"The competition is quite bifurcate," Schultz said. "You can mention McDonald's, Dunkin, and Panera. These are good companies but they don't in anyway resonate with the consumer the way we do."
The Starbucks exec said what his company excels at is the "sourcing and roasting of quality coffees and the experience we create in our stores."
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He also pointed to the strides they've made in social and digital media, saying "all of these things have given us the ability to create significant channels of distribution outside our stores."
Starbucks is also global, with the company fast approaching 1,000 stores in China and Japan.
Dunkin, meanwhile, is focused on growth in the U.S. where it still has plenty of "white space" to open new stores, Travis said.
"We've got over 50 percent of the U.S. still to go," he said. And down the road, growth in Dunkin U.S. should rise above 5 percent.
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"On top of that we've got our other brands," Travis added. "Baskin [Robbins] is coming back to becoming a growth business and the international business is developing very nicely."