Has Yahoo! (NASDAQ:YHOO) finally given up in its pursuit of Facebook? According to Michael Arrington's TechCrunch blog, the Web giant's so-called "Project Fraternity" may be in for a bumpy landing. According to leaked documents that Arrington has received, talks started earlier this year, when Yahoo! offered to buy a 5% stake in the company for $37.5 million.

That seems to be a popular bite-sized morsel, since it occurred around the time that Google (NASDAQ:GOOG) paid $1 billion for a 5% piece of AOL. Facebook balked, and Yahoo! ultimately returned with a $1 billion price tag for all of Facebook.

According to Arrington, Yahoo! was willing to go as high as $1.62 billion (again, another number apparently close to rival Google's heart, given its eventual $1.65 billion stock deal for YouTube), but talks broke down before Yahoo! could raise its offer.

Given slower traffic trends in recent months at Facebook, perhaps Yahoo! should consider itself lucky. In its projections, Yahoo! had assumed that registrations would continue to grow at a healthy clip, and perhaps more importantly, that advertising revenue would skyrocket.

In the document, Yahoo! claims that Facebook generated $0.26 in ad revenue for every 1,000 impressions. Yahoo! was assuming that it could prop that figure up to $3.77 come 2010, and $5.54 by 2015. Those are some perilously dangerous ledges from which to hang your hats, given that online advertising revenue per page may stabilize before then. It's also possible that a mad rush to populate Facebook with ads would send users scrambling to other walled-in social-networking sites.

A deal may still happen, since Facebook remains valuable. However, social networking has been fickle. Remember when Friendster could command a king's ransom as the pioneer? Even News Corp.'s (NYSE:NWS) MySpace has shown some growing pains lately.

Don't get too greedy, Facebook. And Yahoo!, don't take advantage of a less greedy Facebook. One site could use a sugar daddy, and the other could use the high-profile real estate. The deal still makes sense. Time will tell whether it makes dollars and cents, too.

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Longtime Fool contributor Rick Munarriz is a convergence junkie, even if it means that he will ultimately be replaced by a more efficient version of himself. He does not own shares in any of the companies in this story. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.