How much will Paula's departure cost 'American Idol'?

Paula Abdul was the heart of American Idol. Last night she Twittered that she had quit the show. And now Idol producers -- Fox Broadcasting, Fremantle Media and 19 Entertainment -- are left wondering whether they made the right move in letting her go to save a few million dollars in salary and end the drama she generated. The answer boils down to whether an Idol without Paula loses so many viewers that advertising revenues plunge.

Let's review the facts. Idol has been the highest rated program for years, but its numbers have dropped -- for example in the 2009 premier, Idol attracted 30.074 million viewers -- 10 percent fewer than in 2008. Idol charges $500,000 per 30-second advertisement -- rising to $600,000 per half-minute for the finale. Abdul had been making $2 million a year and the producers offered her a $10 million multi-year contract, which somehow amounted to a 30 percent raise. This was less than she believed she was worth to the show.

Meanwhile, Idol producers were making it clear that they were happy to go ahead without Paula. They closed a deal to pay the smarmy Ryan Seacrest $45 million and re-hired Kara DioGuardi at an undisclosed salary. Simon Cowell and Randy Jackson are under contracts that were negotiated years ago.

But along with Paula's emotional responses to Idol contestants came drama. She often sat in the judge's seat, appearing to be under the influence of something. And a former contestant -- Paula Goodspeed -- was found dead inside a car parked near Abdul's Los Angeles mansion. I don't know why Paula should be blamed for this, but it appears she was.

Now that she is gone from the show, Idol producers must hope that Paula was not very important to the show's popularity. Unfortunately for them, Paula supporters claim that Idol viewers voted her the most popular of the four judges. That does not sound like objective research to me, but it raises the question of how much Paula's departure will cost Idol.

One thing is for sure -- Kara is going to have to change in ways that are beyond any human being in order to add as much to the show as Paula did. Assuming Paula would have stayed for an extra $10 million, if Idol loses $10 million or more in advertising revenue due to a drop in its audience post-Paula, letting her go will have proven to a bad business decision.

My hunch is that Idol will be much poorer for Paula's departure -- but it will go on.

Peter Cohan is president ofPeter S. Cohan & Associates. He also teaches management at Babson College. His eighth book isYou Can't Order Change: Lessons from Jim McNerney's Turnaround at Boeing. Follow petercohan on Twitter. He has no financial interest in the securities mentioned.

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