Shares of PayPal Holdings (PYPL -1.80%) got a boost on Wednesday after Bloomberg reported that activist investor Elliott Management is in the process of acquiring a large stake in the company.

When activist investors buy stocks, it's normally for two related reasons. First, they believe the stock is undervalued. And second, they believe the company is being mismanaged (which is often why the stock is undervalued).

Here's why Elliott Management might believe these things about PayPal. And, more important, here's why Elliott Management might be right.

Here's the possible game plan

If the Bloomberg report is true and Elliott Management is building a stake in PayPal, then it will likely vocalize its opinions soon. Typically, the activist firm publishes open letters to management, outlining its criticisms and the changes it wants to see. That's what Elliott did last year with pharma company GSK and earlier this year with computer storage specialist Western Digital

It should be noted that Elliott Management's involvement doesn't always unlock shareholder value. In 2019, the firm bought shares of AT&T, believing it had 65% upside by the end of 2021. As of the most recent filing, Elliott Management still held 5 million shares of AT&T. However, returns have been flat over its holding period.

With PayPal, Elliott might take issue with its operating costs. For context, PayPal's revenue grew just 13% year over year in the fourth quarter of 2021 and was up 7% in the first quarter of 2022. By comparison, total operating expenses were up 14% and 16% in Q4 and Q1, respectively, resulting in a decline in its operating margin.

PYPL Total Expenses (Quarterly) Chart

PYPL Total Expenses (Quarterly) data by YCharts

In short, it's very likely that Elliott Management believes PayPal can be more profitable than it is right now. And since profits tend to drive long-term stock performance, Elliott Management wants to motivate PayPal's management to make its bottom line its top priority.

I'd be remiss if I didn't acknowledge that Elliott Management recently acquired a stake in Pinterest, and this could be an additional clue to its ideas for PayPal. In October, PayPal was reportedly looking to acquire Pinterest for a whopping $45 billion, a plan that fell apart days later. Since then, both stocks are down roughly 70% and significantly trailing the market average.

PINS Chart

PINS data by YCharts

Could Elliott Management look to play matchmaker and put the PayPal acquisition of Pinterest back on the table? It's too soon to know for sure. But what's more sure is that Elliott Management likely believes PayPal stock is undervalued.

PayPal is indeed a value stock

Stocks aren't necessarily cheap when they fall or, conversely, expensive when they go up. Stocks should be valued relative to business fundamentals like sales, profits, and free cash flow (FCF). And applying these more objective valuation measures to PayPal stock shows it's never been cheaper.

As of this writing, PayPal has a market capitalization of $96 billion -- the company's price tag, so to speak. By comparison, it's generated $25.8 billion in revenue over the last 12 months and it's generated roughly $5 billion in FCF over this time. Comparing these numbers to its market cap, PayPal stock trades at a price-to-sales ratio under 4 and a price-to-free-cash-flow ratio under 20, as the chart shows.

PYPL PS Ratio Chart

PYPL PS Ratio data by YCharts

In short, PayPal stock trades within a couple of percentage points of its cheapest valuation multiples ever. Elliott Management undoubtedly recognizes this.

Is PayPal stock a buy?

Value investors should be leery of what are called value traps -- businesses in decline whose low valuations accurately reflect their poor prospects. And to be fair, there are some troubling signs at PayPal. For example, while it does have 429 million active users, management believes it will only add 10 million new accounts to the platform this year. This paltry user growth is partly why it's only expecting 11% to 13% year-over-year revenue growth in 2022.

However, PayPal is still growing. It's not a dying business.

External data also suggests that PayPal is not in decline. According to a recent report from Apptopia, PayPal was the most downloaded finance app in the world in the first half of this year.

Growth has slowed. But PayPal's ongoing growth suggests it's closer to value stock than value trap. And its cheap valuation coupled with ongoing profits -- not to mention profit-growth potential -- make it a good investment right now, in my opinion.

Regardless of Elliott Management's next move, all shareholders' eyes should be on PayPal's next quarterly report. The company is scheduled to release financial results for the second quarter of 2022 on Aug. 2.