Shares of Yahoo slid 5 percent on Thursday, after falling nearly 2 percent overnight. Verizon shares ticked nearly 0.5 percent higher on Thursday.
Jason Helfstein, Oppenheimer managing director of internet equity research, told CNBC's "Power Lunch" he still has an outperform rating on Yahoo. If Verizon knocked $1 billion off its billion offer, that would be an impact of 62 cents a share after taxes, Helfstein said, far below the $2.03 per share that Yahoo fell by Thursday afternoon.
"I think this is a way to reduce the price. At the end of the day, Verizon wants this property," Helfstein said. "They want to put it together with AOL. They want to invest in ad technology across both brands. They want to build ad tech, ultimately to try to be competitive with Google and Facebook."
Yahoo said Wednesday it had discovered a new breach that occurred in August 2013 and involved data associated with more than 1 billion accounts, double the number affected in a different breach disclosed in September.
The earlier breach, which affected at least 500 million user accounts, was one of the world's biggest known cyber breaches of a single site.
After the new breach was revealed, Verizon told CNBC: "As we've said all along, we will evaluate the situation as Yahoo continues its investigation. We will review the impact of this new development before reaching any final conclusions." Earlier Thursday, a source told CNBC that there "is no panic on the part of Verizon."
CFRA analyst Scott Kessler said that given Yahoo's steady user numbers after the last data breach, he doesn't expect any material revisions to Verizon's deal. Still, the new hacking stoked more doubts about a deal that was already said to be shaky.
In October, Verizon's top lawyer Craig Silliman said the company has a "reasonable basis" to believe that Yahoo's earlier data breach of at least 500 million email accounts represents a material impact that could allow Verizon to withdraw from the merger.
"I think we have a reasonable basis to believe right now that the impact is material and we're looking to Yahoo to demonstrate to us the full impact. If they believe that it's not, then they'll need to show us that," Silliman told Reuters at that time.
The latest hackings, which included names, email addresses, telephone numbers, birth dates, and certain passwords and security questions, comes amid a company culture that The New York Times reported was "slower to invest in the kinds of defenses necessary to thwart sophisticated hackers."
"It's clear that Yahoo under invested in both security, and we would even argue, in ad technology," Helfstein said.
Despite a focus on mobile, social and video under CEO Marissa Mayer, Yahoo struggled to keep pace with the rise of digital ads on Google and Facebook, seeing its market share slip to 1.5 percent of the worldwide digital ad market this year, eMarketer estimated. Verizon, which owns AOL, said Yahoo's technology and patents would give the company's media business a greater scale.
Marni Walden, Verizon president of product innovation and new businesses, told CNBC's "Squawk Box" in July that she expected the Yahoo takeover to propel AOL and Yahoo out of their combined single-digit market share.
"Yahoo gives us scale and that's what's most critical here. We go from being in the millions of audience to the billions," Walden said, adding of the combined market share: "We're going to get to double digits."
— CNBC's David Faber and Reuters contributed to this report.
Disclosure: Oppenheimer makes a market in securities of Yahoo.