CBS (NYSE:CBS) thinks it has two of the most valuable networks for subscribers in its flagship network and Showtime. And the success of its direct-to-consumer products for each of those networks is proof that viewers are willing to pay up for its programming. CBS All Access -- CBS's over-the-top service that includes live streams of local CBS stations as well as archives of its old shows -- is adding more subscribers every month.

"We just had our best quarter ever, followed by our best month ever in January, followed by our best day ever for sign-ups this past Sunday," CEO Les Moonves said about the service on the company's fourth-quarter earnings call. The accelerating growth should be very encouraging for investors even though All Access remains a very small part of CBS as a whole.

CBS All Access on a laptop

Image source: CBS.

CBS's expectations are surprisingly conservative

At last year's investors' day, CBS COO Joe Ianniello said the company expects both All Access and Showtime to each have 4 million subscribers by 2020. "As we sit here today, with four years to go and less than 6 million subs to achieve our goal, it appears that our goal may have been too conservative," he said on the fourth-quarter earnings call.

Indeed, customers are flocking to over-the-top services. Time Warner (NYSE:TWX) reported that more than 2 million customers have signed up for its HBO Now service.

Ianniello sees All Access and Showtime OTT growth as additive to its subscriber base. "A lot of this growth is coming from households that are broadband only," he said. While Time Warner also sees HBO Now subscribers coming mostly from broadband-only households, its total subscriber growth has remained relatively flat as customers cut the cord and it renegotiates deals with pay-TV providers.

Supporting $1.5 billion in revenue growth

CBS is using All Access as a negotiating tool for its retransmission rates with pay-TV providers. Its ability to grow subscribers is a key leverage point for CBS to hold against the cable companies. If millions of people are willing to pay $6 per month for CBS All Access, it shows how much they value the network as part of their bundle of channels (whether that's through cable or their own mashup of OTT services).

CBS surpassed $1 billion in retransmission and reverse compensation revenue last year. It expects that number to climb 25% this year. By 2020, CBS thinks it will bring in $2.5 billion through these fees and subscriptions. The growth of All Access will contribute directly and indirectly to that numbers growth as it leads the way for CBS to increase prices with traditional distributors.

CBS will have the opportunity to reset affiliate fees for about one-third of its total footprint over the next 24 months, according to Ianniello. That makes the next couple of years crucial for CBS to execute on its strategy and for the growth of All Access.

CBS is investing heavily in the over-the-top service, including a new deal to stream NFL games as well as several original shows exclusively made for the streaming service. The deal with the NFL began at the beginning of December and led to CBS's strongest quarter followed by its strongest month in January. With the deal in place for the full season in 2017, we could see significant growth in the latter half of the year. In the near term, a steady rollout of new shows like The Good Wife spinoff and a new Star Trek series could bolster subscriber growth as well.

CBS's OTT expectations seemed very lofty initially, but the acceleration in subscriber growth is very encouraging for investors.

Adam Levy has no position in any stocks mentioned. The Motley Fool recommends Time Warner. The Motley Fool has a disclosure policy.