When noted activist investor Carl Icahn sees an opportunity, he rarely goes away quietly. Earlier this year, he set his sights on Internet marketplace eBay (NASDAQ:EBAY). Icahn saw a highly valuable asset being held down under the weight of lesser-performing businesses. His campaign to shake up the company by spinning off PayPal was not received well by management.

Icahn did go away quietly from his pursuit, however, in exchange for a new board member. Unfortunately, the market hasn't responded. eBay shares have lost value over the past year, badly lagging behind the S&P 500 Index.

Shares of eBay exchange hands for 15 times forward earnings, which is actually a slight discount to the broader market's multiple.

eBay could likely enhance shareholder value by letting its prized asset loose from the rest of the group. That's why eBay would be smart to take Icahn's advice and spin off PayPal.

A tale of two companies
On the surface, there wasn't anything alarming about eBay's earnings report. Sales and earnings per share increased 9% and 13%, respectively, which is satisfactory performance.

While there wasn't anything alarming in eBay's report, there wasn't anything overly encouraging, either. Its growth rate is acceptable, but unlikely to convince the market to award the company's stock with an above-average multiple. This is especially the case given management's relatively pessimistic outlook for the current quarter.

eBay expects $4.3 billion-$4.4 billion in third-quarter revenue and adjusted earnings of $0.65-$0.67 per share. This fell short of the average analyst estimate as compiled by Bloomberg, which calls for $4.42 billion in revenue and $0.67 per share in profits.

All the while, PayPal is thriving. Sales in eBay's PayPal payments unit grew 20% last quarter, even better than the 19% revenue growth racked up in the first quarter. By contrast, eBay's marketplaces business grew revenue by just 9% last quarter. Enterprise fared even worse, inching revenue up just 3%.

As a result, it's clear that PayPal is large and successful enough to be a viable stand-alone entity.

PayPal is worth more on its own
PayPal is a $6.6 billion business by annual revenue. It added 4 million new active registered accounts in the last quarter alone and now holds 152 million accounts.

Because of its strong growth, PayPal would likely carry a much higher earnings multiple than eBay currently does.

After Icahn's initial push to spin off PayPal, he was rebuffed by management, which believes PayPal and eBay are stronger together. It's hard to see how that's true, though. The company holds a discounted valuation, and the pervasive bearishness is unlikely to lift given the headline risk surrounding it.

You'll recall that in May, eBay announced that it had suffered a major security breach. Hackers stole a slew of personal information from users, including email addresses, birthdays, and other identity information. The company estimated a large number of its 145 million active users were potentially affected.

This is undoubtedly hurting eBay's brand image just as competitive pressures are heating up. One of eBay's strategic initiatives is to expand its retail channel. In doing so, it's going up against the likes of Amazon.com (NASDAQ:AMZN). According to Bloomberg, sales by retailers on eBay increased just 12% in June, compared to 34% growth for Amazon.

Separately, eBay management points to a recent partnership with Sotheby's to make artwork, antiques, and collectibles available online. Whether that's really enough to move the needle in a meaningful way is questionable at best.

That's why eBay would be doing investors a service by separating PayPal. PayPal can keep doing what it does best while eBay works through these operating challenges on its own.

Market needs a catalyst for a higher multiple
eBay's stock price has languished for the past year. The company's stock is down over the past year and the current year to date. The company is growing, but still holds a below-market valuation. This has to be frustrating for investors.

The reason for this is that eBay has a number of overhangs weighing on investor sentiment. First and foremost is the massive security breach that put a dent in the company's brand. In addition, its core strategic initiatives put it in direct competition with Amazon, the largest online retailer in the world.

All the while, PayPal stands as a diamond in the rough. eBay management believes that the company is better off as a combined entity, but it's hard to understand that argument given the discounted valuation and poor stock performance.

If eBay really cares about enhancing shareholder value, it should seriously consider spinning off PayPal.

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Bob Ciura has no position in any stocks mentioned. The Motley Fool recommends Amazon.com, eBay, and Sotheby's. The Motley Fool owns shares of Amazon.com and eBay. 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.