According to this Yahoo! Finance article, the Department of Education has some analysts who attempt to estimate the value of the Department's student loan portfolio:
For years, bean counters at the department have been writing down the value of its $1.4 trillion portfolio of student debt as they adopted ever-more-pessimistic views of how much borrowers will repay. In September, the analysts made their biggest adjustment yet, valuing loans at just 82 cents on every dollar owed, down from 104 cents in 2015, records show. The debt is now worth $258 billion less than the amount outstanding.
I think I understand what it means for the loans to be worth less than their nominal value. Since the analysts believe that some of the loans won't be paid back, their estimated value is less than the current amount of the loan.
I don't understand the reported historical value: 104 cents per dollar. That seems to mean that on average each $1 in student loans (including interest, payments made, etc.) is worth $1.04 to the Department. At first I thought it was because they expected to earn more from the interest on the loans being paid off, but then I learned that the nominal value of a debt instrument already includes interest and payments to date.
So how can it be worth more than its current value?