Pandora has 54.9 million active users currently, while Rihanna has 63 million fans on Facebook.
So Pandora has claimed only a small part of the music listener universe. And as the chart below shows, user growth at Pandora isn't very aggressive — it doesn't look as if the company is going to double its user base anytime soon.
This isn't a business problem for Pandora until you look at it in the context of Pandora's overall user base and its contractual relationships with artists like Rihanna.
Sound Exchange, the artists' royalties company that distributes fees from online music companies, paid out $122.5 million to its artists in Q3 2012. According to Pandora's most recent quarterly filing, it paid $60 million to Sound Exchange artists, after booking about $90 million in ads played between those songs.
So even though Pandora is the biggest music streamer, it might be less than half of the entire music streaming universe (Spotify and various radio stations make up the rest).
At the same time, Sound Exchange and the artists it represents is lobbying against Pandora's desire to lower the royalties it pays even further. Lower royalties would ensure Pandora's economic survival, but it would make the service even less important to huge artists like Rihanna. If Pandora doesn't get those lower royalties, it will eventually run out of cash (absent debt or third party financing).
In other words, Rihanna doesn't need Pandora financially as much as Pandora needs Rihanna.
And that's a huge problem for Pandora.
Until now, Pandora's argument has been that without it, artists would lose the huge revenue stream it pays them. But for the most important artists, Pandora is something they'll barely notice if it went away.
More From Business Insider