Difficulty: Intermediate | Prerequisites: Bond issuance at discount notes, time value of money, present value tables
This is the mirror image of a discount issuance. When the coupon rate on a bond exceeds the market yield at issue date, investors are willing to pay more than face value to lock in the higher-than-market coupon. The difference is a premium, recorded in a separate adjunct-liability account. The premium is then amortised over the bond's life, reducing interest expense each period. If you have already worked through bond issuance at a discount, the mechanics here are nearly identical, just with the direction reversed.
A bond issued at a premium sells for more than face value because its coupon rate exceeds the market yield. The premium is amortised over the bond's life, reducing interest expense below the cash coupon paid. Under the effective interest method, interest expense decreases each period; under straight-line, it stays flat.
Premium on bonds payable
The amount by which the issue price exceeds the face value. In simple terms, it is the extra money investors pay for a coupon that beats the going market rate. It is an adjunct liability, added to Bonds Payable on the balance sheet.
Adjunct liability account
The opposite of a contra-liability. Instead of reducing the face value (as a discount does), the premium account increases it to the carrying amount.
Carrying amount (premium bond)
Face value plus unamortised premium. This figure declines toward face value as the premium is amortised each period.
Gain on early extinguishment
When a premium bond is redeemed before maturity for less than its carrying amount, the issuer records a gain. This is the reverse of the loss you see with discount bonds redeemed above carrying amount.
Same two-step present value calculation as discount bonds, but now the market yield is lower than the coupon rate, so the price comes out above face value.
Worked example (Masterwear Industries): $700,000 face value, 12% coupon paid semiannually, 10% market yield, three-year term.
Semiannual coupon = $700,000 x 6% = $42,000
Market rate per period = 10% / 2 = 5%, with n = 6 periods
PV of interest payments = $42,000 x PVA(6, 5%) = $42,000 x 5.07569 = $213,179
PV of principal = $700,000 x PV(6, 5%) = $700,000 x 0.74622 = $522,354
Bond price = $213,179 + $522,354 = $735,533
Premium = $735,533 – $700,000 = $35,533
At issuance on 1 January 2019:
Debit Cash $735,533
Credit Premium on Bonds Payable $35,533
Credit Bonds Payable $700,000
Bonds Payable still carries face value. The Premium account sits alongside it and adds to the carrying amount.
Each period, interest expense = carrying amount at start of period x market rate per period. The difference between the cash coupon and this lower expense is the premium amortised.
Date | Cash Interest | Effective Interest | Premium Amortised | Carrying Amount |
|---|---|---|---|---|
1/1/2019 | $735,533 | |||
6/30/2019 | $42,000 | $36,777 | $5,223 | $730,310 |
12/31/2019 | $42,000 | $36,515 | $5,485 | $724,825 |
6/30/2020 | $42,000 | $36,241 | $5,759 | $719,066 |
12/31/2020 | $42,000 | $35,953 | $6,047 | $713,019 |
6/30/2021 | $42,000 | $35,651 | $6,349 | $706,670 |
12/31/2021 | $42,000 | $35,330 | $6,670 | $700,000 |
Notice that interest expense falls each period because the carrying amount declines as premium is amortised.
Total premium / number of periods = $35,533 / 6 = $5,922 per period (rounded). Interest expense each period = $42,000 – $5,922 = $36,078.
Date | Cash Interest | Straight-Line Interest | Premium Amortised | Carrying Amount |
|---|---|---|---|---|
1/1/2019 | $735,533 | |||
6/30/2019 | $42,000 | $36,078 | $5,922 | $729,611 |
12/31/2019 | $42,000 | $36,078 | $5,922 | $723,689 |
6/30/2020 | $42,000 | $36,078 | $5,922 | $717,767 |
12/31/2020 | $42,000 | $36,078 | $5,922 | $711,845 |
6/30/2021 | $42,000 | $36,078 | $5,922 | $705,923 |
12/31/2021 | $42,000 | $36,078 | $5,922 | $700,001 |
Effective interest method, 6/30/2019:
Debit Interest Expense $36,777
Credit Premium on Bonds Payable $5,223
Credit Cash $42,000
Effective interest method, 12/31/2019:
Debit Interest Expense $36,515
Credit Premium on Bonds Payable $5,485
Credit Cash $42,000
Straight-line method (both dates identical):
Debit Interest Expense $36,078
Credit Premium on Bonds Payable $5,922
Credit Cash $42,000
Key difference from a discount bond: the premium amortisation is debited (reducing the premium account), and interest expense is less than the cash paid.
If Masterwear redeems after two interest payments (carrying amount = $724,825 under effective method), paying $720,000 cash:
Remaining premium = $724,825 – $700,000 = $24,825
Gain = Carrying amount – Cash paid = $724,825 – $720,000 = $4,825
Journal entry (effective interest method):
Debit Bonds Payable $700,000
Debit Premium on Bonds Payable $24,825
Credit Gain on Early Extinguishment $4,825
Credit Cash $720,000
Under the straight-line method the remaining premium is $23,689, producing a gain of $3,689.
The bond pricing formula is the same as for discount bonds:
\text{Bond Price} = C \times \text{PVA}(n, r) + F \times \text{PV}(n, r)For premium bonds, the result exceeds F.
\text{Premium Amortised} = \text{Cash Interest Paid} - \text{Effective Interest Expense}Note this is reversed from the discount formula. Cash paid exceeds the expense, and the difference reduces the premium.
\text{Straight-Line Premium Amortisation per period} = \frac{\text{Total Premium}}{\text{Number of Periods}}\text{Gain or Loss on Redemption} = \text{Carrying Amount} - \text{Cash Paid}Positive result = gain; negative = loss.
Companies sometimes issue bonds at a premium deliberately by setting a high coupon rate to attract investors looking for current income. The premium they collect lowers the effective cost of borrowing. Municipal bond issuers frequently structure bonds at a premium to increase the initial cash proceeds while staying within legal borrowing limits tied to face value.
Students often think interest expense on a premium bond is higher than the cash coupon paid. The opposite is true: interest expense is lower because the premium amortisation offsets part of the cash payment.
A frequent error is debiting the Premium account when recording the issuance. The Premium on Bonds Payable is credited at issuance (it is an adjunct liability, not a contra account).
Students sometimes forget that the carrying amount of a premium bond decreases over time toward face value, whereas a discount bond's carrying amount increases. Mixing these up reverses the amortisation direction.
When computing a gain on early redemption, students sometimes subtract in the wrong direction. For a premium bond redeemed below carrying amount, the gain = carrying amount minus cash paid, not the other way round.
Exams frequently pair a discount and a premium problem side by side. Be ready to work both in one sitting.
You may be asked to explain why interest expense declines under the effective interest method for a premium bond. The answer traces back to the declining carrying amount.
Watch for redemption problems where the call price is stated as a percentage of face value. A call price of 103% on a $700,000 bond = $721,000 cash paid.
Know the journal entry differences between premium and discount bonds cold: which accounts are debited and credited, and whether the amortisation credits or debits the premium/discount account.
True or false: A bond sells at a premium when the market yield is higher than the coupon rate.
False. It sells at a premium when the coupon rate exceeds the market yield.
Fill in the blank: For a premium bond under the effective interest method, interest expense each period = ______ x market rate per period.
Carrying amount at the beginning of the period (same formula as discount bonds).
True or false: Premium amortisation increases the carrying amount over time.
False. It decreases the carrying amount toward face value.
Fill in the blank: When a premium bond is redeemed for less than its carrying amount, the issuer records a ______.
Gain on early extinguishment.
True or false: Under the straight-line method, interest expense on a premium bond is the cash coupon minus the per-period premium amortisation.
True.
Q: A company issues $700,000 of 12% bonds (semiannual payments) when the market yield is 10%. The bonds mature in 3 years. What is the bond price?
A: Semiannual coupon = $42,000, market rate per period = 5%, n = 6. PV of interest = $42,000 x 5.07569 = $213,179. PV of principal = $700,000 x 0.74622 = $522,354. Bond price = $735,533.
Q: In the first period, a premium bond has a carrying amount of $735,533 and a market rate per period of 5%. Cash coupon is $42,000. What is the interest expense, and how much premium is amortised?
A: Interest expense = $735,533 x 5% = $36,777 (rounded). Premium amortised = $42,000 – $36,777 = $5,223.
Q: Why does interest expense decrease each period under the effective interest method for a premium bond?
A: Because the carrying amount falls as premium is amortised, and interest expense is carrying amount x market rate. A smaller carrying amount produces a smaller expense.
Q: A premium bond with face value $700,000 has a carrying amount of $724,825 and is redeemed for $720,000. What is the gain or loss?
A: Gain = $724,825 – $720,000 = $4,825. It is a gain because the company paid less than the book value.
Q: How does the journal entry for interest on a premium bond differ from a discount bond?
A: For a premium bond, Interest Expense is debited for less than the cash paid, Premium on Bonds Payable is debited (reducing the premium), and Cash is credited for the full coupon. For a discount bond, Interest Expense is debited for more than the cash paid, Cash is credited, and Discount on Bonds Payable is credited (reducing the discount).
This pairs directly with bond issuance at a discount. The two topics share the same pricing formula, journal entry structure, and amortisation methods; only the direction of the premium or discount differs. Working both together cements the pattern.
The early extinguishment section connects to the broader topic of how gains and losses from debt retirement appear on the income statement and how they differ from operating items.
Installment notes share the same present value of annuity mechanics and amortisation schedule logic.
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