When young, trendy companies prepare for initial public offerings, their financial statements often show rapid growth but little profit. Investors are expected to take a leap of faith and bet that today’s expanding popularity will lead to sustainable earnings down the road.

SoulCycle does not need to ask for that particular leap of faith.

The boutique indoor cycling chain, with 47 studios in seven states and the District of Columbia, is already handsomely profitable, according to documents it filed on July 30 stating its intention to go public. It reported $25 million in profit on $112 million in revenue in 2014, indicating a fat profit margin of 23 percent. Unlike Twitter, which is still losing money by most widely accepted measures, SoulCycle found its revenue model before going to market.

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Not every class sells out, and its prices are modestly lower outside New York City, but average revenue per class is still impressive. The company collected an average of $1,153 in participant fees per class in 2014, when it offered 81,317 classes, the filing says.

But while the math is simple, SoulCycle’s profit margins are surprising. If it has found a way to mint money, competitors should be able to swarm into the fancy indoor cycling world and beat it on price. This is not a business with high barriers to entry: Full-line gyms like New York Sports Clubs offer cycling classes to their members for no additional charge. In short, Economics 101 says SoulCycle’s high profit margins should be eaten away by competition.

Of course, as any committed SoulCyclist will tell you, SoulCycle is so much more than the free indoor cycling class you can take at your local gym. It offers mood lighting, a cadre of support staff to help you adjust your bike, custom playlists that match musical beats to choreographed cycling moves and charismatic instructors who pitch your workout as a path to self-improvement. But how hard would it be for another company to copy those features, charge $32 instead of $35, and steal market share while still collecting a profit?

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The crucial question for potential investors in the SoulCycle public offering is whether the company has a true sustainable advantage: a unique factor that will get customers to keep paying more for SoulCycle than for its competitors. I talked with two groups of people who led me to think it might: business school professors and SoulCycle fanatics.

Jan Rivkin, a strategy professor at Harvard Business School, says businesses’ sustainable advantages can come in three forms. One is a unique resource nobody else can access: Think of De Beers’s onetime monopoly on the diamond market, or the patent on a blockbuster drug, or the secret formula for Coca-Cola. A second is positive feedback, where a company’s market-leading position helps it move even further ahead. Walmart’s huge market share allows it to pressure suppliers for lower prices, which makes it even more appealing to shoppers. Everybody wants to use Facebook because everybody else is on Facebook.

intensely competitive business. When he wants to remind students that an industry can be less lucrative than it looks from the outside, he likes to use a case study about the twice-bankrupt gym chain Bally Total Fitness. SoulCycle “had better have something that’s deeply unique and sustainable,” he said.

SoulCycle does seem to offer something unique: a sense that what it sells is more than a workout. Devotees of the chain cite benefits from their engagement with SoulCycle that go well beyond the physical.

“It’s sold convincingly and addictively as personal growth and therapeutic progress through fitness,” said Ben Dreyfuss, the engagement editor at Mother Jones magazine, who lives in Manhattan and estimates he has taken an average of one SoulCycle class a day for the last 45 days. “It’s got the calming bits of yoga mixed with the group pack mentality of team sports and the weird psychological whatever you want to call it of following a squad leader into battle.”

Eli Radke, a trader and sometime SoulCyclist in Chicago, described the experience as “strangely sexual.”

These endorsements include elements of the first and third categories of sustainable advantage identified by Mr. Rivkin. The brand is closely associated with a transcendent experience other gyms don’t offer. Replicating that experience is not simple for would-be imitators, because convincing people their workout is a path to personal growth involves more than setting a few candles onstage in front of an indoor cycling instructor.

It may be telling that SoulCycle has drawn several competitors that offer similarly upscale indoor cycling experiences but that have not copied what Mr. Dreyfuss approvingly calls SoulCycle’s “hippie-ish logos and creeds.” Studios like Peloton and Flywheel both offer cutting-edge technology and a competitive ethos. At Flywheel, for example, a screen called the “Torqboard” shows who is working hardest, though posting your score on the board is optional.

“I don’t want to compete against others when I work out,” said Katherine Petti, a lawyer in Washington who goes to SoulCycle three times a week. “I want to focus on improving myself, which is what SoulCycle focuses on.”

The self-improvement mantra made its way into the company’s initial public offering filing, which says SoulCycle is “the place people come, regardless of their age, athletic ability, size, shape, profession or personality, to connect with their best selves.”