It’s been a nutty summer for the nation’s largest operator of book stores. Soon after Memorial Day, Barnes & Noble (NYSE: BKS) delivered the sobering news that sales and profit targets would not be met. By late July, shares had fallen all the way down to $12 — a -50% plunge in less than three months. With the smell of blood in the air, activist investor Ron Burkle made a hasty play for the company, hoping to gain control of this once-mighty retail titan.

In early August, I looked at the battle between Mr. Burkle and Barnes & Noble’s founder Len Riggio, questioning whether there was even any real value left for this storied name. [See: Don’t be Fooled by Barnes & Noble’s Desperate Ploy]

At the time, I assumed these men were battling over an asset that had little interest to any other investors. Perhaps I was wrong. The proxy battle has just concluded (with Mr. Burkle coming away empty-handed), yet Barnes & Noble has said that up to 20 other investment firms have expressed preliminary interest. In October, the bidding process will heat up as those preliminary feelers translate into actual offers.

So what’s Barnes & Noble worth? Well the table below shows us how shares trade relative to other large retail chains.

Before trying to figure out what shares would fetch in an offer, a few quick items are worth mentioning. Current sales growth for Barnes & Noble is around +20%, but that is misleading because last year’s results did not include the recently acquired Barnes & Noble college bookstore chain. In the most recent quarter, sales at barnesandnoble.com rose +42% to $142 million, but the core base of bookstores saw sales fall -2% to $1 billion. So sales at the main business are continuing to slump, even as other retailers on this table continue to eke out positive gains.

In addition, this is not a very profitable business — operating margins are a meager 1.2%. Just a few years ago, Barnes & Noble handily posted 5% or 6% operating margins, but those days are likely gone forever as e-reader book sales start to cannibalize business at the brick-and-mortar stores. In fact, it’s unclear that Barnes & Noble will even be able to generate net profits in coming years, unless the company seriously prunes its store base.

#-ad_banner-#Yet it’s clear that the business is quite undervalued on an enterprise value-to-sales basis (EV/Sales), sporting the lowest ratio. (EV/Sales is a handy measure of what each dollar of a company’s sales is worth to investors.) Of those five stocks listed here, Best Buy (NYSE: BBY) actually appears to be the best value thanks to a combination of decent operating margins and a still-low EV/sales ratio. For Home Depot, the measure is fairly high, which partially reflects strong profit margins and also anticipates an eventual strong sales rebound when the housing sector turns up. No such upturn is expected for Barnes & Noble.

To be sure, all of these retailers are trading at somewhat depressed levels relative to historical norms. When the economy is again on firm footing, these EV/sales ratios may all move above 1.0. In that context, potential acquirers of Barnes & Noble may be looking ahead to the days when the entire pack is in better favor. But these potential buyers have their work cut out for them. They’ll need to either boost sales at each store — perhaps expanding the line of goods sold beyond books and music, or they’ll have to take a hatchet to the company’s cost structure to return it to profitability.

Barnes & Noble founder Len Riggio has made it clear that he still thinks this is a richly-valued asset. He has allegedly previously rebuffed a $25 a share offer from Mr. Burkle in 2009. It’s unlikely that any future bids would be at or above that mark — especially as the company’s sales and profit outlook have weakened over the course of 2010.

Action to Take –> Shares have likely found a floor here, now that Barnes & Noble is in play. The shares could move past the $20 mark as the buyout rumors begin to swirl, so this might be a nice short-term trade ahead of a presumed bidding contest that is set to begin in October. But you shouldn’t expect massive gains, and if shares move into the low $20s, you should book profits and move on.