A radical shift in the way Scottish higher education students are funded must be found by Holyrood politicians, according to the principal of Edinburgh University.

Sir Peter Mathieson said it is a "tragedy" that Dundee University faces the possibility of closure if it does not make major cuts, and it would also be a tragedy if others were to run into similar financial difficulties.

Sir Peter is facing anger from staff at the University of Edinburgh at plans to cut £140m from its spending – equivalent to at least a month's expenditure each year.

And in a wide-ranging interview with BBC Scotland, he said he cannot rule out compulsory redundancies at the 442-year-old institution.

Sir Peter said there will have to be a "radical re-wiring" of the way the university operates, with fewer courses and less organisational complexity and duplication.

"There are inefficiencies about the way we deliver things. This is a mammoth university with 22 schools and lots of duplication. We're very good at adding new things, not at taking things away," he said.

"We need to take a seriously look at the way we do things, and be responsible with the scale of operations we can afford to provide.

"So there's radical rewiring (needed) of the way we do our business, but also of political imperatives.

"If it's to be a political priority, then it has to be adequately funded to ensure its future."

He said student numbers are likely to remain at around 50,000 while the number of staff will fall from 18,500 – or 15,000 in equivalent full-time jobs.

But he declined to give a figure for the number expected to go.

The warning follows a sharp unplanned rise in the number and cost of staff over the last three years, which has not been matched by growth in income from overseas student fees.

The principal says there is no intention to close departments, and while some courses will close, existing students can be sure their current courses will be completed.

Sir Peter denied that nearly £1bn of financial assets controlled by the university could be tapped to deal with the shortfall.

And he warned that budget surpluses of £150m and £400m – reported by the university in recent years – cannot be sustained.

He also denied that the scale of the challenge is being exaggerated to push through reform, as staff unions have claimed.

Rapid growth and change

Across Scotland, rapid growth has been funded through a sharp increase in the number of fee-paying overseas students.

In the last academic year, Edinburgh secured £360m from overseas students, while the Scottish government paid £27m in fees for Scotland-based students.

A further £82m came from the fees paid by students from other parts of the UK, which amounts to nearly £28,000 for the standard four-year honours degree.

Universities in Scotland say that the Scottish contribution of around £7,500 per student per year is far below the cost of their education, and that international student fee income is proving an unreliable way to close the gap.

In the rest of the UK, fees are around £2000 more.

Dundee University is having to shed as many as 700 staff in response to a severe financial crisis, which is partly the result of a sudden drop in the number of overseas student recruits.

The most recent one-year figure was a 27% drop, and it is reported to have fallen more sharply in the most recent intake.

Sir Peter said it is "a tragedy" that the interim principal on Tayside says closure or break up of the university there is a possible outcome of the crisis.

"It would be a tragedy for Scotland if other universities were to get themselves into a similar situation," he said. "What we're doing here is to make sure we don't."

Other universities are taking action to reduce costs as student recruitment falls short of growth expectations. On Thursday, the University of Aberdeen followed Dundee, Edinburgh and Robert Gordon universities in announcing multi-million pound cuts.

The Edinburgh University principal laid down a challenge to Scotland's political parties to take urgent action on funding.

He said the funding shortfall in Scotland is worse than in England because of a tighter squeeze on fees per student, and because the number of recruits in Scotland is capped.

An independent assessment of Holyrood funding points to a drop of at least 22% in the real value of Scottish ministers' grants for higher education.

Sir Peter said ministers will either have to fund student tuition at a much higher level, or reduce the number of Scots going to university.

Otherwise, with volatile fee income from foreign students, he believes other funds have to be allowed.

He suggested options of a graduate contribution, or allowing universities to recruit Scottish students who are able and willing to pay towards their fees. At present, they are barred from attending if they cannot get a government-funded place.

There's frustration among vice-chancellors that the future of Scottish education is always framed in terms of 'fee or free', and Sir Peter says he is "not necessarily" in favour of charging for tuition.

"We need more income into the system, either through some kind of means testing or a post-graduate system of earnings repayment.

"Either we have tuition fees which are adequate to pay the costs, or we have another mechanism to pay the costs. If we had a hybrid system, where some people pay fees and some people don't, one possibility is that that's means-tested in some way."

Future funding models

Responding to Sir Peter's comments, the Scottish government's Higher Education Minister, Graeme Day, said:

"The sector is aware we are open to exploring the future funding model of universities, but we are clear that this government will not reintroduce tuition fees.

"Access to higher education must be based on the ability to learn, not the ability to pay.

"Broader financial pressures facing the sector remain, including the UK government's migration policies and its decision to raise employers' National Insurance contributions."

Sir Peter, who was raised by his mother after his father's early death, said he "would not have gone to university if we had to pay fees".

He also backed free tuition for students from lower income homes.

"Providing opportunities to people from less advantaged backgrounds is a very important priority for me," he added.