In this respect, Vaughan did not start well. The loss of 187,000 listeners, 16% of the show's audience, in the last Rajar period - the first since Tarrant's departure - wiped 7.6% off Capital's share price the day it was announced.
The criticism that Vaughan suffered in subsequent newspaper reports was unfair. He had only been in the job for nine weeks and was still learning the DJ trade. It is absurd that the performance of one man, an artiste no less, should have financiers writing down the fortunes of a £365m FTSE-listed company.
But the pressures on Vaughan come not just from Capital's shareholders.
The plummeting of his career from the days when he was taken to the nation's hearts as the quick-witted, cheeky chappy who hosted Channel 4's Big Breakfast is well documented. Failures include a BBC talk show, a sitcom, 'Orrible, and a variety show, Passport to Paradise. Many believe his personal standing cannot survive a high profile failure at Capital.
Nonetheless, now five-and-a-half months into the job, Vaughan appears carefree and goes about his DJ duties in the Capital studio like a veteran.
He is supported by an experienced team, but there is no question who is in control. From ensuring everybody is on cue to provide a spontaneous group vocal backing to a record, to cajoling witty repartee out of his sidekicks - Becky Jago and news reader Gareth Roberts - Vaughan is the director of the mayhem.
His wit comes to the fore during the many, long off-air breaks. He regales the team with tales of his mother's dinner-plate holder in the form of a 'massive cock', and the sickly Siamese kittens he once had. Jago: 'Did they die?' Vaughan: 'They did when they hit the bottom of the river.'
Nobody knows whether to believe his tales, but who cares, it keeps the humour alive until it's time to put on the headphones and fill in the gaps between the music, news, travel and weather reports.
It is evident that the constrictions of this time-filling role do not make the most of Vaughan's talents. His is a big personality, visually expressive - he is made for TV.
Tarrant's light, easy humour came across as matey on radio, whereas Vaughan's humour is deeper, making him seem remote. More intelligent than your typical radio jock, he is prone to profundity on life's banalities. If he is to do radio, he might be better hosting a talk show, as he did with Fighting Talk on Radio 5 Live. Alternatively, Capital needs to let him off the leash, tear up the format and let his personality breathe.
You get a sense of his frustration during an off-air break when he launches into a rant against The Independent, which apparently wrote an unflattering piece about him. 'Don't ever let them in here,' he shouts to a PR. 'They're obsessed with our ratings when they don't have any circulation themselves. It's so hypocritical. They slag everybody off.'
Charming, even matey, in the studio, the mask slips again when I get to ask a few questions. Vaughan professes to be happy at Capital and doesn't feel under any pressure. Yet the defensive hostility indicates otherwise.
In summary, everybody is out to get him and the BBC is to blame for the demise of his chat show by sticking it on BBC3.
Capital invested £2m in a launch campaign that promoted Vaughan solely, not the station's brand values. A second wave broke on 22 September. This means even more pressure for Vaughan to succeed.
The burden of presenting a daily radio show got the better of another talented TV personality, Chris Evans. Capital will be hoping Vaughan doesn't become similarly disenchanted.
CAREER HISTORY
1997-2001: Presenter, The Big Breakfast, Channel 4
2001-2003: Host, Johnny Vaughan Tonight, BBC1, moved to BBC3
2001: Scriptwriter and actor, sitcom 'Orrible, BBC2
2003-2004: Presenter, Fighting Talk, Radio 5 Live
2003-present: Presenter, Superstars, BBC1
2004: Presenter, Passport to Paradise, BBC1
2004-present: Breakfast radio DJ, 95.8 Capital FM