That growth would be driven by growing digital revenues, Iger said, as Disney took more content direct to consumers, and its most popular franchises returned to the big screen.
This rare projection for a company that usually steers clear of sharing any outlook, which comes after the company reported a 4th quarter that fell short of Wall Street expectations on both the top and bottom line - a result Disney attributed partly to the confusing addition of a 53rd week in the prior year.
"We want our investors to know that fiscal 2017 is going to be an anomaly," said Iger, citing higher costs at ESPN due to a new NBA contract, and tough comparisons to the company's record box office on the back of "Star Wars: The Force Awakens."
Disney's future, Iger explained, was in bringing its valuable brands and their premium content to consumers in new, digital ways, with a key part of that being Disney's acquisition of streaming video technology BAM Tech. When Disney launches the new ESPN services that are currently in the works, they'll gather more information about their viewers, to make ads more targeted and valuable.
But in the meantime, ESPN must continue to deal with a declining number of subscribers.
In the face of persistent concerns about ESPN, Iger defended the business, saying when accounting for the tough comparisons, "it was a very strong quarter of a phenomenal year."
And now, Iger said, ESPN was looking better than it did in August 2015 when he raised concerns about subscriber losses.
"What we've seen since then is somewhat of a moderation of losses stemming from the skinny bundles," he said. "We also have a number of new platforms coming into the market."
Iger cited AT&T's direct-to-consumer platform, Hulu's upcoming skinny bundle, and Sling's existing business as examples.
Iger was confident that these new ways of distributing Disney content would be a game changer for the next generation. He said the company believed the new bundles "will be attractive for millennials who thought the expanded price of bundles was too high and the user interface" wasn't good enough.
He was also optimistic about the fact that ESPN "adapts very well to mobile platforms, and that's where we're moving. So we feel really good with ESPN. We're dealing with some near-term issues with ESPN, we're eyes wide open on that. But we think the long-term revenues are going to be just fine."
Iger stressed that the company was seeing growing revenue from these digital bundles - revenues that haven't been included in Nielsen's numbers, which show a rather precipitous decline in subscribers.
"I won't say they're dead wrong; i think it's possible their sample was off," he said.
"We've seen examples lately of samples being off in terms of predicting outcomes," Iger added, citing the surprise win of President-electDonald Trump. Iger said digital revenue "is growing at a compelling rate and will grow at an even more compelling rate when new platforms" such as AT&T's new bundle and Hulu launch."
As for the suggestion by fellow media mogul, Liberty Media's John Malone, that Disney may want to spin off ESPN, Iger laughed: "That's his speculation."