Throughout the recent economic slump, investors began to wonder if the world’s oldest billion-dollar corporation would even survive. Think about that. A hallmark of American industry on the brink. . . Sound familiar?

So what was this ‘mystery’ company? General Electric (NYSE: GE)? Nope. General Motors? Not even close.

After forming in 1902, United States Steel Corp. (NYSE: X), with its high fixed costs, had seen its fair share of ups and downs in the ensuing century-plus, but nothing quite like this. Rivals such as Nucor (NYSE: NUE) perfected the fine art of variable expense management, which means that costs dropped sharply when revenue slowed. But now it’s time once again for an upturn.

The entire steel industry has surged back, and U.S. Steel’s high fixed costs have become an advantage. That’s because new incremental revenues should flow very quickly to the bottom line. For example, sales next year are forecast to rise only +10%, but profits should triple. Similar revenue growth in 2012 could add another 40% to the bottom line.

That moderate sales growth is expected to come from a combination of higher volumes and higher prices per ton. Industry capacity utilization, a measure of how close to capacity the major steel mills are operating, is set to keep rising, and as mills move closer to running full tilt, the major producers can impose meaningful price increases. We’re not there yet. U.S. steel mills are operating at around 74% of capacity, up from 64% last November. As that figure approaches 80%, it becomes far easier to push for price hikes. Right now, processed steel fetches about $700 per ton, though it fetched more than $1,000 back in 2008. As steel prices move back toward that peak, U.S. Steel should benefit from both higher volumes and higher selling prices.

It’s fair to wonder why prices should rise if the Chinese economy is already running flat out. Simply put, industrial demand in the rest of the world is just getting going again. In places like Turkey, Brazil and southeast Asia, steel demand is rising, even as global inventories remain fairly low. In the United States, demand should keep building as auto sales continue their rebound, and eventually, the construction market hums back to life.

Yet steel service centers, which act as a middleman for buyers and sellers, are keeping record low levels on hand, perhaps because they suffered large losses when steel prices plunged two years ago. According to the Metals Service Center Institute, the industry carried 2.0 months of supply in April, down from the 3.0 to 4.0 months of supply they normally carry. That drawdown has modestly muted end-demand for the steel mills, but that headwind should soon become a tailwind.

Yet the clearest read on demand is in scrap steel prices. Scrap is used when supplies are abundant, but supplies are tightening, pushing prices up +100% in the last 12 months. When scrap supplies tighten, traders push up the costs of iron ore, which is used in the production of steel. And that’s just what’s happening now. The good news for U.S. Steel: the company has vertically integrated its operations into iron ore production, and is well-insulated against price hikes for this key raw material.

Rising demand and firming prices should enable U.S. Steel to report its first quarterly profit in several years when results are released in July. And quarterly profits should grow quickly from there, even if pricing and demand improve only modestly, as the company is right at its break-even point with high fixed costs. Analysts think that U.S. Steel can earn more than $2 a share during the second half of 2010, and more than $6 a share next year. The key question is whether the global economy remains on the mend into 2012. If so, U.S. Steel can see per-share profits approach $8 and earnings before interest, tax, depreciation and amortization (EBITDA) should approach $13 a share.

Shares of U.S. Steel have historically traded at around 6 times peak cycle EBITDA, on an enterprise value basis. A rising cash balance should enable the company to have more cash than debt by the end of 2011, so the company’s enterprise value and market capitalization will be roughly the same.

So if shares achieve a six times multiple on projected 2012 EBITDA, then shares have roughly 50% upside to around $78. (As a point of reference, shares trade for nearly $200 less than two years ago). Of course, investors need not wait until 2012 to reach that target price, as investors always look one to two years out in their forecasts to justify a stock’s valuation. As the industry dynamics continue to improve over the remainder of this year, that 2011 and 2012 outlook should come into sharper focus.