Using asset pricing value decompositions
The market value of government debt equals the present discounted value of primary surpluses. Applying present value decompositions from asset pricing to this valuation equation, I find that half of the variation in the market value of debt to GDP ratio corresponds to varying forecasts of future primary surpluses, and half to varying discount rates. Variation in expected growth rates is unimportant.

The Value of Government Debt
Author: John Cochrane
From: Stanford University
Using “policy value”
An analysis of the three measurement bases and the discount rates on which they explicitly or implicitly depend shows that all are unsatisfactory as indicators of the burden that the debt imposes on the government. On the one hand, face value is manipulable: governments can borrow as much as they wish while reporting virtually no debt at all at face value. On the other hand, market value and amortized cost are unsatisfactory because they vary with the government’s creditworthiness. An alternative measurement basis is proposed here that does not suffer from these problems, namely policy value, which is the value of the debt conditional on the government’s carrying out its policy toward the debt, or the present value of planned debt payments at the debt’s market interest rate less any credit‐risk premium in that rate.

Not taking debt at face value, or market value or amortized cost: Policy value as a measure of the burden of public debt
Author: Timothy C. Irwin
From: IMF