Morgan Stanley on Thursday raised its forecast for Disney shares as interest in the media giant's new streaming service puts it on a path for healthy long-term profit.

Analyst Benjamin Swinburne hiked his price target to $160 from $135, predicted over 130 million over-the-top subscribers around the world by 2024 and wrote that Disney+ should boost the company's adjusted earnings per share over $11 over the next five years.

Disney posted $7.08 earnings per share in fiscal year 2018.

"Stepping back and admittedly taking the long view, investing in Disney shares is a play on the durability of its IP," Swinburne said. "Encouragingly, consumers are voting with their wallets today, spending an estimated $15-20bn a year for movies and TV product that will ultimately make its way to Disney Plus."

Disney shares rose 1.4% in premarket trading following the Morgan Stanley note. The stock is up about 24% so far this year. The platform, which was unveiled by Disney's top brass in April, should attract about 13 million subscribers at the end of fiscal 2020 and 70 million by 2024, the analyst wrote.

And while Morgan Stanley isn't the only brokerage positive on Disney+, much of the bullish case behind the new service centers around its extensive film and television catalog as well as the promise of new shows featuring favorite characters from Pixar Studios to "Star Wars."

"Disney already incurs significant marketing costs supporting its brands, notably its films, and as a narrower service, it is not trying from a content perspective to be all things to all people, therefore requiring less content volume," Swinburne added. "We believe the market has often overstated the risk and underappreciated the reward of the transition to streaming."

The service will cost subscribers $6.99 per month, or $69.99 per year, which is at the high end of what many analysts had expected.