A financial liability is derecognised when the obligation is discharged, cancelled or expires. For a bond that means it matured, it was called, or the issuer bought it back. The last case is the interesting one, because the issuer is transacting in its own liability at a price the market set.
How do you calculate the gain or loss on extinguishment?
The arithmetic is one line. Gain or loss on extinguishment equals the carrying amount of the debt less the reacquisition price. A positive number is a gain, and it arises when the issuer pays less than it was carrying.
The carrying amount is what makes this interesting. It's amortised cost and not face value. It equals face less any unamortised discount, less any unamortised issuance costs, plus any unamortised premium. Under both US GAAP and IFRS, debt issuance costs are netted against the liability and amortised through the effective-interest rate, so they are part of the carrying amount and they are part of the gain or loss whether anyone remembers them or not.
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Cascade Instruments issued at 95 with issuance costs, so at the end of year two it was carrying its debt at 96.119841 per 100 of face. It bought back $120,000,000 of face at 97, which is three points below par, and lost $1,056,191.34. How do you lose money paying less than you owe? Read the decomposition, because it shows the whole mechanism. The company was carrying the debt 3.880159 points below par, worth $4,656,191.34 on the face repurchased. It bought that debt back only 3.000000 points below par, worth $3,600,000. The difference is the loss, and it is 0.880159 points, or 0.9074% of the cash paid.
The general statement is worth keeping. An issuer repurchasing debt below par still books a loss whenever the discount in the market price is smaller than the unamortised discount and issuance cost in its own books. A company can pay less than it owes and still report an expense.
The tempting shortcut, comparing the repurchase price with face value, gets the sign wrong roughly half the time.
Where does the gain or loss show up in the statements?
Presentation and geography come next, and both matter more than the number.
Under US GAAP the gain or loss goes to continuing operations in the income statement. The extraordinary-item category was eliminated altogether in 2015, and extinguishment gains and losses had stopped being automatically extraordinary well before that, in 2002.
Filers often present it on its own line or inside other income and expense. Either is acceptable, and neither makes it operating.
In the cash flow statement the full reacquisition price is a financing outflow, because it is a repayment of borrowings. The gain or loss is non-cash and is reversed out in the operating section of an indirect-method statement. This creates the pattern to look for: a large non-operating gain subtracted from profit at the top of the operating section, with a matching financing outflow far below it and no investing movement at all.
What is the 10% test for modified debt?
Both rulebooks apply a 10% test to an exchange or a substantial modification of terms with an existing lender. Compare the present value of the new cash flows, including fees paid to the lender, with the present value of the remaining old cash flows, both discounted at the original effective interest rate. Ten percent or more apart and the old liability is extinguished, so a gain or loss arises and the new liability goes on at fair value.
Below ten percent the two rulebooks part company, and the difference is worth carrying. Under US GAAP no gain or loss arises at all. The fees adjust the carrying amount and a new effective rate is computed over the remaining term. Under IFRS 9 the gross carrying amount is recalculated as the present value of the modified cash flows discounted at the original effective rate, and the difference goes to profit or loss as a modification gain or loss, which can be substantial on a long-dated instrument. An exchange with a different lender is generally an extinguishment under US GAAP whatever the test says.
Is the accounting gain taxable?
The tax point is worth one sentence because it changes the cash consequence entirely. In the United States, cancellation of indebtedness produces taxable income, subject to exclusions where the taxpayer is insolvent or in a bankruptcy case, in which case tax attributes are reduced instead (check the current provisions and thresholds against the Internal Revenue Code before advising on any real transaction). A distressed issuer that books a large accounting gain may therefore also acquire a tax liability, an attribute reduction, or neither, and which of those applies is not visible from the income statement.