When you issue a debt instrument at a discount, the beginning value on your B/S is the discounted issuance price. 

This effectively understates the balance repayable at maturity as the face value must be repaid at full - not the original book value that is discounted. 

Therefore, to ensure that the book value of the liability matches the face value upon repayment (or rather the repayment obligation is correctly stated), an OID liability (which is amortised over life of loan) is recorded on the BS
 

Without the OID, the book value would understate the claim over the business that the debt holders have. 

 
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The OID is not a liability technically. It is a contra-liability against the par (face) value of debt. Intuitively you can see it as an asset but it's best accounted for as a contra-liability.

Assume face value of debt is 100. The coupons/interest payments are all based off of the face value of 100. If the debt gets issued at a discount of 99, then on the balance sheet you'd record the debt at face value of 100 with a subsequent contra-liability of 1 OID (written as -1) to yield the book value of debt as 99.

Over time, you amortize the OID contra-liability to zero (non-cash expense) so that the book value of debt accretes to the face of 100. The amortization process is best thought of as how you'd amortize financing fees for issuance of debt in a LBO (these, too, serve as contra-liabilities that lower the value of debt on the balance sheet).

 

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