When stocks fall fast and far, they sometimes set themselves up for remarkable rebounds. The following equities suffered dramatic drops over the past week. With help from the 180,000 members of Motley Fool CAPS, we'll see whether any of them have the potential to bounce back.

It's been a while, but thanks to last week's sell-off, we once again have a chance to stand beneath Mr. Market's silverware drawer in hopes of snagging a bargain. Let's meet today's contenders:

Companies

How Far From 52-Week High?

Recent Price

CAPS Rating (out of 5)

Veolia Environnement (NYSE: VE) (68%) $10.32 *****
RF Micro Devices (Nasdaq: RFMD) (46%) $4.54 ***
Elan (NYSE: ELN) (8%) $13.01 ***
SINA (Nasdaq: SINA) (67%) $48.49 ***

Companies are selected by screening on finviz.com for abrupt 5% or greater price drops last week. Recent price and 52-week-high data provided by finviz.com. CAPS ratings from Motley Fool CAPS.

Four super falls -- one superball
So far, so good. Stock markets are looking relatively healthy as we begin the New Year, with a 1.2% gain for the Dow booked in Week 1, and further gains heading into Week 2. Not everyone's cheering, however. Up above you see a quartet of stocks that took heavy losses last week. So what went wrong?

At SINA, reports of a Web security flaw sent investors scurrying to update their portfolios last week. Analysts at Piper Jaffray don't seem to think there's anything to worry about, arguing the incremental cost of fixing the bug will be just a few cents per user. CAPS members, too, are taking the news in stride and remain cautiously optimistic, giving SINA a three-star rating.

Likewise with Elan, a 5% decline in market cap isn't shaking confidence on CAPS. The Irish biotech had no bad news to report last week, and with Elan reasonably priced at just 12.6 times earnings, Foolish investors see no need to join in the selling.

Not so with RF Micro, however. The week's weakest performer on this list, RF shed 20% of its market cap Friday after cutting Q3 guidance. That said, all RF really said was that revenues would come in about 10% lighter than expected. Subtracting 20% from market cap for a 10% miss seems a bit of an overreaction to me -- and CAPS investors agree, again preserving the stock's three-star rating.

Last but not least, we come to Veolia Environment. Suggestions that the company waited too long to take a series of "impairment charges" on its businesses, and otherwise engaged in "improper accounting," have lawyers swarming, and alleging securities fraud against the French conglomerate. But many investors think the allegations are overblown ... and Veolia is undervalued.

The bull case for Veolia Environnement
CAPS member nubblyman lists the company's positives as "P/E, price less than book value, strong cash flow, need for the services it provides, & its dividend."

Fool jimscottage11 jumped on this dividend at the "15%" level as recently as last month.

And while Veolia's waste management, water utility, and transportation businesses aren't exactly "sexy," CAPS member sanctifiedsoldie says "VE is a solid company providing a basic need to sustain life."

The big issue for Veolia going forward is its dividend. At 29 times earnings, and with few analysts willing to venture an estimate for its growth rate, valuing Veolia on its PEG ratio is going to be tricky. But buying the company for its dividend? That's an argument any investor can understand.

Right now, Veolia is paying 1.21 euros per share in dividends. But management says it plans to pay a lower, 70 euro-cent dividend (about $0.90, or an 8.3% yield) in each of 2012 and 2013. The company is also restructuring, selling off its least profitable division (transportation), as well as certain water and waste assets in a bid to raise more than 3 billion euros in cash.

This plan should ensure the company can maintain the new dividend, even as it permits an acceleration of the firm's debt paydown. Veolia also predicts that restructuring will result in an immediate benefit to earnings that will grow as years progress -- ultimately adding 420 million euros to operating income by 2015. That could help the company restore its old dividend after the restructuring is complete.

Foolish takeaway
Heavily in debt, and stranded in a country that has arguably even worse debt problems, investing in Veolia Environment is not for the faint of heart. But at least investors can rest assured about one thing: Veolia's huge dividend yield is no mirage. But if Veolia delivers on its promises, I think its dividend cut will be temporary and that investors can count on a secure payout in years to come.

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Editor's note: A previous version of this article did not consider Veolia's decision to reduce its dividend in 2012 and 2013. The Fool regrets the omission.