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)

NXP Semiconductors (NXPI 3.18%)

-19%

$22.51

*****

MannKind (MNKD 1.22%)

-34%

$2.40

**

Green Dot Corp (GDOT 2.07%)

-71%

$10.24

**

Companies are selected by screening on finviz.com for abrupt 10% or greater price drops last week. 52-week high and recent price data provided by finviz.com. CAPS ratings from Motley Fool CAPS.

Five super falls -- one superball
A rotten week, one that sent the Dow down 2.1%, savaged the stock market last week. Investors in some 4,800 separate stocks lost money. Some folks lost quite a lot of money, with more than 220 companies getting literally decimated -- down 10% or more -- including all three of the stocks named up above. So what went wrong?

Beginning at the bottom, prepaid plastic-card pioneer Green Dot took a huge hit on Wal-Mart's (WMT -1.75%) announcement that it will be partnering with American Express (AXP 2.56%) to distribute a prepaid "Bluebird" card in its stores. Rumors that CVS may be reconsidering its partnership with Green Dot didn't help the stock much, either. But with Green Dot shares now selling for less than eight times earnings (and nearly half their market cap backed up by cash), you have to wonder if the selling here has gotten a bit overdone.

The week wasn't kind to MannKind either, with the stock falling 15%. (And in this case, even our analysts are at a loss for what might have been behind the sell-off.) Meanwhile, NXP Semiconductors lost nearly as much -- 13% -- on a similar lack of news. Unless you count the earnings warning from AMD, there just doesn't seem to be any reason why NXP suffered a TKO -- and herein may lie an opportunity.

The bull case for NXP Semiconductors
Alone among the three headlining losers named up above, you see, NXP sports an above-average rating on CAPS. Actually, the best rating investors can give it -- a full five stars!

Why do Fools like it? Well, CAPS member wealthwiser tells us that "they invented the NFC chip and own many patents on this technology." Fellow CAPS player chalmer thinks the company's "patent chest presents a solid growing gem." And wealthwiser argues that with so many smartphones these days "implementing NFC chips, NXP will see demand for their chips grow. Also just developed a new audio chip for smartphones that drastically improves Audio output and volume..."

Meanwhile, the Fool's own TMFMattyA says the company turned in "solid Q2 2012 results" and predicts that "new NFC products, strength in China and Asia-Pacific markets, and growing adoption across mobile OEMs should keep growth flowing."

How fast could NXP grow? Analysts on average predict that the company will average 34% profits growth over the next five years. And while that may not look like much relative to the company's ultrahigh P/E ratio, what you need to keep in mind when examining NXP is that "GAAP earnings" don't tell the whole tale. Fact is, this company generates gobs more cash than it gets to report as "net income" under GAAP -- a whopping $331 million over the past 12 months.

Valuation matters
Compare this $331 million to NXP's $5.6 billion market cap, and what you find is that the stock actually costs less than 17 times the amount of cash it generates in a year today. And what this means is that, if the company comes anywhere close to achieving the 34% growth rate Wall Street expects of it, NXP is really quite a bargain at today's prices.

Maybe even a big enough bargain to bounce.