Oxford University lacks the income to maintain its world-class status, John Hood, the institution's new vice-chancellor warned this week.
Dr Hood, who this week replaced Sir Colin Lucas, said in his inaugural address on Tuesday that Oxford's budget "remains its most troubling challenge".
He said that "the cost of providing a world-class university and the revenue available to fund that cost are not in harmony".
Trustees of the university "must work cooperatively and assiduously to remedy this position", said Dr Hood. They would have to balance the needs of students and access issues against the desire to increase income from fees. He also said there was a need to invest endowments wisely in capital growth.
His comments came as Michael Beloff, president of Trinity College, Oxford, warned that the university could reject state funding and go private within 15 years rather than submit to growing Government pressure to recruit more students from poorer backgrounds.
Dr Hood, vice-chancellor of the University of Auckland for the past five years, also raised questions over Oxford's complex collegiate system of governance, which is soon to be reviewed.
He warned that "organisational complexity inevitably carries with it costs". He added: "We cannot afford to allow complexity to confuse, obfuscate or confound."
It was the first time that the incoming and outgoing vice-chancellors both made speeches to mark the handover.
Sir Colin, Oxford's vice-chancellor for the past seven years, said the university had to build a larger endowment fund in a "sustained way over time". In order to succeed "the whole university really must subscribe to this as a collective action", he said.
Currently, Oxford's 36 colleges manage their own endowments and rarely pool resources.
Sir Colin said the most serious funding issue facing higher education as a whole was the "gross imbalance" in resources available for the humanities compared with the sciences. This was "leading towards a damaging destabilisation of the ecology of universities".
* Oxford University's ongoing battle with animal rights extremists who have been targeting employees and property in protest at the university's use of animals in scientific experiments also attracted Sir Colin's ire.
He said Oxford had assumed "iconic status" in its battle with animal rights activists and it must defend its right to conduct bioscience research as "a serious point of principle".
He spoke out as Oxford returned to the High Court on Tuesday to seek an injuction against campaigners who intimidated staff and contractors working on a new biomedical building.
A decision was due after The Times Higher went to press.