Should be a lot more than 10 for a second offence, especially when the owner "misled" the Football League when he took over. They will not like that and tend to be quite emotive when handing out these punishments.
They will lose just the 10 points, that will only increase if admin find any dodgy dealings. Interesting that the last bloke to do the admin. was refused the chance to do so again, which is unusual, so could there be a bit of a wiff in the air.