NEW YORK — An activist investor has proposed taking Barnes & Noble private but the company does not consider the offer genuine, the book chain said Thursday. Its shares soared on the report.

Sandell Asset Management approached the company with a proposal valuing it at more than $650 million, the company said. The proposal would require debt financing of about $500 million, according to the bookseller. Sandell’s CEO previously said the chain would be better served if it were private or part of a larger company.

The chairman of Barnes & Noble, Leonard Riggio, owns an 18 percent stake in the New York company.

In a statement, Barnes & Noble said, “The company does not take Sandell’s proposal as bona fide in that Sandell is the beneficial owner of 1 million common Barnes & Noble shares worth approximately $7 million, Mr. Riggio has no intention of rolling his shares into such a transaction, and the company believes a debt financing of $500 million is highly unlikely.”

Barnes & Noble, long struggling with increasing competition from Amazon, has been cutting costs but in September reported results that showed even online sales dropped.

Sandell Asset Management Corp. CEO Thomas E. Sandell had said in a letter to Barnes & Noble’s board in July that the company is the only “truly national bookstore chain” and compared its locations to “beachfront property.” He said the company could get more than $12 per share.

Trading in Barnes & Noble stock was halted briefly after the proposal was made public. In afternoon trading, its shares rose more than 7 percent to close at $7.10. They’ve fallen more than 41 percent in the last year.

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