Activist hedge fund Pershing Square owns about 14.3% of Ceridian (NYSE:CEN), and it has been waging a proxy fight. To avoid the heat, Ceridian announced late last week that it has agreed to a $5.3 billion buyout from private equity firm Thomas H. Lee Partners and Fidelity National Financial (NYSE:FNF). Looking at Wall Street's reaction, it appears the ploy will work.

Ceridian provides outsourced human resources services for things like payroll, tax filing, and benefits. The company also processes credit cards and debit cards through its Comdata subsidiary.

While Ceridian has 110,000 customers and a recurring revenue model, Pershing Square's William Ackman has not been impressed; he wrote a stinging letter to the board in mid-January. He thinks it is too tough to run two different businesses and that there should be a spinoff of the Comdata division.

Escalating things even more, Pershing filed a lawsuit in March against Ceridian to force the disclosure of various letters from high-level employees. Then, a couple of months later, Ceridian fired Comdata's president, Gary Krow, alleging that he was in cahoots with Pershing Square.

Such drama is common in proxy fights, and it's no surprise that Ceridian decided to go private. We have seen this in other cases, such as the buyout of Triad (NYSE:TRI).

Might we see more bidding for Ceridian? It's possible. The stock price is less than a buck off the $36 buyout offer, and Pershing Square has a nice chunk of stock.

Yet if you look at other comparable companies like ADP (NYSE:ADP), First Data (NYSE:FDC), and Paychex (NASDAQ:PAYX), Ceridian's valuation looks reasonable at 13 times EBITDA. So for Foolish investors, there's probably not much upside left on this one.

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Fool contributor Tom Taulli, author of The Complete M&A Handbook, does not own shares mentioned in this article. He is currently ranked 1,161 out of 29,574 rated investors in CAPS. The Fool has a disclosure policy.