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If company recently issues new debt then would its MV be equal to its balance sheet value?
On the Statement of Financial Position (it is not called the Balance Sheet any more), the debt appears at its nominal value (which is $100 per bond unless told otherwise).
The company may issue the debt for $100 in which case the MV initially will be $100. However they may issue the debt at a discount and if (for example) it was issued for $90 then the initial market value will be $90 (even though on the SOFP it will appear at its nominal value of $100).