If there's one thing a majority Tory government is likely to achieve it's a solution to the BBC problem.

Since the 1940s, the broadcaster has been funded by a compulsory licence fee and here we are 70 years on in the new world of digital and it's still using the same old-world solution. The Conservatives need to sort it out.

An early sign that they will do so is the appointment as Culture Secretary of John Whittingdale, a former chairman of the Commons Media Select Committee. Mr Whittingdale indicated his scepticism over how the BBC is paid for some time ago when he said the fact the licence fee wasn't means-tested made it worse than the poll tax. But what are his options for reform and how likely are they to happen?

The first is full privatisation and the end of the licence fee altogether but, however much some libertarian Tories would like to see that, it is not going to happen in the immediate future. Much more likely is the privatisation of Channel 4. There was a little bit of pushing by Tories in the last government to go for it, only for the idea to be squashed in the end by Vince Cable. Now he's gone and there's no Coalition, the idea is back on the to-do list.

Another option short of privatisation for the BBC would be reducing the compulsory part of the licence fee and introducing an element of choice. There are various ways this could work but one option would be to use a reduced licence fee for the core public sector responsibilities (news, weather, BBC1, perhaps BBC2 as well, and Radio 4) and everything else would be paid-for by viewers as an add-on if and when they want it (they would probably be charged by the hour). It's not as clean an idea as getting rid of the licence fee altogether, but as a staging post, it has its merits.

Another option which will almost certainly happen is an end to the criminal sanctions that back up the licence. It is extraordinary but true that it can be a criminal offence to watch television in the UK and it's an anomaly that should be brought to an end swiftly and cheaply and probably will be under Whittingdale. Staff at the BBC are worried decriminalisation would cost millions in lost revenue, but at least we would separate the act of watching Strictly Come Dancing from the threat of going to prison.

The final option, and again very likely, is a continuation of the five-year freeze to the licence fee. The BBC has been desperately pushing for a raise, with staff already saying they are at tipping point. But the idea of the government supporting a rise in a fee imposed on viewers when there will be more cuts in government spending is an absolute non-starter.

The freeze would inevitably mean some BBC programmes and departments making cuts. But as part of a bigger process of soul-searching about the corporation, that's no bad thing. As Michael Grade, the BBC's former chairman, put it: the idea that the BBC will keep the status quo and get a bit more money as well is out of the question. Change has to happen and under the new government, it is more likely than ever.