Sears Holdings

(SHLD)

sweetened its offer for its Canadian subsidiary to

Vornado Realty's

(VNO) - Get Report

liking, but at least one investor is holding out for more.

With the extended deadline for its tender offer approaching, Sears on Monday raised its bid for the remaining portion of

Sears Canada

it doesn't own to C$18 a share from C$16.86. In addition, the company said Vornado agreed to tender its 7.5 million shares for the higher price.

Meanwhile, a person familiar with the matter said hedge fund Pershing Square Capital Management is holding on to its stake, based on a belief that Sears Canada's real estate assets make it worth closer to C$30 a share.

William Ackman, the manager of Pershing Square, showed his sweet tooth for real estate plays in retail late last year when he publicly pressured

McDonald's

(MCD) - Get Report

to spin off its real estate holdings into a separate trust. He speculated that shares of the fast-food giant could trade anywhere from $10 to $15 higher if the market fully realized the value of its real estate. McDonald's ultimately rejected the plan, but did address some of Ackman's criticism.

For its part, Sears said "the decision by the two largest independent shareholders, Natcan Investment Management and Vornado Realty Trust, to tender their shares, representing over one-third of the minority shares, is clear evidence that our revised C$18.00 offer represents a full and fair price."

Sears estimated it now owns more than 70% of its Canadian counterpart, having scooped up 35% of the minority shares since it began its effort to take the company private. The company's latest offer expires April 18.

Natcan Investment Management, whose 9% stake in the retailer makes it Sears Canada's largest independent shareholder, tendered its 9.7 million shares at the original offer price, despite advice from the retailer's independent directors, who said the offer was too low.

Citing a report from Sears Canada's financial adviser, Genuity Capital Markets, the independent directors valued the Canadian unit at C$19 to C$22.25 a share. But in what many view as a sign of protest, all six of those directors have said they won't seek re-election to the company's board at its annual meeting on April 27, even if shareholders follow their advice and reject the parent's offer.

When its original deadline came and went in mid-March, Sears had only succeeded in raising its stake in Sears Canada to 63.2% from 53%. The result came as a defeat for the U.S.-based retailing giant, which was cobbled together last year when hedge fund manager Ed Lampert orchestrated the merging of Kmart and Sears. In response, the company extended the deadline without raising its offer and threatened to cut off dividend payments to Sears Canada shareholders.

Back in February, Sears Holdings Vice Chairman Alan Lacy warned Sears Canada's shareholders in a press release that after the original March 17 deadline, "shareholders will only have two choices: either tender to the Sears Holdings offer

of C$16.86 or continue to hold shares, which we believe will thereafter trade at a significant discount to our offer."

Now, more than two weeks after that date, shareholders have another two options -- sell their shares to Sears for its higher offer, or continue to hold out under the belief that more sweetening is in store. Shares of Sears Canada closed Monday at C$18.55, 55 cents above the raised bid.

Vornado may have chosen to sell its shares, but its mere presence at Sears Canada suggests the retailer may be sitting on the same sort of hidden real estate asset value that drove a frenzy of speculation in shares of Sears and Kmart before they merged.

Vornado, run by highly regarded value investors Steven Roth and Michael Fascitelli, has a long history of carving real estate wealth out of broken retail businesses, and it makes no secret of its strategy. In its 2004 annual report, Roth portrays himself as retail's version of another legendary speculator.

"Some of you may remember an oilman named T. Boone Pickens, who in the 1970s discovered that one could mine for oil cheaper on the

New York Stock Exchange

than in the oil fields," Roth wrote. "We learned that lesson too, with respect to mining for retail square footage in the stock market, where irreplaceable retail real estate can be obscured by a failing retailer. Extracting these values is indeed a core competency of ours, and one that has created vast wealth for our shareholders."

The size of Pershing Square's stake in Sears Canada isn't publicly disclosed. Whatever value lies in store at the retailer, only time will tell if the hedge fund and its fellow remaining holdouts up north can hold off the third-largest retailer in the U.S.