On CNBC's "Halftime Report," Pachter, who had a "neutral" rating on Twitter stock, said he expected the company to improve revenues.
"We modeled it to double in size in about five years, and if it does that, I'm optimistically at about $37," he said. "If it doubles faster, then it's probably worth what it's trading at and maybe more."
Pachter noted that National Public Radio had started to promote its contributors' Twitter handles on the day of the company's IPO, adding that it was indicative of how much it still had to grow.
(Read more: Jim Cramer: At $44, is Twitter about to nosedive?)
"So, I think as we start to see Twitter permeate media – and you've seen it on reality shows – that's when you're going to see the ramp in users because more people are going to be aware of it," he said. "More people are going to get on, and they're going to follow more interesting people. That's where the growth comes from that drives engagement that drives ad revenue. "
(Read more: Will Twitter become profitable?)
Pachter said he had high hopes for the company.
"I'm optimistic it's going to work," he said. "I'm just not sure about the share price."
— By CNBC's Bruno J. Navarro. Follow him on Twitter @Bruno_J_Navarro.