Robert A. Iger has insisted for months that his turnaround plan for Disney was working. But distinct proof has been elusive, and investors, as evidenced by the company’s underperforming stock price and multiple proxy campaigns by activists for board seats, have been hesitant to buy in.

On Wednesday, Mr. Iger delivered financial proof — along with a flurry of announcements about future entertainment offerings, including a “Moana” sequel, the arrival of Taylor Swift’s concert movie on Disney+, a partnership with Epic Games to create a Disney universe connected to Fortnite, and the 2025 rollout of a flagship ESPN streaming service that includes the sports giant’s primary programming.

“Just one year ago, we outlined an ambitious plan to return the Walt Disney Company to a period of sustained growth and shareholder value creation,” Mr. Iger said in a statement. “Our strong performance this past quarter demonstrates we have turned the corner.”

Mr. Iger said that Disney’s multiyear partnership with Epic Games was the company’s “biggest entry ever into the world of games and offers significant opportunities for growth and expansion.” Disney acquired a $1.5 billion stake in Epic as part of the deal.

Disney shares climbed 7 percent in after-hours trading to about $106.

Disney’s per-share earnings for the most recent quarter totaled $1.22, or 23 percent more than Wall Street had expected. Breaking from a long practice of not providing guidance about profit, Disney said per-share earnings for its full fiscal year would increase by at least 20 percent compared with 2023, in part because of record highs in revenue, profit and operating margins at its theme parks.

Mr. Iger, Disney’s chief executive, announced a $3 billion stock buyback plan, the company’s first since 2018, and a cash dividend of 45 cents a share, a 50 percent increase compared with the previous dividend, which was paid in January.

Disney’s streaming service had been expected to lose $400 million in the quarter. Instead, losses were trimmed to $138 million, as Mr. Iger reiterated that streaming would be profitable by the fall. Disney+ subscribers dipped 1.3 million in the quarter, as expected given a monthly price increase. But Disney said the service was on track to add at least 5.5 million subscribers in the current quarter.

Some investors have been worried about Disney’s ability to generate free cash flow, a closely followed measure of financial health, at a time when its television business has been undercut by streaming services. Disney, however, said it was on track to deliver $8 billion in free cash flow this year, nearing prepandemic levels.

The results come amid severe pressure on Disney from activist investors, including Trian Fund Management, which is seeking multiple board seats as it pushes for streaming profitability and a clear plan for chief executive succession, something that has bedeviled Disney. Trian, founded by Nelson Peltz, has cited Disney’s depressed stock price as its motivation.

Disney sees a revenge story: Mr. Peltz is aligned with Ike Perlmutter, who was ousted from an executive job at Disney, and Jay Rasulo, a former Disney executive who was passed over for chief executive in 2015 and resigned. Disney has asked shareholders to reject Trian and another activist investor, Blackwells Capital, arguing that giving them board seats would slow the company’s turnaround effort. (Mr. Peltz waged an unsuccessful campaign for a Disney shake-up last year.)

“The last thing that we need right now is to be distracted, in terms of our time, our energy, by an activist or activists that frankly have a completely different agenda, and don’t understand our company, its assets, even the essence of the Disney brand,” Mr. Iger said on CNBC on Wednesday.

Trian brushed aside Disney’s strong quarterly numbers and many announcements. “It’s déjà vu all over again,” a Trian spokesman said, apparently referring to February 2023, when Disney unveiled its turnaround effort. “We saw this movie last year and we didn’t like the ending.”

Mr. Iger used part of Disney’s quarterly conference call with analysts to emphasize progress in fortifying ESPN amid an uncertain future.

Disney will introduce a flagship ESPN streaming service in 2025, “probably in the fall, maybe as early as late August,” Mr. Iger said. The service will feature most of the programming currently seen on the primary ESPN cable channel. It will also offer sports betting, extensive statistics, fantasy sports, e-commerce and have “robust” personalization capabilities. (The flagship ESPN service will be separate from ESPN+, a streaming app that offers more niche programming.)

In addition, Disney, Fox and Warner Bros. Discovery announced on Tuesday that they would join together and sell access to all of the sports they televised (across 14 cable channels) through yet another new streaming service. It will be available this fall. Other details, like price or who would run the service, are not yet known.

Disney’s theme park and consumer products division delivered $3.1 billion in profit, an 8 percent increase compared with a year ago. Revenue climbed 4 percent to $6.3 billion. For the first time ever, all of Disney’s overseas theme parks were profitable, including the long-troubled Hong Kong Disneyland.

Lauren Hirsch contributed reporting.