Why would student loans be valued at $1.04 for every dollar of debt?

Question

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?

Answer 1

I am not very familiar with the way student loans work for Department of Education, nor can I be sure that the author of the article used accurate terms.

One possibility that the loan is valued at 104 is that the loan is Fixed Interest Rate arrangement at the beginning, and the subsequent market interest went down, causing the market value of the loan going up. This is the inverse relationship between Bond Price and Market Yield.

Imagine that you lent $100 on 1 Jan for 1 year to someone at an agreed interest rate of 3%. The next day on 2 Jan, the market interest rate went down by 2% to 1%. Suppose that you want to sell this loan contract to another lender, the lender will be willing to pay ~$102 ($101.984 to be exact) on 2 Jan, and collect $103 on 31 Dec, because 1% is the new market interest rate.

In case of a fixed rate loan of 30 years, every 1% decrease in the market interest rate expectation of the future will result in instant 14%+ increase in the value of the loan contract. The multiplier "14" is called the Modified Duration (Although the formula only applies to a bond-style instrument of interest-only payment, and 1 final payment of the principal).