I've repeatedly seen the media describe Citigroup (NYSE:C) as desperate because it had to pay 11% on the capital it recently raised. True, that percentage probably doesn't make chairman Robert Rubin feel like frolicking through the roses. But it's hardly the end of the world, either.

The deal
Abu Dhabi Investment Authority, a sovereign fund, agreed to buy $7.5 billion worth of equity units. The units pay an 11% interest rate, and they're convertible into Citi's stock between 2010 and 2011, at prices ranging from $31.83 to $37.24 per share.

What the media thinks
The media is calling it a horrible deal for Citi. The reasoning goes that 11% is more than junk bonds are trading for. Thus, Citi's stock and credit rating now have junk status.

However, that's not entirely accurate. First of all, if Citi were to sell equity, it would have to pay a dividend of $2.16 per share, or about 7% of today's stock price. Thus, the extra premium for the capital from Abu Dhabi roughly represented a 4% interest rate.

In addition, you simply cannot compare the rates paid on debt and equity. It just doesn't make sense. It doesn't matter whether you're discussing banks that are under the gun, like Bear Stearns (NYSE:BSC) or Merrill Lynch (NYSE:MER), or banks still sailing relatively smoothly, like Wells Fargo (NYSE:WFC) or Income Investor recommendation Bank of America (NYSE:BAC). The cost of equity, whether implied or explicit, is always higher than the cost of debt.

This should be intuitive: Debt is higher in the capital structure. If Citigroup were to default, debtholders would get paid first. Stockholders? Back of the line. So why didn't Citi just sell some bonds and pay a lower rate? Simple: The company needs equity, not debt, to appease regulators. The $7.5 billion from Abu Dhabi will shore up the company's capital ratios.

Another way to think about it
Citi is selling roughly 5% of itself, and it's paying a 4% premium over its dividend rate. In return, it gets the use of $7.5 billion of cash forever. As an added bonus, if the stock recovers, it doesn't suffer additional dilution until shares rise past $37.24. That's a pretty decent premium to its recent $30-$32 trading range.

Here's an even simpler way to look at it. Let's say you, like the Abu Dhabi government, thought that Citi's stock might be worth a gamble. You could buy Citi's long-term calls, with a strike price of $30, for somewhere around $8.50 per contract. Thus, your buy-in rate would be $38.50 -- not too far from what Abu Dhabi would be paying.

Of course, Abu Dhabi also gets an 11% interest rate every year, and you get 0%. On the other hand, if the stock goes to 0, Abu Dhabi would probably lose its entire investment, while you'd only lose $8.50 per share.

Foolish thoughts
I'm not making any predictions about the future of the credit markets, or Citi's ability to navigate them without taking additional writedowns. My only point here is that Citi's cost of funds, while relatively steep, isn't as bad as the headlines would have you believe.

Citi needed a ton of cash, and it got $7.5 billion fairly quickly, at a price that compensates the investor for the opportunity cost of dividends, then adds an equity risk premium. I'd say it was a relatively fair deal for both parties.

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