Just as we examine companies each week that may be rising past their fair value, we can also find companies potentially trading at a bargain price. While many investors would rather have nothing to do with companies tipping the scales at 52-week lows, I think it makes a lot of sense to determine whether the market has overreacted to the downside, just as we often do to the upside.

Here's a look at three fallen angels trading near their 52-week lows that could be worth buying.

Digging deep
I think we'll start the week off with a controversial bullish call on deepwater driller Transocean (NYSE: RIG). Ever since the Deepwater Horizon disaster last year, the future of deepwater drilling has pretty much been up in the air. Following the $40 billion pre-tax charge BP (NYSE: BP) took to cover expected costs of the worst oil spill in history, BP filed a lawsuit against Transocean and Halliburton (NYSE: HAL) in April with the hope of recovering some of the money it had paid out.

To make matters worse, Transocean made the decision last week that in order to avoid a debt downgrade it would offer 29.9 million shares on the open market as well as offer bonds in order to raise much needed capital. So with troubles mounting, who would be masochistic enough to consider investing in Transocean? Apparently only me!

We have to remember that when it comes to deepwater drilling, no other companies even hold water (pun intended) compared to Transocean. Transocean's 138 mobile offshore drilling rigs make it almost twice as big as the second-largest offshore driller, Ensco (NYSE: ESV), and its equipment can simply go deeper into the ground than its peers. The federal government gave the OK for drilling in the Gulf of Mexico to recommence last year and, while it's a slow-and-go process, things are moving along. Based solely on metrics, Transocean is about as cheap as it's been in a decade at just 66% of book value and less than seven times cash flow. Even if its astronomically high 7.4% dividend were to be cut in half, it still looks like a solid value and a great long-term bet on an oil-dependent U.S. economy.

Buy a champion?
You might not think of an underwear manufacturer as a hot company, but the results at Hanesbrands (NYSE: HBI) would speak otherwise. Hanesbrands, which markets familiar brand names Hanes, Champion, Playtex, and Wonderbra, has been putting up some very impressive results of late, yet investors have been too busy scratching their heads to realize what a great deal they have lying in front of them.

Hanesbrands reported a modest 5% jump in revenue in the third quarter, but the company's margins are what really stole the show. Operating margin rose 270 basis points over the year-ago period and marked the highest levels in company history at 12.4%. Gross margin also expanded by 360 basis points despite higher cotton and commodity costs. Nearly every aspect of Hanesbrands' business showed enormous strength in profitability, including innerwear up 44%, outerwear up 45%, and its direct-to-consumer division up 16%.

To add icing on the cake, Hanesbrands announced on Tuesday that it would buy back $200 million worth of outstanding debt early using its existing cash flow. So to recap, Hanesbrands is deleveraging its balance sheet, earnings momentum is on its side, operating margin is at an all-time high, and the stock is trading at less than eight times 2012's estimates. A very compelling company, if you ask me.

Think MENA
It's a pretty tough stretch to call anywhere in the world a safe haven from Europe's debt crisis, China's slowing economy, or the United States' economic stagnation, but I think you'd be overlooking an opportunity for significant long-term growth by ignoring the Middle East and North African region. Luckily for us, there's an ETF that can expose you to just that: the PowerShares MENA Frontier Countries (Nasdaq: PMNA).

While not completely devoid of European debt, the PowerShares MENA ETF is heavily weighted toward Egypt, Kuwait, and Qatar -- all countries rich with investment capital, with the bonus of Kuwait and Qatar sitting on large oil exports. In fact, close to half of the weighting of this ETF is for financial banks in various countries in the Middle East and North African regions. With the Middle East failing to participate in the global rally off the 2009 lows, it could be time for that region to step into the limelight. Clearly political turmoil remains the primary concern for investing in this region, but it's considerably safer than trying to guess who will be the next China and buying into a single-country ETF like the Market Vectors Egypt Index (NYSE: EGPT). The key here is diversification, and PowerShares MENA offers investors a good chance at price appreciation with reasonable levels of risk.

Foolish roundup
I'm definitely going outside of the box this week with deepwater drillers, underwear, and the Middle East being the main focus. Keep in mind that when others are down on companies, sometimes that's the best time to pick them up. I'm confident enough in these three near their 52-week lows that I'd bet my CAPS points on them. The question now is, would you?

What do you think? Do these fallen angels deserve a second chance or should we toss them off a tall bridge? Share your thoughts in the comments section below and consider adding Transocean, Hanesbrands, and PowerShares MENA Frontier Countries to your free and personalized watchlist to keep up on the latest news with each stock.

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.