but also noted there is no age limit for the position of chief executive at Time Warner.
"I will try to eat healthy; I'd like to exercise more," he quipped.
Bewkes also noted that the company had recently upped the age limits for board members from 72 to 75.
"Our board members are alert and energetic, they're all awake here," he said.
Time Warner shareholders voted against a proposal to separate the positions of chairman and chief executive.
One shareholder attacked Time Warner's CNN news channel for having what he believes is a liberal bias and little interest in real news, particularly the Benghazi story.
"CNN should remove the middle N from its name," the shareholder said, before asking Bewkes if he would admit that there is a bias to the left at the cable news network.
Bewkes responded that CNN isn't making news decisions based on "serving a given part of the political spectrum or religious spectrum; we are trying to be an objective news organization."
Another shareholder questioned Warner Bros.' strategy with DC Comics, which has lagged behind
Warner Bros.' Tsujihara ackknowledged that DC Comics has not done as well as he would like but added that there is wonderful opportunity there and promised that the shareholder will be "happy and proud" down the road.
DC Comics President Diane Nelson chimed in that Warner Bros. is trying to differentiate from Marvel, which will become apparent soon. As for exploiting more female characters from the DC Comics properties, Nelson said a priority is creating properties that will appeal to young girls.