LONDON -- BP (LSE:BP) (NYSE:BP) issued decent first-quarter results earlier this week, but its shareholders are probably more interested in whether the eventual outcome of the firm's Clean Water Act trial in New Orleans could threaten its attractive 5.1% dividend yield.

This trial will determine whether BP was guilty of gross negligence on Deepwater Horizon, and the fine it has to pay for the oil spilled in the Gulf of Mexico.

Worst-case scenario
If BP loses and is found to have been grossly negligent, then the worst-case scenario would be a $21 billion fine. This might also open the floodgates for increased claims from the 2,200 or so other parties that are suing BP for compensation.

It could be some time until we find out what will happen, though. The first stage of the trial, which will determine whether BP is guilty of gross negligence, has just ended, but a ruling is not expected from Judge Carl Barbier until after the second stage of the trial.

In the second stage, which is due to start on Sept. 16, Judge Barbier will determine how much oil was spilled. Depending on the degree of negligence, the fine under the U.S. Clean Water Act ranges from $1,100 to $4,300 per barrel.

Current estimates are that around 4.9 million barrels of oil were spilled, so the negligence ruling will be important, because it could cause the fine to increase from around $5 billion to $21 billion.

Can BP afford $21 billion?
If BP isn't found guilty of gross negligence, then shareholders don't need to worry. According to its first-quarter accounts, BP has already made a $3.5 billion provision for fines under the Clean Water Act, so anything up to around $5 billion should be easily affordable.

If BP's fine rises above, say, $15 billion, then payment of the fine could become a bit more uncomfortable, raising the risk of further asset sales, or even a dividend cut. Although this could happen, I think that BP might just manage to pay $21 billion without having to resort to such drastic measures.

At the end of March 2013, BP had $27 billion in cash and cash equivalents on its balance sheet and had reduced its net debt from $28 billion at the end of 2012 to $18 billion, thanks to its sale of TNK-BP. Although some of this cash is reserved, BP also has $3.5 billion of asset sales that are expected to complete this year.

Safer dividends than BP?
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Roland Head owns shares in BP. The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.