Packaging Corp. of America (NYSE: PKG) has many pressing problems.

Such as:

• Helping analysts figure out why business boomed this spring while the economy continued to plod

• Making sure that its 9,500 customers stayed well supplied during maintenance downtime at mills long operating at full capacity

• Helping Wall Street understand why its margins keep improving

• Making sure that the dividend yield keeps up with a stock that has run up 77 percent in the last year

• And, most annoyingly of all, figuring out what to do with all the cash flow that will begin piling up in earnest in the coming months.

Last month, the fourth-largest US containerboard producer tried to solve several of these pleasant problems at a stroke with its second big dividend hike this year, a 28 percent increase from the prior level on top of January’s 25 percent raise, for cumulative growth of 60 percent from 2012. The first 40 cents per share will be paid July 15 to holders of record as of today’s close. The new rate works out to a 3.3 percent yield at the current share price. But a nice yield is just the ribbon and the bow on top of this attractive package.

Because while PCA is only the fourth-largest on a variety of operating metrics it’s the best, with nicest margins and the most efficient containerboard mills, as well as corrugated plants that have, in many cases, been acquired or expanded to meet demand from loyal, long-time customers.

The containerboard industry has consolidated rapidly in recent years, and PCA benefits from the increased pricing power wielded as a result by rivals like International Paper (NYSE: IP), which swallowed Temple Inland in 2011, and RockTenn (NYSE: RKT), which grabbed Smurfit Stone the same year, as well as Georgia Pacific, a Koch Industries subsidiary.

In contrast, the corrugated container industry that turns commodity containerboard into boxes, other packaging materials and retail displays is highly fragmented, and here PCA competes against 570 mostly smaller suppliers. Many of them lack the efficiency that PCA enjoys because of its scale and dogged investment in operating improvements at its plants and mills which can alternate raw materials and fuels to maximize profits.

PCA’s four mills sent 83 percent of the containerboard shipped last year to PCA corrugating plants, which in making their products produced 35 percent of the recycled fiber PCA used to make containerboard. It’s a virtuous circle that minimizes costs, and the company’s long term goal is to consume more than 90 percent of its containerboard internally. What PCA doesn’t use gets sold to purchasers domestic and foreign, and containerboard prices have risen of late at home and abroad.

Meanwhile, while the company has the scale to cater to national accounts, two-thirds of its corrugated products sales go to regional and local accounts well diversified across the business spectrum and typically located within a 150-mile radius of one of its 71 plants.

For each account, the PCA aims “to do the hard to do,” in other words to keep moving up the value chain. Towards that end it has in the past acquired businesses specializing in custom projects and the unavoidable displays that bookend supermarket aisles. One of its seven dedicated graphic design centers is located in Bentonville, Arkansas, home base of Wal-Mart (NYSE: WMT).

This strategy has been wildly successful to this point. While industry-wide shipments of corrugated products were down 2.1 percent year-over-year in the first quarter of 2013, PCA’s rose 3.8 percent, and 7.1 percent adjusting for the number of workdays. What’s more, sales surged 12.5 percent thanks to higher containerboard export prices but also a higher percentage of higher-value product sales. “If you do more of the hard to do, you’re going to get paid more for that,” the executive in charge of corrugated products explained on last month’s conference call.

As a result, gross profit margin improved to 24.2 percent, from 21.6 percent a year ago. Cash flow from operations net of changes in working capital rose 30 percent to $128 million, and is set to rise significantly from that level in the course of the year.

As an efficient domestic manufacturer serving overwhelmingly domestic customers, PCA is fairly well insulated from the ups and downs of the global economy. Its operating improvements have limited the volatility of its business relative to the US economy’s performance as well. (The stock did get sliced in half in 2008 only to recoup much of the loss the following year.)

Top management is made up of industry veterans who’ve been with the company for two to three decades, and many were groomed for another decade or two before that at International Paper.

A US recession looms as the main investment risk. But it’s also worth noting that contracts with unions representing some 4,500 of PCA’s 6,000 hourly workers begin to expire this year after a five-year extension in 2008, and that higher wages could further increase labor costs that are already on the rise. PCA has also been named, along with other containerboard manufacturers, in a private class-action suit alleging antitrust violations that is grinding through the discovery stage.

On the whole though, business prospects look bright as the US economy keeps growing modestly, whittling containerboard inventories to the second-lowest level in 30 years. This pickup in underlying demand and profitability has drawn the attention of famous hedge fund manager Dan Loeb, whose first-quarter letter to clients extolled the virtues of International Paper. Those virtues are real, but PCA boasts the efficiency and margins that IP is still seeking to emulate. And on a cash flow basis, PCA is hardly more expensive, despite the fact that its stock has handily outperformed IP’s of late.

Earnings are widely expected to increase significantly next year yet Wall Street remains relatively skeptical of the recent runup, with most analysts rating the stock a Hold.

This year’s aggressive dividend hikes are a big tell about how the confidently PCA’s management views the future. Consider the forthcoming 40 cents a share a down payment on the next $10 a share in shareholder value. Packaging Corp. of America is an American success story, one whose numbers speak louder than the loudest retail display.