Updated from 12:24 p.m. EDT

SAN FRANCISCO -- Hope springs eternal at eBay ( EBAY), despite the company's core business providing little justification for it.

The online auction site's stock was 4.4% higher to $12.14 Thursday, a day after the company laid out to analysts its plan to re-focus itself on growing businesses that are actually growing and scaling back the ambition of its main marketplace site.

Helping eBay shares along was management's projection that it would reach overall revenue of $10 billion to $12 billion in 2011, up from $8.5 billion in 2008.

Let's start there: If battered investors have learned anything from the past six months it's that a projection for what a business will do three years from now -- even with the generous $2 billion leeway -- is about as valuable as the 2004 Eric Gagne Los Angeles Dodger bobblehead that eBay will currently help you buy.

Don't you suppose Citigroup's ( C) forecast was fairly cheery in 2006?

Consider the current Street estimates for eBay. In 2009, analysts are calling for a pullback in revenue to $8 billion. For the sake of argument, let's say that seems reasonable enough given the state of consumer fear (note to Thursdays' retail-sales watchers: Consider the impact of the 8% month-to-month gain in gas prices).

So, too, then do estimates for 2010 revenue to essentially climb back to 2008 levels at $8.43 billion.

But then, in 2011 we're supposed to look for as much as a 40% jump in revenue? Either eBay will be proven wrong or Wall Street will, and not a lot of money has been made betting on eBay over the past four years.

The company's forecast, which includes expecting operating earnings to grow in the mid-single digits by 2011, lies in part on the assumption that the global economy, as CFO Bob Swan put it, "returns to some sense of normalcy."

But what's normal for eBay? Unfortunately, it appears to be repeated missteps and miscalculations that have stagnated the company's auction site and thrown it under the bus driven by Amazon.com ( AMZN), which now appears destined to be the No. 1 look-no-further online destination for consumers.

Aah, but you say eBay isn't really eBay anymore. eBay is its PayPal e-commerce payment system and its Skype Internet phone division. This is becoming increasingly true, and the company has said itself that PayPal revenue could more than double by 2011 to become the largest part of eBay's business.

Here, too, lie some near-term problems, however. JPMorgan analyst Imran Khan noted on Thursday that the division still faces margin issues related to integrating its recent Bill Me Later purchase. Khan also sees about $3 billion in 2010 revenue at PayPal, suggesting, if he's right, that eBay's projection of as much as $5 billion in 2011 is perhaps reaching a bit much.

The company's updated plan for its still-core marketplace site is to retreat from competing against the likes of Amazon and Wal-Mart ( WMT) as a broad retailer of original goods, falling back on its original kingdom of sales of used and over-stocked goods.

But in this dreadful economy, which is getting more dreadful by the day, wouldn't you think bargain-hunters would already be flocking to eBay?

That they're not underscores the magnitude of the problems with the company's main reason for existence. Until a turnaround is engineered there, not much hope exists for a significant stock gain.

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