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"Apple is out of the gate now and we know what it is and it's nothing special,"

Wedge Partners analyst Martin Pyykkonen said two days after iTunes Radio launch.

It is hard to tell if Pandora's (NYSE:P) shareholders are illiterate, or simply choose to disregard concrete facts. Pandora has been failing for the past 13 years; Apple's (NASDAQ:AAPL) launch of iTunes Radio might finally put Pandora out of its misery.

This week Pandora's CFO Mike Herring responded when asked about iTunes Radio being a threat, stating:

"It's not that it isn't a threat to Pandora. Don't get us wrong, we take them very seriously and do see them as a credible threat. Keep in mind there have been lots of credible threats over the years, from startups to Microsoft to Google, to Apple and Twitter this year. We absolutely see iTunes as a competitive option out there, but we think we are a great service that does this better than anybody else."

It appears Pandora and its supporters are starting to retract their original statements that iTunes Radio is no threat; possibly in an attempt to reduce the impact of future news.

Simple Math

Now I am no math major but… according to the complicated laws of subtraction...

Pandora cannot afford to lose one user, yet they stand to lose anywhere from 5 million to 36 million users, directly to iTunes radio. The 5 million figure is an extremely conservative number and the absolute best case scenario for Pandora. The 36 million figure would be the absolute worst case scenario for Pandora, as half of Pandora's 72 million user base uses iOS devices. (There are not many figures available at this time about iTunes radio performance, so I will be extremely conservative with my numbers as they will be the absolute minimum, realistically the figures could be more than double, triple or even quadruple.)

Five days after iTunes radio launched it had already attracted 11 million unique iOS 7 users. That was a month ago, and chances are that the 11 million users have doubled if not increased significantly more since then.

Again, an extremely conservative estimate would lead one to believe that upwards of 20 million iOS 7 users have now used iTunes radio. It is reported that 42% of the 67 million monthly iTunes users use Pandora, and around 50% of Pandora users access Pandora with an iOS device. Those are two incredibly threatening statistics to Pandora's livelihood.

42% of 67 million is 28 million; thus 28 million iTunes users used Pandora on a regular basis. If there are 72 million monthly Pandora users, almost 40%, of those users use iTunes on a monthly basis. Out of those 28 million iTunes-Pandora users it could be conceivable that half, 14 million, have already sampled using iTunes Radio. For conservative purposes, let's cut that figure in half again and assume that 7 million of those users are going to go on to using iTunes radio monthly. Of course, those 7 million less Pandora users only account for those who used iTunes-Pandora on a monthly basis. There are still hundreds of millions of iOS 7 users not included in that 7 million figure who neither use Pandora or iTunes.

50% of Pandora users use an iOS device. That means 36 million Pandora users access Pandora using an iPhone, iPad, Mac or iPod touch. This means that on top of the 28 million users who already use iTunes and Pandora, there are another 8 million iOS users who use Pandora but not iTunes Radio. Now it could be assumed that these 8 million users have less loyalty to Apple since they do not use Pandora monthly. So if we divide this number in half we would get 4 million; now since these users are less loyal, let's shave off another million. This 3 million figure represents iOS users (who do not use iTunes but use Pandora) that have sampled iTunes Radio. Now dividing that number in half again would equate to 1.5 million monthly iTunes users.

Adding 7 million to 1.5 million gives 8.5 million users who have already migrated from Pandora to iTunes. This would mean Pandora has already lost 12% percent of its monthly users, in a month.

Although Pandora did put out figures for September, like they do every month, claiming that they were not losing ground to iTunes radio, the effects were already noticeable. iTunes Radio was out for less than half a month in September and had a noticeable effect on Pandora's growth. In July Pandora users numbered 71.2 million. One month later in August, Pandora users were 72.1 million, a 900,000 users increase. Then in September, monthly users totaled 72.7 million, an increase of just 600,000; thus growth slowed by 300,000 users between August and September.

Although this is not a significant amount, iTunes Radio was out for only 12 days in September, with the amount of iOS 7 downloads nearly doubling since September.

There's a chance Pandora will not crash and burn like some predict since half of their users do not have devices that can run iTunes radio. Though Pandora's share price is going to significantly drop, the stock's price will most likely remain over 20 dollars for another few weeks until Pandora announces their next monthly metrics around November 5th or 6th. Although Apple has not announced any plan to reveal iTunes radio metrics, it is likely they will within the next two weeks. Until then, the short-squeeze that has been occurring will likely keep the stock significantly higher than it should be.

Pandora still has hope to stay afloat as a leading internet radio company, as they still have the most advanced music taste technology. The stock price though remains unjustifiably high, and could easily face a correction of 50% or more.

It will be very interesting to see if my predictions are true that 8.5 million Pandora users have gone to iTunes Radio. If I am right, and Pandora has lost 12% or more of its user base in the past month, panic could carry the stock to single digits by Christmas.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: No of these estimates are facts, they are simply my opinions based off of research I presented in the article.

Source: Simple Math Proves Pandora's Doomed