The government has sold a student loans book with a face value of £890m for just £160m, angering student union groups.

A consortium called Erudio Student Loans led by the investment fund manager CarVal bought the remaining book of mortgage style loans which were taken out by around 250,000 students between 1990 and 1998.

The National Union of Students (NUS) and University of London Union (ULU) expressed alarm at the sale and said it made "no economic sense".

Toni Pearce, the NUS president, said the sale was "extremely concerning" and effectively meant the public is subsidising a private company to profit from government debt.

She added: "The impact of this sale won't only affect borrowers, but will affect everybody. The simple fact is that having these loans on the public books would be better off for the government in the long run. Selling off the loan book at a discount to secure a cash lump sum now doesn't make economic sense."

Michael Chessum, the ULU president, said privatisation of the loan book stemmed from "a poisonous ideological motive to make students consumers, with a lifetime of increasingly malign debt".

The price paid by Erudio reflects the consortium's assessment of the proportion of loans likely to be paid back in full or in part, with the majority of the book in arrears or deferred. Of the loans sold, just 14% of borrowers are currently repaying their debts. Around 46% are earning below £28,775, the level at which the repayment threshold kicks in.

A further 40% are not repaying their debts in line with the terms of their loans.

The Department for Business, Innovation and Skills revealed plans to sell the last remaining tranche of loans in March, arguing the private sector was best placed to collect the outstanding debt.

Announcing the sale on Monday, the universities and science minister David Willetts said the deal represented "good value for money, helping to reduce public sector net debt by £160m". Total public sector net debt was £1.2 trillion or 75.4% of gross domestic product at the end of October, according to figures published last week by the Office for National Statistics.

Willetts added:"The private sector is well placed to maximise returns from the book which has a deteriorating value. The sale will allow the Student Loans Company to focus on supplying loans to current students and collecting repayments on newer loans."

He said there would be no change to borrowers' terms and conditions, including to the interest rates charged.

But Chessum said students should not be reassured by the government's promises.

"It could result in a massive retroactive hike in tuition fees if parliament lifts the cap on interest. The reassurances being offered by the government are largely meaningless – there is every reason to believe that current and future governments will simply flout commitments on higher education funding, because that is what has happened consistently under both Labour and Tory governments," he said.

The sale to Erudio follows two previous sales of such loans by the former Labour government in 1998 and 1999, which transferred £2bn of student debt to the private sector.