Source: Flickr user Shawn Carpenter.

The allure of high-dividend yields is endlessly enticing, but often, high-dividend stocks come with higher-than-anticipated risks. In a bid to help identify high-dividend-paying companies that may stumble, we asked three Motley Fool analysts which companies they think may pose a danger to portfolios. Read on to learn which three worry them.

Leo Sun: PetMed Express (NASDAQ:PETS), which is known as 1-800-PetMeds, is an online pet pharmacy. Its forward annual dividend yield of 5% certainly looks tempting, but the numbers don't add up.

PetMed's payout ratio during the past 12 months comes in at 82%, but it has a whopping free cash flow, or FCF, payout ratio of 111%. That ratio is troubling, since a smaller company like PetMed -- which has a market cap of $270 million -- should invest more of its cash flow back into growing the business instead of funding dividend payouts.

PetMed should certainly consider reinvesting in its own business. During the past five years, PetMed's annual revenue slipped 2%, operating margin fell 29%, and net income plunged 31%. Last quarter, PetMed reported a profit of $2.7 million, or $0.14 per share, down from $4.2 million, or $0.21 per share, in the prior-year quarter. Revenue slipped 4.8%, to $57.6 million, whereas analysts polled by Thomson Reuters had expected PetMed to earn $0.21 per share on revenue of $61.2 million.

PetMed blamed the decline on a shortened flea and tick season, but its long-term top and bottom line declines suggest otherwise. That's why the stock slumped 19% during the past year, and why income-seeking investors should avoid this high-yielding dividend trap.

George Budwell: PDL BioPharma(NASDAQ:PDLI) looks like a screaming buy based on its 7.43% dividend yield, and a rock bottom forward price-to-earnings ratio of 3.7. By comparison, the average healthcare stock yields roughly 2.4% and has a forward P/E exceeding 20. The 23% short interest in PDL, though, suggests that danger is ahead.

What's key to understand is that PDL makes money by licensing out its patent portfolio. Chief among them, PDL owns the so-called "Queen patents," which cover the humanization of monoclonal antibodies.

So why is the Street pessimistic about this dividend stock? The main reason is that the Queen patents are set to expire this month, forcing the company to invest heavily in new income sources. As such, PDL looks ripe for a dividend reduction.

The good news is that PDL was able to secure another two years of revenue from the Queen patents after concluding a lawsuit with Genentech last February. All told, the company has two years to purchase additional patents, and monetize them in a manner that offsets the loss of the Queen revenue. Given the large number of moving parts here, I think PDL and its massive yield are a pass.

Brian Orelli: With a dividend yield above 5%, GlaxoSmithKline (NYSE:GSK) tops the list of big pharma dividends by a wide margin. While the dividend looks attractive, investors should be careful.

Unlike most pharmas that issue the same dividend for four quarters in a row and then (hopefully) increase the dividend, GlaxoSmithKline dividends can vary widely from quarter to quarter. The company typically issues a larger dividend in the fourth quarter, but the increase over previous dividends is hard to predict.

The dividend is also priced in the Great British Pound, so investors who buy GlaxoSmithKline's ADR, which trades on the NYSE, are subject to currency changes from the GBP to the U.S. dollar. For example, the second and third quarter dividends were both 19 pence, but the dividend slipped from $0.65 to $0.61 because of the stronger dollar.

Finally -- and this is a big one -- there's a reason the dividend yield is so high: Investors are worried that there will be little to no growth in the share price. A new round of layoffs was recently announced as the big pharma has struggled with insurers pinching the price of its megablockbuster lung drug Advair. The company hopes to rebound its respiratory franchise with new lung drugs, Breo and Anoro, but switching patients takes time. 

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.