Warren Buffett, the chairman and chief executive officer of Berkshire Hathaway (BRK.A -0.28%) (BRK.B -0.68%) is considered one of the greatest investors of all-time and his expertise has made him a billionaire many times over. So, when Buffett and his team add stocks to the $300 billion Berkshire Hathaway portfolio, it moves markets.

But, there are certain stocks Buffett can't invest in -- particularly, small-caps. He has acknowledged this fact, saying in the past that he must invest in "elephants" and avoid "mosquitoes," even if the elephants are less attractive. The reason is, the mosquitoes are too small to have any real impact on his massive portfolio and loading up with too many shares would create reporting requirements and more risk.   

Now, getting into the brilliant mind of Buffett is impossible, but based on his philosophy and track record, there is one "mosquito," at least, that he might like right now as an investment if he could -- The Bancorp (TBBK -3.72%). Here's why. 

The bank for fintechs

The Bancorp is a small bank with only about $7.1 billion in assets -- making it the 173rd largest in the country, according to the Federal Reserve. But it plays a much bigger role in a niche it carved out for itself a few years ago -- as a banking-as-a-service (BaaS) provider to fintechs who offer their own products, under their own name, using The Bancorp's platform. 

The company provides these nonbank lenders with the back-end services that are costly and complex for companies that want to offer a product like a prepaid card or debit card. It handles the regulatory compliance, provides access to the payment networks, takes deposits -- since nonbank lenders can't -- and issues cards. It has more than 100 clients -- including PayPal (PYPL 0.64%), Chime, Fiserv (FI -2.02%), and SoFi (SOFI 0.26%), through its Galileo BaaS platform, among others. It was ranked the No. 1 issuer of prepaid cards in 2021 and No. 8 last year in debit card transaction volume by the Nilsson report.

The Bancorp Bank also offers commercial lending, institutional banking, and real estate bridge lending. So, while it doesn't have bank branches for consumer banking, it does have offices around the country for its business and institutional banking services. It recently got its national bank charter from the Office of the Comptroller of the Currency (OCC) for its subsidiary The Bancorp Bank, and relocated its main offices from Delaware to Sioux Falls, South Dakota.

With its business model, The Bancorp generates both interest income from its loans, but also fee income through its Baas platform, generating both service and transaction fees. In the most recent quarter, the bank saw an 8.1% year over year increase in noninterest income to $28 million and a 1% year over year increase in interest income to $54.6 million. Net income was up 3.4% to $30.4 million compared to the previous year's quarter. 

Based on its business pipeline and expected growth, along with increases in interest rates, company officials expect profitability to gradually rise over the next 18 months. In the second quarter it raised its earnings guidance for 2022 from $2.15 per share to a range of $2.25 to $2.30 per share.

The Bancorp has qualities that Buffett likes

The Bancorp has a market cap of about $1.8 billion, which make it smaller than any stock in Buffett's portfolio, including StoneCo (STNE 0.32%), which has a market cap of about $3.2 billion.

The stock is down about 10% year-to-date as of Sept. 27, which is better than most of its peers. It is trading at about $22 per share, and analysts forecast a median price target of $34.50 – which would be a 58% increase over current levels.

Banks and lenders are cyclical in that they tend to perform better when the economy is growing and strong. That is the opposite of where we are now. But Buffett has made clear, through words and actions, that he is a fan of banks, because they offer essential services and can take advantage of periods of economic expansion -- which are typically much longer than recessions.

The Bancorp is not a large, blue-chip bank like Bank of America (BAC -0.13%), Citigroup (C -0.32%), and U.S. Bancorp (USB 1.56%) that Buffett typically invests in, but it has a unique advantage through its BaaS platform that sets it apart from others. While there is growing competition in this area, The Bancorp is one of the pioneers and had a significant first mover advantage. While revenue in that business could slow if we enter an extended economic downturn, higher interest rates should boost interest income.

The Bancorp is also extremely efficient -- another quality that Buffett appreciates. It maintains a 19% return on equity, which is well above the 12.2% average for banks of its size. It also has a wide operating margin of 49.2% and a profit margin of 26.4%, which speaks to the ability of bank to keep expenses down. It has built up its technology infrastructure over the years, while newer still competitors are ramping, plus it has no branches, which reduces overhead. Trade publication Bank Director recently named it the best bank with assets between $5 and $50 billion.

But the bottom line, as far as Buffett would likely be concerned, is The Bancorp's value. With a price-to-earnings ratio of about 11 and a price-to-book value of 1.9, it is trading at a pretty moderate valuation. Including its attractive valuation, The Bancorp has many of the qualities that might pique Buffett's interest if it ever becomes an elephant. Or if it had been available before he became a billionaire.