For those people who get furious every time a report that a CEO has just received a paycheck worth millions, the news that Jeff Smisek, CEO of United Airlines, saw his total 2012 compensation shrink 41 percent last year after stumbles in the airline's merger with Continental, will make them grin ear-to-ear cynically.

According to USA Today, "Smisek compensation was $7.9 million last year, down from $13.4 million after a cut in his incentive payments."

As for the hard numbers, "his base pay for the year was unchanged at $975,000. But the value of his stock awards fell to $3.1 million, from $7.5 million in 2011. And non-stock compensation pay dropped to $3.5 million, from $4.4 million a year earlier," reported USA Today.

This comes in stark contrast to to United/Continental stock rising 24 percent.

These numbers are reported by the Associated Press, who used its own formula that "calculates an executive's total compensation during the last fiscal year by adding salary, bonuses, perks, above-market interest that the company pays on deferred compensation and the estimated value of stock and stock options awarded during the year." 

However, the Associated Press did noted that their formula "does not count changes in the present value of pension benefits. That makes the AP total slightly different in most cases from the total reported by companies to the Securities and Exchange Commission."

To understand the formula and numbers a bit better, think of it like this:

"The value that a company assigned to an executive's stock and option awards for 2012 was the present value of what the company expected the awards to be worth to the executive over time...the number is just an estimate, and what an executive ultimately receives will depend on the performance of the company's stock in the years after the awards are granted."