Wintergreen, which owns 2.5 million shares of the company, also hosted an investor presentation Wednesday, when it said Coca-Cola was "hijacking" the company's shareholder buyback plan. "This may be one of the most outrageous grabs of shareholder money in the history of commerce," the company said.
The comments come several days after Wintergreen wrote a letter to Coca-Cola and Warren Buffett, the company's largest shareholder, criticizing the proposed executive compensation plan.
Winters said Buffett hasn't responded to him and Berkshire Hathaway, Buffett's firm, didn't respond to a request for comment from CNBC. Buffett's son Howard is on Coca-Cola's board of directors.
Coca-Cola has responded by saying its new plan doesn't differ materially from past plans and that executives will only be awarded options if they hit certain performance targets. The company declined to comment further on Winter's latest comments.
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The dispute focuses on Coca-Cola's 2014 equity plan, which includes up to 340 million new options to be issued to executives over four years. The 2008 plan, meanwhile, allowed the company to issue 280 million options.
But there's another number that Wintergreen has used to make its argument. In its latest proxy statement, Coca-Cola says that investors could face up to 14.2 percent dilution if the new plan is approved.
What may have caused some confusion is that the 14.2 percent number includes a large amount of options Coca-Cola has already issued but haven't been exercised. The additional 340 million shares would only increase the current share count by 7.7 percent.
Even so, share buybacks are a critical component of Coca-Cola's growth in earnings per share because they have helped the company reduce its share count over the years. When employees receive stock awards or exercise options, however, the impact of the buyback is reduced.