When the Walt Disney Company (DIS 0.16%) held its investor day in April, the company provided some ambitious growth assumptions for its soon-to-be-launched streaming service, Disney+. The platform, which will be stocked with beloved titles from the Disney, Pixar, Marvel, and Lucasfilm studios, is expected to grow to between 60 million and 90 million subscribers over the coming five years.

That's not all. ESPN+, which already has 2 million paying customers on its roles, is expected to increase to a range of 8 million to 12 million during that time. Hulu, which is now fully controlled by Disney, announced last month that paying members surged past 26.8 million, and Disney believes that number will reach between 40 million and 60 million by 2024.

One analyst has gone a step further and believes that Disney's U.S. customer base will surpass Netflix (NFLX -9.09%) within five years.

Two rows of Disney movie DVDs, including Snow White, The Lion King, Beauty and the Beast, and Peter Pan.

The Disney Signature Collection will be streaming on Disney+ at launch. Image source: Disney.

There's a new sheriff in town

In a bullish research note, Morgan Stanley analyst Benjamin Swinburne recently boosted Disney's price target to $160, up 18% from Wednesday's close, arguing that Disney's U.S. subscriber base is set to take off, even as Netflix's domestic growth is slowing. While the streaming giant's user growth has historically topped 25% year over year, those increases have been significantly bolstered by international subscriber gains.

Netflix added 5.14 million new U.S. customers during the trailing-12-month period, down from 5.71 million in the year-ago period. Swinburne believes the slowing growth will continue, resulting in about 79 million domestic Netflix subscribers by 2024. Swinburne estimates that the combination of Disney+, Hulu, and ESPN+ will attract about 95 million U.S. subscribers, a number that will outpace Netflix at some point in the coming five years.

Even in Swinburne's scenario, however, Netflix will still be the worldwide leader in streaming video, with an estimated 280 million paying customers around the globe within five years' time.

It's also notable that between Hulu and ESPN+, with 28 million and 2 million subscribers, respectively, Disney already commands about 20% of the U.S. streaming market, according to Swinburne.

The bigger picture

The House of Mouse is forecasting 135 million total subscribers at the midpoint of its range by 2024, with each of the three streaming services achieving profitability. Swinburne believes those targets are ambitious but achievable, as each of the brands offers a unique value proposition and path to success.

Disney+ will offer a broad range of well-loved programming including Disney classics and original content, which should lead to rapid adoption. Hulu has already achieved scale in the U.S. with a variety of ad-supported, subscription, and live-TV options that will continue to appeal to a broad range of viewers, both in the U.S. and as it expands to international markets. ESPN+ offers the most extensive package for the sports lover, and Disney could potentially renegotiate upcoming rights renewals to bolster the nascent streaming service. The company has also indicated that it will likely be interested in bundling those services at some point.

The Disney+ logo.

Image source: Disney.

Not a zero-sum game

This clearly isn't an apples-to-apples comparison, as it aggregates Disney's streaming ventures against Netflix. It's all fun with numbers and it's academic at this point. The real test will be in the months and years to come.

During the company's Q4 conference call, Netflix CEO Reed Hastings said, "We like Disney -- they have great content. We're excited for their launch." He went on to say, "We compete so broadly with all of these different providers that any one provider entering only makes a difference on the margin."

Hastings points out that about 1 billion hours of television content is consumed each day, and Netflix is "winning about 10% of it." That means there are plenty of potential subscribers to go around.