Shares of eBay (NASDAQ:EBAY) hit an all-time high today, after the company fired back at well-known billionaire and activist investor Carl Icahn. eBay's chairman came out and said that Icahn's statements earlier this week were "false and misleading," after Icahn called on the company to spin off the PayPal segment of its business.

In this segment of Thursday's Investor Beat, host Chris Hill and Motley Fool analyst David Hanson look at whether spinning off PayPal would unlock value for shareholders, and whether it makes sense for the business. While David sees it as something that could happen one day down the road, he's taking eBay's side for the time being, saying that for now, it makes sense for eBay and PayPal to stick together.

Chris Hill owns shares of eBay. David Hanson has no position in any stocks mentioned. The Motley Fool recommends and owns shares of eBay. Try any of our Foolish newsletter services free for 30 days. We Fools don't 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.