At The Motley Fool, we poke plenty of fun at Wall Street analysts and their endless cycle of upgrades, downgrades, and "initiating coverage at neutral." Today, we'll show you whether those bigwigs actually know what they're talking about. To help, we've enlisted Motley Fool CAPS to track the long-term performance of Wall Street's best and worst.

2013: Happy New Year for Facebook investors?
It's Dec. 31, Fools, the last day of 2012. And you know what that means: There's still time for Wall Street analysts to squeeze out one last upgrade for Facebook (META -2.87%). One last chance to coax reluctant investors into a stock that's already lost 30% from its IPO. And so it was that this morning, analysts at BMO Capital announced they were resuming coverage on Facebook, and switching from "underperform" to "outperform" stance.

Why? As StreetInsider.com explained today, analysts at BMO think Facebook is "experiencing a reacceleration of ad spending from large brands that are returning for mobile 'reach & frequency' and more video ads." BMO also sees good things happening in both the Facebook Exchange and Custom Audiences ad businesses, and sees Facebook as "more fully embracing native monetization like Sponsored Stories and Gifts." Ideally, these developments will offset any downside from the company's split from Zynga (ZNGA) on social gaming.

In a related development, news reports  over the weekend noted that Google's (GOOGL -0.85%) search engine has been flagging Twitter's Twitpic service for potential malware infection. Combined with Facebook's recent Twitter tiff, over the posting of Instagrammed photos on the microblogging site, this appears to increase the pressure on a key Facebook rival.

The numbers
What it all comes down to, in BMO's view, is a better year ahead for Facebook. The analyst is now projecting Street-topping revenues of $1.7 billion for Facebook as we exit the 2012 fourth quarter. That's 30% revenue growth over last year's Q4. The analyst sees earnings doing even better as well, positing a pro forma $0.72 per share for fiscal 2013, versus BMO's previous estimate of $0.60.

Based on these numbers, BMO argues that if you apply a 45 multiple to pro forma earnings, it falls "comfortably ... between Google's 15x multiple and LinkedIn's (LNKD.DL) 100x."

But is that reasonable?

Valuation matters
I won't argue that 45 is not a number "comfortably between 15 and 100." That's just math. But BMO could just as easily have pointed out that "16" is also such a number. Or "99." It makes you wonder why BMO seems to think 45 is the right number to be using here.

I mean, consider: BMO is saying Facebook will grow revenues 30% in Q4. Well and good. Most analysts on Wall Street see long-term earnings growing at a similar rate for Facebook -- 29% being the current consensus. This suggests that a more appropriate multiple for Facebook might be not "45," but "30."

Now here's the problem: When we apply a 30 multiple to Facebook's $524 million in trailing earnings, or to its more modest $219 million in trailing free cash flow, what we come up with is a valuation of anywhere from $6.6 billion to $15.7 billion on the stock. Not to belabor the obvious, but either of those numbers would be a far sight from the $57.2 billion market cap Facebook currently carries.

And either of those numbers, if applied to the stock in 2013, will mean more pain ahead for Facebook shareholders.