While investors have begun to prep for a rebound in the U.S. housing market — the PHLX Housing Sector Index has risen 50% in the past six months — they may be early to the party. So many homes still in the process of foreclosure have yet to hit the market, and this “shadow inventory” could impede any rebound in home prices for quite some time to come.

Meanwhile, far to our south in Brazil, a more moderate housing downturn has played out. A crucial distinction: Brazil doesn’t need to work through the same foreclosure process because mortgage-lending standards were stricter while a bubble was underway.

#-ad_banner-#And Brazilian housing surely had a bubble. Homebuilders constructed too many homes while the economy was strong, but didn’t see a slowdown coming. The Brazilian economy grew 7.5% in 2010, but just 2.7% in 2011, leading to a glut of unsold homes. The International Monetary Fund (IMF) expects the Brazilian economy to grow just 3% this year, which should still be strong enough to absorb many of the unsold homes. And the IMF expects Brazil’s economy to expand at a slightly better 4% pace in 2013.

This should set the backdrop for a Brazilian housing rebound well before the U.S. experiences its own rebound.

Meanwhile, even as U.S. homebuilders have rallied sharply from their lows of last summer, a leading Brazilian homebuilder has been steadily falling in value. Gafisa (NYSE: GFA), one of Brazil’s largest homebuilders, has seen its stock fall more than 75% since late 2010. At current levels, the stock possesses both strong downside support and some potentially robust upside.

Said another way, this homebuilder was worth more than $4 billion on the stock market in late 2010, but is worth less than $1 billion today. Considering the fact that the company has $1.5 billion in shareholder’s equity on the balance sheet, I’d say this looks like a pretty compelling value so far.

The fact that Gafisa lost $600 million in 2011 helps explain the big investor exodus. Yet dig into that $600 million loss, and you’ll find a different story. Embedded in that loss is a series of one-time charges to reflect a wide-range of projects that went over budget and are likely to sell for less than what it cost to build them. In effect, management chose to clear the decks when 2011 results were released a few weeks ago, and the results for the periods ahead should be a lot cleaner.

Based on current projects underway, Gafisa expects to generate roughly $300 million in operating cash flow. Add in the fact that Gafisa has roughly $500 million in cash, and concerns that the company’s debt load is too large to handle appear off the mark. The company must cover roughly $100 million in annual interest expense, and has less than $200 million in bonds coming due this year. Looked at another way, this is a company valued at little more than three times projected 2012 cash flow, and 2012 is likely to be a sub-par year.

Yet this isn’t a stock that should be measured by 2012 results. Instead, you need to look ahead. Brazilian demographics are still extremely favorable. The country’s population, which is larger than Spain, Italy and the U.K. combined, is relatively young — two-thirds of all Brazilians are under 35. Millions are being swept up in a rising economy that has lifted many out of poverty. About 1.7 million new households are being formed each year.

Just as important, there are several catalysts in place that should help housing in coming years. First, there is expected to be an upturn in housing demand and construction ahead of the 2014 World Cup and the 2016 Olympics. The government is looking to provide ample homebuilder incentives to build more solid rental housing so the shantytowns in major cities can be steadily reduced.

It helps that Brazil’s interest rates are starting to come down, which helps Gafisa’s financing costs and consumers’ ability to qualify for mortgages.

The final catalyst: major investors are circling. This stock has fallen so far that takeover chatter has bubbled up. Real estate investor Sam Zell may lead the charge. His firm, Equity International, reportedly made a bid for Gafisa in February at an undisclosed price. Shares moved above $6 on that speculation, but traded lower after Gafisa said that “After an analysis by the company’s board, we concluded the offer undervalued significantly the company’s assets.” Presumably, with shares now close to $4, Zell’s offer looks a bit more enticing.

Risks to Consider: Falling inflation is a key catalyst for this stock, so if inflation bubbled up anew in coming quarters, leading to higher interest rates, it could snuff out a housing recovery before it starts.

Action to Take –> This is a tricky stock for investors, as it’s hard to determine a specific target price, and few near-term catalysts exist. Still, it’s quite undervalued in the context Brazil’s powerful long-term demographic trends. Why bother now? Because Sam Zell’s clear interest in Gafisa means shareholder value may get unlocked before the industry fundamentals turn back up.

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