American Express (AXP -0.62%) just released fresh financials revealing that revenue (net of interest expense) and diluted earnings per share increased by 11% and 27%, respectively, year over year in the fourth quarter. While these headline figures missed Wall Street expectations, the stock was up more than 6% (as of the morning of Jan. 26) immediately following the news due to an upbeat forecast.

The momentum continues, as this top financial stock has doubled in the last five years. And if we zoom out over the last three decades, shares have skyrocketed 2,390%, crushing the broader S&P 500 index.

Can American Express be a millionaire-maker? Let's take a closer look at the business.

A unique payments company

Investors are likely familiar with banking institutions like JPMorgan Chase and Bank of America, to name just two. At a high level, they take in deposits from customers and approve borrowers for different products, of which credit cards are a big piece. They get compensated with interest income for taking on this risk.

And investors have probably heard of Visa and Mastercard. Neither of these card giants extend credit like the banks do, but they provide the critical communications infrastructure that allows payments to be processed. They make money by charging a tiny fee anytime their networks are used.

American Express's business is a combination of these two types of companies just described. It issues credit cards, thus taking on default risk, and it operates the payment rails that allow these cards to be used. This is what's known as a closed-loop system.

It has been a lucrative business model. American Express can keep its defaults in check because it targets a more affluent customer base. The company's net charge-off rate of 2% in Q4 was lower than Chase's 2.8%.

And because American Express also authorizes and settles transactions, it gets to capture all the economics anytime one of its cards is swiped. This includes discount revenue from merchants, which represented 55% of the company's total in 2023. And it includes interest income when cardholders pay down their balances.

A powerful brand coupled with network effects has supported American Express over the years. And I see no reason that this won't still be the case decades from now. This should give confidence to investors looking to own the stock for the long haul in the hopes of becoming a millionaire.

It's also very encouraging to know that Warren Buffett's Berkshire Hathaway is a top shareholder. The conglomerate owns 20.8% of the business, a holding that's currently worth $30.7 billion. That's certainly a major vote of confidence.

These factors are important

There's no denying that American Express is a great business. But there are some variables to keep in mind when trying to assess whether the shares can make you a millionaire.

First, we have to consider the valuation. The stock's current price-to-earnings ratio of 18.9 is roughly in line with its trailing 10-year average. This means investors wouldn't be overpaying right now.

Growth also matters. Management believes revenue can rise more than 10%, and diluted EPS can increase in the mid-teens annually over the long haul. These would be healthy double-digit gains.

Perhaps more important, though, is a prospective investor's time horizon and initial capital outlay. The longer you plan to be a shareholder and the bigger the investment you make in the stock, the greater the chances are that this American Express holding could be worth $1 million one day.