Writing off existing student loans could cost the government as little as £10bn, well below the £100bn figure quoted by politicians, according to new analysis by the Institute for Fiscal Studies.

The IFS calculated that immediately scrapping the debt for university tuition would add £20bn to government debt, but that delaying the decision until the end of the current parliament in 2022 would add £60bn.

A cheaper alternative would be to write off tuition fee debt above the £3,465 level of undergraduate fees charged before 2012 – which would add £10bn to government debt.

The figures are well below the £100bn quoted by the universities minister, Jo Johnson, and other members of the government this year as they sought to push back against suggestions by the Labour leader, Jeremy Corbyn, that his party would end tuition fees and “deal with” existing student debts.

The £100bn figure was also quoted by the shadow education secretary, Angela Rayner, in July, when she said: “It is a huge amount, it’s £100bn, which they estimate currently, which will increase. It’s a huge amount of money but of course we also know that a third of that is never repaid.”

But as the IFS pointed out, the £100bn is the total for all student loans, including those for maintenance, for students from outside England, and for those incurred after fees were introduced in 1998 but before they were raised to £9,000 a year in 2012.

If only post-2012 debt for tuition for students from England was scrapped, the policy would increase government debt by around 1% of national income by 2050, or around £20bn in today’s terms.

“Suggestions that debt would rise by £100bn are wrong. £100bn is the outstanding value of all tuition fee and maintenance debt since 1998 – it is not the answer to the question: what would be the impact on public debt of writing off fee loans accumulated under the £9,000 tuition fee regime?” the IFS said in a research note published on Friday.

The current level of £9,000-era tuition fee loans held by the government through the Student Loans Company is £34bn. However, the loan repayment calculations assume that £14bn will never be paid back.

The analysis also cautioned that the main beneficiaries of wiping out the debts would be high-earning graduates, who pay back a higher percentage of their loans than other graduates. Under the current system, student loan debt that is not repaid after 30 years is written off.

The government could pay for the additional debt with a “modest increase” in the top rate of income tax, the IFS suggested.

“This would do something to alleviate concerns that the policy is regressive, although high earners without student debt – people who didn’t go to university as well as those who went but do not have any outstanding debt – would lose out,” it said.

The calculations come as parliament’s education select committee announced it is to hold hearings next month on value for money in higher education, including the controversial issue of high pay among vice-chancellors and senior academics.

“We want to examine to what extent the individual student and the taxpayer receives value for money for this considerable financial investment,” said Robert Halfon, the Conservative MP who chairs the committee.

“We want to explore how far our universities are delivering a good-quality service for their students and the extent to which the high salaries of vice-chancellors are linked to positive student outcomes.”

The results of a recent survey found that a third of students said they had received good or very good value for money while in higher education.

Earlier this year the IFS calculated that young people from the poorest 40% of families entering university in England for the first time this year will emerge with average debts of around £57,000.

Sally Hunt, general secretary of the University and College Union, said her union would tell the committee about the use of zero-hours contracts in universities.

“It cannot be right that the people teaching our students are constantly anxious, not knowing from term to term, or even week to week, whether they will have a job or how much they might earn,” Hunt said.