What was initially a somewhat forceful opinion from well-known billionaire and activist investor Carl Icahn that eBay (NASDAQ:EBAY) should spin off its PayPal business to unlock shareholder value has now turned into all-out rancor. eBay's refusal for now to consider spinning off the payments transfer operation has Icahn calling attention to other parts of the online auctioneers business, and stating publicly that this is one of the worst-run companies he's ever seen.

In his most recent point of ire, Icahn is calling attention to eBay's handling of its Skype spinoff a few years ago. The company sold Skype to an investor group led by eBay board member Marc Andreessen, who was able to turn around and sell Skype to Microsoft (NASDAQ:MSFT) for significantly more money, which Icahn saw as eBay leaving a huge amount of money on the table.

Regarding PayPal, however, the question remains: is Icahn right? Would separating PayPal into a stand-alone company be worth more to shareholders than leaving the two united? In this video from today's Stock of the Day, Motley Fool financial analyst Matt Koppenheffer says that he thinks it probably would. Despite Icahn's prickly approach, his track record in these crusades has been good, and the market very likely could attach a premium to PayPal if it were independent. That said, Matt isn't an eBay buyer today. While he is drawn to the stock for the strength of the PayPal business, Matt says he's more inclined to wait until the fervor Icahn has created dies down.