At yesterday's Citigroup (NYSE:C) annual shareholder meeting, CEO Vikram Pandit tried desperately to follow in the footsteps of Goldman Sachs (NYSE:GS) and JPMorgan Chase (NYSE:JPM), vowing that his bank would repay taxpayers in full. "Every dollar with interest," he said.

That's encouraging, but highly unlikely. Especially for Citigroup.

You see, Citigroup is set to convert $25 billion worth of taxpayer-injected preferred stock into common equity. Taxpayers will get a 36% ownership stake after the conversion, which will come in the form of the same common stock you and I can buy on the open market.

That makes repaying TARP much trickier than simply writing a check, as other banks have proposed. For one thing, taxpayers are taking a massive haircut on that conversion. Citigroup currently has a market cap of about $17 billion, valuing that 36% stake at roughly $6.1 billion. Is it just me, or is $6.1 billion somewhat less than $25 billion?

Therefore, Citigroup common shares will need to be a four-bagger from today's prices before taxpayers can hope to break even. While that's not outside the realm of possibility, it still seems like quite a stretch -- especially since shares already rose over the past month.

I have a feeling that similar situations will become the norm. For banks such as Bank of America (NYSE:BAC) that still likely need additional capital, preferred-share conversions are a quick and easy solution. What's more, the Obama administration has hinted that converting preferred shares for common stock might be the next big step in shoring up the banking system.

So while big share conversions are a viable solution to stabilize and recapitalize banks, they do make repaying taxpayers in full a sticky issue, tied exclusively to stock market values. Alas, dear taxpayers, there's no such thing as a free lunch.

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Fool contributor Morgan Housel doesn't own shares in any of the companies mentioned in this article. The Fool has a disclosure policy.