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Tully’s Coffee needs a quick answer in bankruptcy court Friday about who is going to buy it, because the chain is on the verge of shutting down altogether, the company said in a court filing Thursday.

Financial advisers have determined Tully’s ability to operate into February is “very questionable,” the filing said.

The Seattle-based coffee shop chain and its creditors chose a $9.15 million offer from actor Patrick Dempsey’s investment group during a private auction last week.

But Starbucks and a Filipino company called AgriNurture plan to argue in court that their bids, which together total $10.56 million, should be chosen instead.

And Tully’s founder Tom O’Keefe, still a major shareholder, asked the court in a filing to continue the auction, which concluded last week with the selection of the Dempsey bid.

However, Tully’s CEO Scott Pearson said in a filing Thursday that O’Keefe appears to have no stake in the outcome of a sale.

O’Keefe owns no shares in the class that would be paid first, and the purchase price would have to exceed $29 million for O’Keefe to be paid, Pearson said.

In its filing, Tully’s said it chose Dempsey’s bid for a number of reasons, including one cited earlier by AgriNurture.

That issue involved Tully’s doubts about whether Green Mountain Coffee Roasters, which bought naming rights for Tully’s in 2009, would agree to a deal in which the buyer purchased only some Tully’s locations.

Green Mountain subsequently told the court it would work with either Dempsey’s group or AgriNurture.

Under its bid, the Filipino company would acquire only those stores Starbucks would not purchase.

However, Tully’s and its creditors had other reasons to select Dempsey’s offer.

The actor’s group promised to keep the company’s roughly 480 employees, Tully’s said in its Thursday’s filing, whereas Starbucks promised only to consider their applications.

A Starbucks executive has since said the employees would receive priority treatment.

The filing added that Starbucks said it would not honor prepaid Tully’s cards, even at the 12 shops at Boeing locations it wants.

Boeing has a payroll-deduction program for Tully’s cards, and about 40 percent of Tully’s card activity occurs at those locations.

Tully’s has about $5.4 million in liabilities associated with the cards, $1.8 million of which it estimates could be redeemed if the new owner or owners honor the cards.

“If the cards are not honored at some stores, a consumer backlash may well dwarf the $1.8 million of estimated redemptions, under the business-as-usual assumptions,” the Tully’s filing said.

Melissa Allison: 206-464-3312 or Twitter @AllisonSeattle.