Friday is turning into a lousy day to own Pandora Media (NYSE:P) stock. After reporting disappointing Q4 earnings Thursday, the stock is down 14% in Friday trading. But according to one analyst, all this is bad news is just prelude to some really good news:

Pandora stock could double.

Or at least FBR Capital thinks so.

The news
Pandora shares popped Thursday after The New York Times reported that the company had hired Morgan Stanley to assist in selling itself. Later that same day, however, Pandora released its fourth-quarter 2015 results, and the news was not good: Revenue jumped 25%, but Pandora lost money for the quarter.

The stock is down 17% now (3% more than I wrote just four paragraphs ago), and as I type these words, Pandora shares are changing hands for less than $8. But here's the good news: FBR thinks Pandora stock is worth $16 a stub, and upgraded the stock to outperform.

Here are three things you need to know about that upgrade.

Thing 1: FBR isn't looking for a buyout
The New York Times thinks that Pandora is for sale, presumably at a price higher than what the stock sells for now. But Pandora's earnings release made no mention of an imminent sale of the company.

No matter, says FBR. Rather than look for a buyout, FBR focuses its buy recommendation on a "conviction" that "the company can approach its new five-year goal to create a new on-demand streaming service with over 10 million subscribers while growing its core radio revenues at a solid pace."

Thing 2: Pandora actually beat on revenue
Speaking of revenue, Pandora's 25% revenue growth in Q4 sounds impressive, but it was actually more impressive than that. Management had predicted the company might collect as little as $325 million last quarter -- $330 million at most. Instead, the company recorded Q4 revenue of more than $336 million.

Pandora's latest guidance calls for the company to produce better than $1.4 billion in revenue in the current year, which would work out to better-than-20% revenue growth. So there's at least some basis for FBR's optimism.

Thing 3: Revenue isn't profits
On the other hand, one thing that Pandora definitely did not promise in Thursday's guidance was that the company would earn a profit this year. Instead, management guided toward an "adjusted EBITDA loss" of $60 million to $80 million.

That's not encouraging -- but it probably is accurate. Turns out, according to data provided by S&P Global Market Intelligence, Pandora Media has never earned a full-year profit in any year it's been in business. Neither has the company ever generated a single cent of positive free cash flow.

Instead, last year, the company reported losses of $160 million, and negative free cash flow of $74 million. And judging from management's guidance, the news in 2016 won't be much better.

And one more thing...
So why does FBR think all of this adds up to a buy rating for Pandora? At the risk of sounding harsh...because FBR is really bad at math.

A StreetInsider.com recap of FBR's Pandora recommendation Friday laid out the banker's math thusly: FBR, says StreetInsider, "sees radio worth $9.79 per share and On-demand worth $4.47 per share." Investors hoping those two numbers would work out to FBR's professed valuation of $16 on Pandora stock are bound to be disappointed. But here's an even more disappointing number for Pandora fans:

26%.

That, according to our data here at Motley Fool CAPS, is FBR's record of accurately picking winning stocks in the Internet software and services sector over the past decade. Ten years of stock picking in this sector has seen FBR pick far more losers than winners, and rack up a record of 355 percentage points' worth of market underperformance along the way.

A better way to make money
Suffice it to say, none of the above gives reason to be optimistic that FBR's buy rating on Pandora Media will make you money. But here's an idea that might:

Established in 1990, Sirius XM Holdings (NASDAQ:SIRI), a Pandora competitor in subscription and Internet radio, has been around a lot longer than Pandora. It's also done a much better job than Pandora at earning its keep.

Consistently profitable for the last six years, Sirius earned GAAP profits of $510 million in 2015, and generated more than twice that amount of free cash flow -- $1.1 billion. Valued on those cash profits, Sirius stock sells for less than 16 times free cash flow (or about 20 times FCF with debt factored in). Analysts who follow the stock predict that Sirius will grow its profits at about 20% annually over the next five years -- roughly the same rate at which Pandora aims to grow revenue next year.

But whereas Pandora is growing revenues, Sirius is growing profits. Given my druthers, I'd rather own a piece of a company growing the latter. And given my druthers, I'd rather own Sirius than Pandora.

Fool contributor Rich Smith does not own shares of, nor is he short, any company named above. You can find him on Motley Fool CAPS, publicly pontificating under the handle TMFDitty, where he's currently ranked No. 241 out of more than 75,000 rated members.

The Motley Fool still owns shares of and recommends Pandora Media. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.