David Winters may not be Coca-Cola's (NYSE:KO) biggest investor, but he is probably the loudest. Earlier this year, Winters, whose investment group Wintergreen Advisers owns over $100 million in Coke stock lambasted the beverage company for its profligate executive compensation plan. Now, he is calling for CEO Muhtar Kent to be replaced.

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Winters spells out his case in an eight-page letter entitled "Coca Cola's Fizzy Math: How Bad Performance, Excessive Pay and Weak Governace are Harming Shareholders."

So what's his beef?
In his letter, the fund manager again took aim at Coke's executive compensation despite the company's decision to amend it in October. There has been debate over the potential payout of the plan as Winters said at one point that it could dilute shareholders by as much as 14%, or $24 billion, though upon closer examination by two Stanford two finance professors, the plan seemed to only pay out as much as $5 billion to the 6,400 senior managers over the next five years. Warren Buffett, whose Berkshire Hathaway is Coke's largest shareholder, called the plan "excessive" when it was first announced in March and many shareholders voted against or abstained from voting for it.

In October, Coke amended the plan to incentivize managers mostly with cash instead of equity awards. Coke did this to appease investors like Buffett and Winters, who did not want to see Coke stock so severely diluted. and limited those eligible for equity awards to only 1,000 managers, meaning share dilution will remain under 1%.

Still, Winters was not satisfied, saying the new plan was actually worse than the original, and that it could cost shareholders between $1 and $3 billion a year, or $0.17 and $0.51 per share, lowering the value of shares by as much as $10. Winters also says the plan could threaten Coke's 50-year record of dividend increases as the company has increasingly relied on debt to fund dividend payouts, share buybacks, and capital expenditures. Since 2010, debt has nearly doubled while operating cash flow growth has been nearly flat.

It's not just the pay plan
Winters also criticized management for earning high pay for poor performance, noting that incentive bonuses have increased 40% since 2010 while profit growth has disappeared.

Finally, Winters brings his case to the feet of CEO Kent, accusing him of throwing billions of dollars away on two expensive acquisitions. The first was Coca-Cola Enterprises' North American bottling business for $12.2 billion. Winters said management had said at the time of the purchase that the company would fix up the business and sell it off to bottling partners, though results seem to have disappointed. Winters also criticized Coke for its $4.1 billion acquisition of Glaceau, the maker of VitaminWater, in 2007, noting that there has been little production innovation and competition is increased in the enhanced water segment. Similarly, he notes that Coke has been late to trends such as energy drinks and coffee, arguing that the company overpaid for its minority stakes in Monster Beverage and Keurig Green Mountain, for which it spent $3.6 billion.

As Winters acknowledges, Coke discloses little information about the performance of its individual segments so its hard to assess the wisdom of the two above acquisitions. While it may be wrong to call them an "abject failure" as he does, there is certainly an argument that the money could have been better spent. Regarding Coke's investments in Monster and Keurig, it's really too soon to tell if those will pay off.

Winters also calls for new blood on Coke's board, noting that three of its current directors have served for a combined 102 years.

Is new leadership the right answer?
Winters' math may be exaggerated at times, but his underlying arguments seem valid. Coke's performance-based compensation plan, for instance, seems especially ridiculous, coming at a time when performance has been so poor. Profit and revenue growth have stagnated, and over the last two years, Coke stock has gained just 15% while the S&P 500 has improved 45%.

But some of Coke's challenges are beyond its own control. Soda consumption has been on the decline in North America since 2015, threatening its flagship brand and many other of its key products. A change in leadership is unlikely to solve that problem.

Still, Coke is a cash machine, and that position does make it an attractive business. Winters is right to expect management to avoid waste, be it through excessive compensation or bad acquisitions. Regardless of who's running Coca-Cola, the company will only be successful if it can find new growth outlets and maintain its strong margins with effective cost management. So far, Kent has not been up to the challenge.

Jeremy Bowman has no position in any stocks mentioned. The Motley Fool recommends Berkshire Hathaway, Coca-Cola, Keurig Green Mountain, and Monster Beverage. The Motley Fool owns shares of Berkshire Hathaway and Monster Beverage and has the following options: long January 2016 $37 calls on Coca-Cola and short January 2016 $37 puts on Coca-Cola. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.