Founded in 1903, Harley's sales have been shrinking, with an aging customer base hurting prospects.

Harley-Davidson Overseas 'Americana'

According to Wedbush analyst James Hardiman, many people willing to buy motorcycles are opting for used ones.

"(Harleys) sell Americana, essentially," Hardiman said. Currently, Harley produces a small amount overseas, along with India and Brazil facilities that assemble bikes from U.S.-made components. But being the target of Trump's ire could hurt, he said.

"They have been big advocates of free trade," he continued. "But at the same time the last thing you want to do is get in a Twitter war with the president of the United States, whose support base clearly overlaps with their customer base."

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