Difficulty: Intermediate | Prerequisites: bond valuation and issuance at a discount (see companion notes), time value of money, basic journal entries
Once a bond has been issued at a discount, the issuer cannot simply ignore the difference between what was received and what is owed. That discount must be systematically allocated to interest expense over the bond's life. This is where amortisation schedules come in, and there are two methods: the effective interest method (required under IFRS and preferred under US GAAP) and the straight-line method (a simpler approximation permitted under US GAAP when results are not materially different). This topic also covers what happens when a company retires its bonds before maturity, which produces a gain or loss on early extinguishment.
The effective interest method multiplies the carrying amount by the market rate each period, producing interest expense that grows as the carrying amount rises. The straight-line method spreads the discount evenly, producing constant interest expense. When a bond is retired early for more than its carrying amount, the difference is a loss on early extinguishment.
Effective interest method
An amortisation approach where interest expense each period equals the carrying amount multiplied by the market rate. In simple terms, this method recalculates interest based on how much is actually owed, so the expense changes each period.
Straight-line method
An amortisation approach where the total discount is divided equally across all periods. Think of it as the "lazy but close enough" method: equal amounts each period, simpler to calculate, but not as precise.
Discount amortisation
The portion of the discount allocated to a given period. Each period, this amount is added to the carrying amount, gradually bringing it up to face value by maturity.
Carrying amount (book value of bond)
Face value minus the remaining unamortised discount. This is what appears on the balance sheet as the net bond liability. It increases each period as the discount is amortised.
Cash interest
The actual cash paid to bondholders each period: face value times the coupon rate per period. This stays the same every period regardless of the amortisation method.
Early extinguishment (early retirement)
When the issuer buys back its bonds before the maturity date. If the price paid exceeds the carrying amount, the difference is a loss on early extinguishment.
Loss on early extinguishment
The amount by which the repurchase price exceeds the carrying amount of the bonds at the date of retirement. This is reported on the income statement.
Using the example of a $700,000 bond issued at $666,633, with a 12% coupon (6% semi-annual) and a 14% market rate (7% semi-annual), over 3 years (6 periods):
Each period:
Cash interest = $700,000 x 6% = $42,000 (constant every period)
Effective interest = Carrying amount at start of period x 7%
Discount amortisation = Effective interest minus Cash interest
New carrying amount = Prior carrying amount + Discount amortisation
Date | Cash Interest | Effective Interest | Discount Amortisation | Carrying Amount |
|---|---|---|---|---|
1 Jan 2019 | $666,633 | |||
30 Jun 2019 | $42,000 | $46,664 | $4,664 | $671,297 |
31 Dec 2019 | $42,000 | $46,991 | $4,991 | $676,288 |
30 Jun 2020 | $42,000 | $47,340 | $5,340 | $681,628 |
31 Dec 2020 | $42,000 | $47,714 | $5,714 | $687,342 |
30 Jun 2021 | $42,000 | $48,114 | $6,114 | $693,456 |
31 Dec 2021 | $42,000 | $48,544 | $6,544 | $700,000 |
Totals | $252,000 | $285,367 | $33,367 |
Notice the effective interest increases each period because the carrying amount grows. The total discount amortised ($33,367) equals the original discount.
The straight-line method divides the total discount equally: $33,367 / 6 periods = $5,561 per period (rounded).
Date | Cash Interest | Straight-Line Interest | Discount Amortisation | Carrying Amount |
|---|---|---|---|---|
1 Jan 2019 | $666,633 | |||
30 Jun 2019 | $42,000 | $47,561 | $5,561 | $672,194 |
31 Dec 2019 | $42,000 | $47,561 | $5,561 | $677,755 |
30 Jun 2020 | $42,000 | $47,561 | $5,561 | $683,317 |
31 Dec 2020 | $42,000 | $47,561 | $5,561 | $688,878 |
30 Jun 2021 | $42,000 | $47,561 | $5,561 | $694,439 |
31 Dec 2021 | $42,000 | $47,561 | $5,561 | $700,000 |
Totals | $252,000 | $285,367 | $33,367 |
Interest expense is the same every period. The total interest ($285,367) and total amortisation ($33,367) match the effective interest method.
Effective interest method (30 Jun 2019):
Debit Interest Expense: $46,664
Credit Cash: $42,000
Credit Discount on Bonds Payable: $4,664
Straight-line method (30 Jun 2019):
Debit Interest Expense: $47,561
Credit Cash: $42,000
Credit Discount on Bonds Payable: $5,561
The pattern is the same for both methods: Interest Expense is debited for the full economic cost, Cash is credited for the coupon payment, and the difference (the amortisation) reduces the Discount on Bonds Payable account.
Suppose the company retires the bonds after two interest payments (after 31 Dec 2019) by paying $685,000 in cash.
Under the effective interest method:
Carrying amount at 1 Jan 2020 = $676,288
Remaining discount = $33,367 minus $4,664 minus $4,991 = $23,712
Cash paid = $685,000
Loss = $685,000 minus $676,288 = $8,712
Journal entry:
Debit Bonds Payable: $700,000
Debit Loss on Early Extinguishment: $8,712
Credit Discount on Bonds Payable: $23,712
Credit Cash: $685,000
Under the straight-line method:
Carrying amount at 1 Jan 2020 = $677,755
Remaining discount = $33,367 minus $5,561 minus $5,561 = $22,245
Cash paid = $685,000
Loss = $685,000 minus $677,755 = $7,245
Journal entry:
Debit Bonds Payable: $700,000
Debit Loss on Early Extinguishment: $7,245
Credit Discount on Bonds Payable: $22,245
Credit Cash: $685,000
The loss is a "plug" figure: it makes the entry balance after you account for the face value, remaining discount, and cash paid.
\text{Effective Interest} = \text{Carrying Amount} \times \text{Market Rate per Period}\text{Discount Amortisation (effective)} = \text{Effective Interest} - \text{Cash Interest}\text{Straight-Line Amortisation per Period} = \frac{\text{Total Discount}}{\text{Number of Periods}}\text{Straight-Line Interest} = \text{Cash Interest} + \text{Straight-Line Amortisation}\text{Loss on Early Extinguishment} = \text{Cash Paid} - \text{Carrying Amount at Retirement Date}\text{Remaining Discount} = \text{Original Discount} - \text{Cumulative Amortisation to Date}Companies regularly retire bonds early when interest rates drop, because they can refinance at a lower rate. The accounting for these transactions is tested by auditors and reported prominently: a large loss on early extinguishment can materially affect reported earnings. Both IFRS and US GAAP require the effective interest method for most issuers, though the straight-line method remains common in textbook problems and is still permitted under US GAAP when the difference is immaterial.
Students often think interest expense under the effective interest method is constant. It is not. Because the carrying amount increases each period, the interest expense (carrying amount x market rate) also increases.
Students confuse which rate to use where. The coupon rate sets the cash payment. The market rate is used only in the effective interest calculation.
Students sometimes think the straight-line method and the effective interest method produce different totals. They do not. Both methods amortise the same total discount ($33,367) and produce the same total interest expense ($285,367) over the bond's life. Only the per-period allocation differs.
When computing the loss on early extinguishment, students frequently forget to use the carrying amount (net of remaining discount), not the face value. The loss is cash paid minus carrying amount, not cash paid minus face value.
Constructing an amortisation schedule from scratch is a classic exam question. You will need to fill in every column for every period.
Be prepared to record journal entries for any period in the schedule, under either method.
Early extinguishment problems typically give you the retirement date and the cash paid, then ask for the journal entry. The key is computing the remaining discount (original discount minus cumulative amortisation to date).
The loss on early extinguishment is frequently labelled a "plug" because it is the balancing figure in the journal entry. Exams may test whether you can identify it as such.
True or False: Under the effective interest method, interest expense is the same every period.
Fill in the blank: Discount amortisation under the effective interest method equals ______ minus ______.
True or False: The straight-line method and the effective interest method produce different total interest expense over the bond's life.
Fill in the blank: Loss on early extinguishment equals ______ minus ______.
True or False: Under both methods, the carrying amount reaches face value at maturity.
Answers: 1. False (it increases each period as the carrying amount grows). 2. Effective interest; cash interest. 3. False (total interest expense is the same; only the per-period amounts differ). 4. Cash paid; carrying amount at the retirement date. 5. True.
Q: Under the effective interest method, what is the interest expense for the period ending 30 June 2020, given a carrying amount of $676,288 at the start of that period and a market rate of 7% per period?
A: $676,288 x 7% = $47,340.
Q: How does the discount amortisation change over time under the effective interest method, and why?
A: It increases each period. Because the carrying amount grows (as prior amortisation is added), the effective interest (carrying amount x market rate) grows too, while cash interest stays fixed. The widening gap between effective interest and cash interest is the increasing amortisation.
Q: A bond with face value $700,000 has a carrying amount of $676,288 on 1 January 2020. The company retires the bond by paying $685,000. What is the loss on early extinguishment?
A: $685,000 minus $676,288 = $8,712.
Q: In the early extinguishment journal entry under the effective interest method, why is Discount on Bonds Payable credited for $23,712?
A: Because $23,712 is the unamortised discount remaining at retirement ($33,367 original discount minus $4,664 minus $4,991 of amortisation through two periods). The entry removes the entire Bonds Payable and its related Discount from the books.
Q: If you used the straight-line method instead, would the loss on early extinguishment be the same?
A: No. The straight-line method produces a different carrying amount at the same date ($677,755 vs. $676,288), so the loss differs: $685,000 minus $677,755 = $7,245 under straight-line, versus $8,712 under effective interest.
This material builds directly on bond valuation and issuance at a discount (companion notes). It also connects to the broader topic of long-term liabilities on the balance sheet, and to income statement presentation (interest expense, gains and losses on extinguishment). Understanding these amortisation mechanics is essential for later topics such as bond premiums (the mirror image of discounts) and more complex debt instruments like convertible bonds.
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