The child, who cannot be named due to his age, smashed the window of a town shop in the early hours – only days after a previous probation order had been imposed.
The Youth Court heard that he missed his first probation meeting later that morning because he had a hangover, having been drunk at the time of the incident.
Then, five days later, the youth started a fire by setting fire to paper in the toilets at Liberation Station.
Legal adviser Samantha Morris, prosecuting, said the fire had been “readily put out”.
She added: “He has a number of offences on his record.”
He admitted the charges of malicious damage and arson.
The Magistrate, Bridget Shaw, imposed the new probation order and told him: “You need to take some responsibility.”
She also told his father to pay £150 towards the cost of repairing the window.