Shares of Barnes & Noble (NYSE:BKS) bounced 20% on the news that billionaire Ron Burkle, through his Yucaipa investment company, proposed to nearly double his stake in the bookseller. Burkle has called the shares undervalued -- but do they deserve a place in your portfolio?

A tough pill to swallow
Through Yucaipa, Burkle already owns some 19% of B&N, and his recent salvo across the deck involves the "poison pill" issued by the bookseller's management when he originally bought his stake last year. After the company became aware of Burkle's aggressive buying, B&N crafted an innocuous-sounding "shareholder rights plan," which prohibits any outside shareholder from accumulating more than 20% of outstanding shares. Essentially, this will thwart any hostile takeover and allow management to remain entrenched.

B&N founder and chairman Leonard Riggio and other insiders own roughly 37% of shares, according to The Wall Street Journal. Burkle is protesting this disparity, and he's entreated the board to allow him to purchase as much as 37% of shares, placing him on an equal footing with the insiders.

But despite Burkle's interest in the retailer, I wonder whether the company is a "buy." After all, Burkle seems interested in deep-value situations, such as Great Atlantic & Pacific Tea Company (NYSE:GAP), which sports a ton of debt relative to its market cap.

Here come the e-readers
Notwithstanding Burkle's assertion that Barnes & Noble is undervalued, the company faces a daunting challenge from electronic media. America's second-largest bookseller, Borders Group (NYSE:BGP) is poised to pop (in the bad way), which will undoubtedly help B&N.

But newer rivals such as Amazon.com (NASDAQ:AMZN), with its Kindle e-reader, and Apple (NASDAQ:AAPL), with its recently announced iPad, threaten to eclipse paper books with the sex appeal of their electronic gizmos. Google (NASDAQ:GOOG) seems poised to create an e-bookstore, too. And Barnes & Noble can't even catch a break in bricks-and-mortar land, as Wal-Mart Stores (NYSE:WMT) continues to slash book prices.

A whole new meaning of "book value"
As the industry dynamics change, shares of B&N look cheap. But how cheap?

Currently, the company is valued at just $1 billion. It has $157 million in cash and no debt. Barnes & Noble has managed to produce $318 million in free cash flow over the last 12 months. That performance was enabled by tightened working capital, which decreased $166 million over the same period. Even as the economy slowed, B&N prudently pared back capital expenditures.

For a company whose earnings growth has been spotty in the last five years, B&N's P/E looks high at around 15. However, lofty depreciation expenses make net income look much smaller than operating cash flow. Look closer, and the company appears cheap, trading at an enterprise value that is less than four times its trailing free cash flow. That's no typo! Even if the company returns to the lackluster performance of fiscal 2008, when free cash came in at $190 million, the multiple comes to just five.

So Barnes & Noble's shares appear to be priced as if the giants were going to throw the book at it. But that's the way all value traps appear. If online titans find the book space this interesting, B&N's shareholders should be mighty careful, no matter how cheap its shares look.

Do you think Barnes & Noble is a buy? Share your comments in the space below.

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Fool contributor Jim Royal, Ph.D. does not own shares in any company listed here. The Fool has a disclosure policy.