Every day, Wall Street analysts upgrade some stocks, downgrade others, and "initiate coverage" on a few more. But do these analysts even know what they're talking about? Today, we're taking one high-profile Wall Street pick and putting it under the microscope...

In January, eBay (EBAY 3.03%) dropped a bombshell.

More than 15 years after buying PayPal (PYPL 0.10%) for $1.5 billion, and three years after spinning it off as a separate company, eBay has decided to sever its special relationship with the online payments processor. Over the next couple of years, eBay will gradually shift payments that are currently processed by PayPal in-house, as it "intermediates" its payments business and cuts PayPal out of the picture.

What effect will this have on eBay stock? If you asked Morgan Stanley as recently as yesterday, the megabanker would have been downbeat. But this morning the analyst had a bit of a rethink, and came to an entirely different conclusion: eBay, which the analyst previously thought was a sell, is now a buy. Morgan Stanley is upgrading eBay shares all the way to overweight and assigning the shares a $58 price target that implies more than 40% upside, according to a write-up today on StreetInsider.com (subscription required).

Here's what you need to know.

Triple Dollar sign

Morgan Stanley's eBay upgrade may hinge on eBay earning triple the extra profits it's promising. Image source: Getty Images.

Positive on PayPal

Six months ago, before eBay and PayPal agreed to finalize their divorce, Morgan Stanley declared itself firmly on the side of Team PayPal, arguing that with or without eBay PayPal could grow its sales in the high teens and its earnings at 20%. As such, you might expect the analyst to look askance at any company that chose to distance itself from PayPal.

This morning, however, Morgan Stanley ultimately decided that eBay's move into PayPal's line of business was just too attractive to ignore. By bringing its payments business in-house, eBay says it hopes to "deliver value to customers through an improved shopping experience, enhanced selling tools and streamlined costs." This improved experience, argues Morgan Stanley, will help eBay drive more sales through its website.

Result: Morgan Stanley estimates that eBay could grow its pre-tax earnings by 20% by cutting PayPal out of the loop, and that combined with more ad dollars and the increased sales could increase its free cash flow by 60%.

What is eBay stock worth?

Improvements to the company's core business, says Morgan Stanley, will make "core EBAY" worth about $49 a share. New, high-margin revenue from an in-house payments business, says the analyst, will add another $9 in intrinsic value to the stock, resulting in the analyst's new target price of $58 a share -- up from $36 previously.

Does that make sense?

Running a discounted cash flow analysis to check its assumptions, Morgan Stanley says it thinks the company can grow earnings by about 12% annually through 2021. Furthermore, the analyst argues its new price target values eBay stock at a "13X EV/EBITDA multiple," relative to its expectations for fiscal 2021 EBITDA. (In contrast, eBay today at $41 and change sells for an enterprise value of more than 15 times EBITDA.)

So does this valuation make sense?

It depends. Personally, I prefer to value stocks on their free cash flow (a less fudge-able number than EBITDA). On that basis, I see eBay generating about $2.5 billion in FCF last year (according to data from S&P Global Market Intelligence), selling for an enterprise value of $44.5 billion, and thus an EV/FCF ratio of about 17.8.

That seems a bit pricey for a stock that most analysts believe will grow earnings at only 13.9% annually over the next five years. Then again, Morgan Stanley is predicting a 60% increase in free cash flow once eBay has its payments business mostly in-house -- growth that appears to be much faster than the consensus 13.9% rate.

The upshot for investors

Morgan Stanley's prediction that eBay will grow free cash flow 60% means eBay could soon be producing annual cash profits about $1.5 billion greater than what it produced in 2017 -- about $4 billion total. If the analyst is right about that, it's probably also right about eBay being worth a whole lot more than its stock is selling for today.

The only problem with that prediction, though, is that eBay says bringing payments in-house will add only $500 million to its operating profit. Assuming the benefits to free cash flow are similar to operating profit, therefore, Morgan Stanley appears to be expecting eBay to generate triple the profits increase that eBay management itself is promising.

That's a big leap of faith Morgan Stanley is making. Investors should gut-check themselves before making that same leap, following Morgan Stanley's advice, and buying eBay -- because it might not pan out at all.