(FORTUNE Magazine) – In the early 1960s, back when the St. Joe Co. was still in the business of growing Florida pines, not developing Florida real estate, legend has it that a Hollywood movie mogul by the name of Walt Disney paid a visit to the timber company's then-CEO, Ed Ball. Disney, you see, was in the market for some Florida land--something about an amusement park--and land was what St. Joe had in spades. St. Joe owned then (and still owns today) about a million acres in the Florida Panhandle. All Disney needed was 30,000.

There was just one problem: Ball was a curmudgeon who refused to sell land to anyone. According to St. Joe company lore, Ball made Disney wait in his foyer for hours. At the end of the day Ball's secretary emerged from his office with a handwritten note for the movie man. The message: "We don't deal with carnival people."

Oops. Ball's act of arrogance may well have been a $100 billion blunder, considering the princely sums now paid for land in Orlando and around Walt Disney World. Yet as St. Joe CEO Peter Rummel tells this tale--he says it checks out, but for the record, the folks at Disney suspect it's a tall one--he sheds no tears over what might have been. "Sure, it was a missed opportunity," says Rummel, himself a former Disney executive. "But I'd argue that we're in a better position today, able to take advantage of a demographic movement unlike any in the history of the U.S."

Baby-boomers, he's talking about you. The U.S. Census Bureau expects Florida to add 13 million new residents--equivalent to the combined populations of New Jersey and Connecticut--between 2000 and 2030. With so many boomers eyeing a Florida retirement and the panhandle an unspoiled alternative to the clogged roads and beaches to the south, St. Joe (JOE) may well be the best aging-of-America play this side of pharmaceutical stocks. Of course, that's assuming that killer hurricanes and breathless news coverage don't scare off all the snowbirds. "I don't care what happens this year or next," says Michael Winer, portfolio manager of the Third Avenue Real Estate Value fund. "For us, the St. Joe story boils down to some 800,000 acres of spectacular real estate that is ripe for generations of development." Third Avenue, the fund family headed by famed stock picker Marty Whitman, is so bullish on St. Joe that it now owns just over 10% of the outstanding shares--a $470 million stake.

Founded by the Du Pont family as a timber company in 1936, St. Joe is the largest private landowner in Florida, holding more than 855,000 acres. Florida has been a booming real estate market for decades, yet it wasn't until the 1990s that St. Joe's board of directors realized home sites were more valuable than timber or wood pulp. In 1997 the board hired Rummel--then Disney's top in-house real estate developer and the creator of the Celebration, Fla., planned community--to lead St. Joe's transformation from timber company to land company.

Rummel recalls being stunned the first time he laid eyes on maps and aerial photos of St. Joe's land holdings. The properties included hundreds of miles of panhandle beachfront, lakefront, and riverfront as well as 352,000 acres within ten miles of the Gulf of Mexico. Of course, anyone with half a brain can sell a beach house. What has distinguished St. Joe's development plans under Rummel is a keen sense of how to adapt non-beachfront land to boomers' active vision of retirement. For instance, St. Joe has turned 1,000 acres of woodlands, creeks, and marshes in Panama City Beach, Fla., into the kind of place where you'd expect a modern-day John Muir to retire--assuming the famed naturalist had a taste for luxury living and the cash for a $500,000 home. Called RiverCamps, this soon-to-be-completed development will offer a boathouse for canoeing, paths for walking and mountain biking, and onsite naturalists to guide morning birding expeditions. The showcase home at RiverCamps boasts the usual array of luxury amenities but with "cracker chic" design touches that evoke all the charm of the backwoods South--from the huge screened-in porch to the melodic patter of rain against the corrugated metal roof.

Even if St. Joe weren't such a creative developer, the company's $60 stock price (as of Sept. 28) would still be something of a head-scratcher. With St. Joe's total stock market capitalization now standing at $4.6 billion, Wall Street is valuing the company at the equivalent of roughly $5,400 an acre--about a week's rent for an upscale Florida condominium.

That's even cheaper than it sounds. St. Joe right now has 19 active developments spanning about 13,000 acres. Recent sales range from a $2.9 million beachfront condominium at WaterSound Beach in Santa Rosa Beach, Fla., to a $130,000 lot in a Tallahassee subdivision called Southwood. (Ball would not be amused: Southwood used to be his personal estate.) In the second quarter of 2005, St. Joe recorded an average profit on all home and home-site sales equivalent to $160,000 an acre. St. Joe won't make that much on all its sales, but even now, the company is selling remote unimproved ranch land for upwards of $7,000 an acre. And that's before the population boom that everyone knows is coming.

Why is the stock so undervalued? For one, Wall Street likes to price stocks on current profits. But because St. Joe has only 1.5% of its land under development, its profits don't come close to reflecting the underlying value of its assets. And its modest earnings give St. Joe a price/earnings ratio of 32, which is high relative to the S&P 500, making the stock look expensive.

A more immediate problem is the weather. Neither Hurricane Katrina nor Hurricane Rita did any physical damage to St. Joe developments, but coming on the heels of Florida's 2004 storms, this year's extreme weather has put a dent in demand for gulf-front and near-gulf-front property. And it has raised the prospect that flood insurance will become much more expensive and harder to find. Rummel reports that two potential buyers backed out of WaterSound beach-home purchases in the wake of Katrina and that, "in general, our sales have slowed down from where they were."

That's not what investors like to hear, especially with the dark cloud of a possible housing bubble hanging over all housing-related stocks. St. Joe was hit hard, with its shares dropping to $60 from a high of $84 a share in July. Of course, that's exactly what makes this such a good time to buy. As Ryan Beck & Co. analyst Sheila McGrath wrote in mid-September, "We do not believe JOE's land values have declined over 15% since July 1, yet its share price has."

For his part, Rummel has no doubt that sales will rebound once hurricane season ends. "I will guarantee that if demand does weaken for things near the coast, it's only temporary," he says. "There's something in our DNA that draws people to water." Genetics aside, he's probably right. Economists and geographers who have studied how natural disasters affect real estate values have generally found there to be no lasting impact.

Consider 1989, the year Hurricane Hugo ripped through Charleston, S.C., and the World Series earthquake rocked San Francisco. In both cases, local home values were higher one year later. Grant Thrall, a professor of economic geography at the University of Florida, explains that it's only when natural disasters start affecting communities with true regularity--a flood plain that is inundated every other year, for instance--that residents move and home prices fall. "I don't see [Katrina and Rita] having a negative impact on real estate values," says Thrall. "Generally speaking, homebuyers have very short memories."

The storms could even have a positive impact for St. Joe. With Katrina having rendered so many ports in Mississippi or Louisiana damaged or inoperable, the Port of Panama City has experienced a huge surge in traffic, including the arrival of its first-ever container ship and its first-ever oil tanker. Meanwhile, several thousand people displaced by Katrina have taken up residence in the panhandle region, many of them enrolling their children in local school systems. "A lot of those folks aren't going back anytime soon," says Rummel, explaining why he may accelerate development plans for nonresort, primary-residence communities.

Any surge in economic activity and population growth in the panhandle would buoy the case for one of St. Joe's top priorities: a new airport in Panama City. Because so few commercial flights serve the region, most second-home owners in the panhandle hail from Atlanta, Birmingham, Memphis, or other Southern locales within driving distance of northwestern Florida. A new airport would change all that, opening up the region to snowbirds and tourists from all over the country.

Government officials in Panama City have been debating the need for a new airport for years. (The runway on the existing one is too short to support large jets.) Lately, though, St. Joe has been the driving force behind the airport project--which could break ground as soon as 2006--going so far as to donate the land. "Of course it's self-serving," Rummel groans when queried about criticism that St. Joe is providing land for the airport only to further its own real estate interests. "But we have been very consistent about saying it's the right thing for the region, and if it's the right thing for the region, it's the right thing for us."

The hope is that the airport would give the region the same kind of boost Fort Myers and Naples got from the opening of Southwest Florida International Airport in 1983. "That whole area just exploded after that airport was built," says Third Avenue's Winer. "There's no reason the same thing couldn't happen in the panhandle." At $5,400 an acre, that's a bet we'd happily take.