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Spotify, the streaming music service, said last week that it had grown to 10 million paying global subscribers, a long-awaited disclosure as the company faces potential competition from Apple and also prepares for a probable initial public offering.

The numbers show rapid growth for Spotify, which offers access to millions of songs for about $5 to $10 a month, or free with advertising. The company, which is privately held, has doubled its customer rolls since December 2012, when it reported 5 million paying subscribers and 20 million active users in total.

That ratio of three free users for every paying subscriber has remained steady throughout Spotify’s recent history. The service was introduced in Sweden in 2008 and came to the United States almost three years ago. When the company last reported customer numbers, in March 2013, it had 6 million subscribers and 24 million total users. On Wednesday it said that its total had grown to 40 million. Last month, Spotify announced a deal with Sprint to bundle its service with phone plans.

“We’ve had an amazing year, growing from 20 markets to 56 as people from around the world embrace streaming music,” Daniel Ek, Spotify’s chief executive and co-founder, said in a statement. “Ten million subscribers is an important milestone for both Spotify and the entire music industry.”

Among Spotify’s many competitors are Rhapsody, Rdio, Deezer and Google Play Music All Access, and it may soon face a major challenge from Beats Music, an affiliate of the successful Beats Electronics headphone brand. Beats, which opened in January, is still small, with only about 200,000 users, according to industry estimates. But news recently emerged that Apple was in talks to buy Beats’ audio brand and music service for $3.2 billion.

Neither Beats nor Apple has confirmed those talks, but an alliance between those companies could put tremendous pressure on Spotify, which has been the biggest player in subscription music.

The music business has started to see streaming as its salvation, as both CD and download sales decline rapidly. Last year, global download sales fell for the first time, by 2.1 percent, and in the first quarter of this year U.S. downloads were off by 13.3 percent compared with the same period last year, according to Nielsen SoundScan.

In 2013, streaming services yielded $1.1 billion in income for the music industry, a number that has been growing fast. Still, many artists complain that the revenue is not trickling down to them in sufficient quantities to replace the larger royalties paid by CD and download sales.

Spotify, which has been valued by its investors at more than $4 billion, is said to be preparing for an initial public offering, although the company has declined to comment on these plans. Despite the company’s success, doubts have persisted in the music business and among media analysts about how big Spotify and other all-you-can-eat subscription services can grow, particularly at a price of about $10 a month for full access.

For most of the company’s history, Spotify executives have pointed to a goal of 40 million paying users to replace the revenue the music industry has lost since its peak of around $40 billion at the turn of the millennium. At its current growth rate, it would take Spotify another three years to reach that level.

Another concern is whether services like Spotify can ever be profitable. In its most recently reported financial results, for 2012, Spotify lost about $78 million on $578 million in revenue. At the same time, it has raised more than $500 million in investment capital to finance its expansion. The company, which reports its financial results in Luxembourg, has not yet filed its accounts for 2013.