The four activist investors attempting to take over Kohl's (KSS -26.31%) board of directors fired another salvo at the retailer after its fourth-quarter earnings report.

The group of hedge funds that own almost 10% of the department store chain's stock published a letter calling into question many assumptions the board has made about how much progress the company is making on its own. 

And in one section, the activist investors cast doubt that Kohl's partnership with Amazon (AMZN -0.99%) to process the e-commerce giant's returns is helping business as much as claimed. In fact, they believe the retailer is not fully disclosing the costs of the program to investors.

Man taping up a box

Image source: Getty Images.

Setting the bar low

Macellum Advisors, Ancora Holdings, Legion Partners Asset Management, and 4010 Capital have nominated nine candidates for Kohl's 12-person board, saying the retailer needs more directors with retail experience to help turn around an ailing business that perennially underperforms the competition.

While the private equity firms pointed to numerous issues, from subpar guidance to a weak dividend, the activist investors also said they were "skeptical" the Amazon partnership was providing much benefit.

Although sales, general, and administrative charges (SG&A) have increased, revenue has not responded in kind. Moreover, Kohl's says investors need to consider a customer's "lifetime value" to the company, which is different from the previous claim the program was accretive to earnings today.

The hedge funds write they believe "there are certain 'royalty payments' paid to Amazon related to this program that have not been adequately disclosed to investors."

That would be a serious omission on Kohl's part if true, but the activist investors don't provide evidence to support the claim.

They stress once more, though, that shareholders need a board possessing "strong, relevant retail, capital allocation, and governance expertise" to effect the turnaround.