At the behest of a key shareholder, bookseller Barnes & Noble (NYSE: BKS) is in search of a potential suitor. Yet the company’s prospects are dimming, and it’s unclear if any such buyer exists. If you own this stock, look to take profits now. If you don’t, it may be ripe for a short position.

Running hard to stay in place
As we’ve noted before Barnes & Noble is ill-equipped to compete in the e-book segment against the likes of Amazon.com (Nasdaq: AMZN) and Apple (Nasdaq: AAPL). Soon after noting this, Barnes & Noble stated that it will need to spend large sums of money to retain market share, in effect running hard just to stay in place. Just 90 days ago, analysts thought Barnes & Noble would earn close to $1 a share both this year and next. Now, the bookseller will be hard–pressed to eke out a very tiny profit.

Buying what exactly?
In the face of such anemic profits, Ron Burkle, a 19% shareholder that tends to focus on the publishing business, has pushed the board to put Barnes & Noble in play. Before you get too excited, know that Burkle has a very spotty record in terms of unlocking value in the publishing space. For example, he amassed a large position in Source Interlink, one of the nation’s largest distributors of magazines, and similarly agitated for moves to unlock shareholder value. Source Interlink went on to declare bankruptcy in 2009.

Of course, this is not to suggest that Barnes & Noble will suffer a similar fate. But it’s fair to wonder just what potential investors would be getting. There’s the company’s massive retail store base, a growing and profitable online site (bn.com), and a fledgling division focusing on the e-books opportunity. Of the three, only bn.com holds real appeal. The other two have real challenges.

Any potential buyer is likely to be turned off by the e-books division. Amazon has begun to pull away with an impressive razor-and-razor blades strategy, selling its Kindle Reader at a likely loss but attracting surging volume for e-book titles. Barnes & Noble had planned to spend heavily to try and catch up, but by putting the company on the block, that’s now in question. Potential buyers would likely decide against such an expenditure, especially if they are looking to simply wring cash out of the business.

Large fixed costs
If a potential buyer wanted to simply focus on that retail footprint, they will likely cast a wary eye on the company’s base of more than 700 stores. That’s because e-books are really starting to impact the publishing business. Amazon.com noted late last week that e-books now outsell hardcover books. Most industry watchers thought it would be several more years before that transition took place.

So if hardcover book sales are entering into a secular decline, what does that mean for the stores? Well, the high fixed costs associated with operating a book store will likely mean that an increasing number of stores will generate losses and need to be shuttered. Again, the question must be asked, what exactly is a potential buyer getting into?

Prior to today’s spike, Barnes & Noble was valued at about $750 million, and after the spike is valued at about $930 million. A very reasonable price when you consider that Barnes & Noble typically generated around $400 million in annual free cash flow in the middle of the last decade. Yet free cash flow was negative in fiscal (April) 2010, and will likely be this year as well. The company’s EBITDA margin is on track to decline for the seventh straight year.

As to who would buy Barnes & Noble, several media outlets are floating names such as Amazon.com and Microsoft (Nasdaq: MSFT) — which is absurd. Ideally, the company would find a buyer in the Private Equity (PE) space, but PE buyers typically like companies with lots of cash flow, and at least as of now, Barnes & Noble’s spending plans likely entail negative cash flow in the near-term. PE firms like to have a chance to take a company public at a higher price down the road. No such exit appears to be in the cards for Barnes & Noble.

The company’s founder, Len Riggio, who along with relatives still controls about a third of the company, might step in. He has cashed out enough stock over the years to be able to make a bid. But he never appeared to have real interest in doing so until Ron Burkle turned up the heat. For that matter, Ron Burkle also has the financial firepower through his Yucaipa hedge fund, but has a history of trying to acquire companies on the cheap and is unlikely to buy the bookseller at a premium to today’s price.

Today’s New York Times notes that Mr. Burkle “considered” making an offer of $25 a share back in November. But that was before this business model really started to sink into the mud.

Action to Take –> By agitating for change, Ron Burkle is hoping that a White Knight will emerge from parts unknown. But that’s unlikely to happen. When the dust settles, and no buyers emerge, shares could give back all of today’s gains — and then some, as investors increasingly focus on the broken nature of this business model. Watch how shares trade in coming sessions. If they strengthen any further, then shorts might be looking at an enticing play. Downside for shorts is likely limited, as there isn’t much more upside after today’s run.