Difficulty: Intermediate | Prerequisites: Basic journal entries, time value of money concepts, present value tables
When a company issues bonds, the coupon rate it promises rarely matches the market's required yield on that date. If the market demands more than the coupon rate, investors will only buy the bonds at a price below face value, creating a discount. This topic walks through calculating that discounted price, recording the issuance, building amortization schedules under both the effective interest and straight-line methods, journalising periodic interest, and handling early redemption. You need to be comfortable with present value arithmetic and basic debits and credits before diving in.
A bond issued at a discount sells for less than its face value because the market yield exceeds the coupon rate. The discount is amortised over the bond's life, increasing interest expense each period under the effective interest method (or keeping it flat under straight-line). At maturity, or upon early redemption, the carrying amount should equal the face value, and any difference between the redemption price and the carrying amount produces a gain or loss.
Face value (par value)
The principal amount printed on the bond, repaid at maturity. In simple terms, it is the amount the issuer promises to hand back when the bond matures.
Coupon rate (stated rate / nominal rate)
The annual interest rate the bond contract specifies. Think of it as the rate that sets the size of each cash interest payment.
Market yield (effective rate / yield to maturity)
The rate investors require given current conditions. This is the rate used to discount the bond's future cash flows and determine its price today.
Discount on bonds payable
The difference between face value and the lower issue price when the market yield exceeds the coupon rate. In simple terms, this is the "markdown" investors demand for accepting a below-market coupon.
Effective interest method
Amortisation approach that multiplies the carrying amount by the market yield each period. It produces a rising interest expense over the bond's life and is required under IFRS (and preferred under US GAAP).
Straight-line method
Amortisation approach that spreads the total discount equally across all periods. Simpler to calculate, but does not match expense to the changing carrying amount.
Carrying amount (book value / outstanding balance)
Face value minus unamortised discount. This is what the bond liability reads on the balance sheet at any given date.
Early extinguishment (redemption before maturity)
Calling or repurchasing bonds before their scheduled maturity date. The difference between the cash paid and the carrying amount is recognised as a gain or loss on the income statement.
The bond price equals the present value of two cash flow streams, both discounted at the market yield per period:
PV of the annuity of coupon payments (using the PV of ordinary annuity factor)
PV of the single lump-sum repayment at maturity (using the PV of $1 factor)
Worked example (Masterwear Industries): $700,000 face value, 12% coupon paid semiannually, 14% market yield, three-year term.
Semiannual coupon payment = $700,000 x 6% = $42,000
Market rate per period = 14% / 2 = 7%, with n = 6 periods
PV of interest payments = $42,000 x PVA(6, 7%) = $42,000 x 4.76654 = $200,195
PV of principal = $700,000 x PV(6, 7%) = $700,000 x 0.66634 = $466,438
Bond price = $200,195 + $466,438 = $666,633
Discount = $700,000 – $666,633 = $33,367
At issuance on 1 January 2019:
Debit Cash $666,633
Debit Discount on Bonds Payable $33,367
Credit Bonds Payable $700,000
The Bonds Payable account always carries the face value. The contra-liability account (Discount on Bonds Payable) reduces it to the carrying amount on the balance sheet.
Each period, interest expense = carrying amount at start of period x market rate per period. The difference between this and the cash coupon is the discount amortised.
Date | Cash Interest | Effective Interest | Discount Amortised | Carrying Amount |
|---|---|---|---|---|
1/1/2019 | $666,633 | |||
6/30/2019 | $42,000 | $46,664 | $4,664 | $671,297 |
12/31/2019 | $42,000 | $46,991 | $4,991 | $676,288 |
6/30/2020 | $42,000 | $47,340 | $5,340 | $681,628 |
12/31/2020 | $42,000 | $47,714 | $5,714 | $687,342 |
6/30/2021 | $42,000 | $48,114 | $6,114 | $693,456 |
12/31/2021 | $42,000 | $48,544 | $6,544 | $700,000 |
Notice that effective interest expense rises each period because the carrying amount grows as discount is amortised.
Total discount / number of periods = $33,367 / 6 = $5,561 per period (rounded). Interest expense each period = $42,000 + $5,561 = $47,561.
Date | Cash Interest | Straight-Line Interest | Discount Amortised | Carrying Amount |
|---|---|---|---|---|
1/1/2019 | $666,633 | |||
6/30/2019 | $42,000 | $47,561 | $5,561 | $672,194 |
12/31/2019 | $42,000 | $47,561 | $5,561 | $677,755 |
6/30/2020 | $42,000 | $47,561 | $5,561 | $683,316 |
12/31/2020 | $42,000 | $47,561 | $5,561 | $688,877 |
6/30/2021 | $42,000 | $47,561 | $5,561 | $694,438 |
12/31/2021 | $42,000 | $47,562 | $5,562 | $700,000 |
The interest expense is the same every period. Simpler, but less precise.
Effective interest method, 6/30/2019:
Debit Interest Expense $46,664
Credit Cash $42,000
Credit Discount on Bonds Payable $4,664
Effective interest method, 12/31/2019:
Debit Interest Expense $46,991
Credit Cash $42,000
Credit Discount on Bonds Payable $4,991
Straight-line method (both dates identical):
Debit Interest Expense $47,561
Credit Cash $42,000
Credit Discount on Bonds Payable $5,561
If Masterwear redeems the bonds after two interest payments (carrying amount = $676,288 under effective method), paying $685,000 cash:
Remaining discount = $700,000 – $676,288 = $23,712
Loss = Cash paid – Carrying amount = $685,000 – $676,288 = $8,712
Journal entry (effective interest method):
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 the remaining discount differs ($22,245), so the loss changes to $7,245. The structure of the entry is the same.
\text{Bond Price} = C \times \text{PVA}(n, r) + F \times \text{PV}(n, r)Where C = coupon payment per period, F = face value, n = total number of periods, r = market rate per period.
\text{Effective Interest Expense} = \text{Carrying Amount}_{\text{beg}} \times r\text{Discount Amortised} = \text{Effective Interest Expense} - \text{Cash Interest Paid}\text{Straight-Line Amortisation per period} = \frac{\text{Total Discount}}{\text{Number of Periods}}\text{Gain or Loss on Redemption} = \text{Cash Paid} - \text{Carrying Amount at Redemption Date}A positive result is a loss; a negative result is a gain.
Corporations issue bonds at a discount whenever market interest rates sit above the coupon rate they are willing to print. This happens routinely when rates rise between the time a bond is structured and the time it reaches the market. The amortisation schedules you build here are the same ones corporate treasurers and auditors use to track interest expense on their financial statements each quarter.
Students often think the coupon rate is the rate used to discount the bond's cash flows. It is not. The market yield is the discount rate; the coupon rate only determines the size of each cash interest payment.
Students sometimes believe the discount is an expense at issuance. The discount is not expensed in one lump sum; it is amortised over the bond's life and added to interest expense each period.
A common error is using the annual market rate directly when interest is paid semiannually. You must halve the annual rate and double the number of years to get the correct per-period rate and number of periods.
Students sometimes confuse the carrying amount with the cash paid at maturity. The carrying amount converges to face value over time through amortisation, but cash paid at maturity is always the face value (unless redeemed early at a call price).
Expect to be asked to calculate the bond issue price from a given face value, coupon rate, market yield, and term. This is a near-certainty on intermediate accounting exams.
You will likely need to prepare a full effective interest amortization schedule and show the journal entries for at least two interest dates.
Early extinguishment problems test whether you can compute the remaining unamortized discount and determine the gain or loss. Watch for questions that give you a redemption price as a percentage of par (e.g. 102% of face value).
Know the difference between the effective interest method and the straight-line method, and be ready to explain why IFRS requires the effective interest method.
True or false: When the market yield exceeds the coupon rate, a bond sells at a premium.
False. It sells at a discount.
Fill in the blank: Under the effective interest method, interest expense each period = ______ x market rate per period.
Carrying amount at the beginning of the period.
True or false: Straight-line amortisation produces the same total interest expense over the bond's life as the effective interest method.
True. The total is the same; only the period-by-period allocation differs.
Fill in the blank: The contra-liability account that reduces Bonds Payable to the carrying amount is called ______.
Discount on Bonds Payable.
True or false: A loss on early extinguishment means the company paid more cash than the bond's carrying amount.
True.
Q: A company issues $500,000 of 10% bonds (semiannual payments) when the market yield is 12%. The bonds mature in 5 years. What two present value calculations do you need to find the bond price?
A: You need the PV of the ordinary annuity of $25,000 coupon payments at 6% for 10 periods, and the PV of the $500,000 face value at 6% for 10 periods. Sum the two to get the bond price.
Q: In the first period of an effective interest amortisation schedule, a bond has a carrying amount of $666,633 and a market rate per period of 7%. The cash coupon is $42,000. What is the interest expense, and how much discount is amortised?
A: Interest expense = $666,633 x 7% = $46,664. Discount amortised = $46,664 – $42,000 = $4,664.
Q: Why does interest expense increase each period under the effective interest method for a discount bond?
A: Because the carrying amount grows as discount is amortised, and interest expense is always carrying amount x market rate. A larger carrying amount produces a larger expense.
Q: A bond with a face value of $700,000 has a carrying amount of $676,288 and is redeemed for $685,000. What is the gain or loss?
A: Loss = $685,000 – $676,288 = $8,712. It is a loss because the company paid more than the book value.
Q: Under the straight-line method, how do you calculate the discount amortised per period?
A: Total discount / total number of interest periods. For a $33,367 discount over 6 periods, that is $33,367 / 6 = $5,561 per period (rounded).
This connects directly to bond issuance at a premium, which is the mirror image: the coupon rate exceeds the market yield, so investors pay more than face value. The same present value tools, journal entry logic, and amortisation methods apply, just with the numbers moving in the opposite direction.
Installment notes use the same present value of annuity arithmetic to calculate periodic payments, and their amortisation schedules follow an identical effective-interest structure.
Early extinguishment ties into the broader topic of gains and losses on the income statement and how they differ from operating income.
Bond discount, discount bonds, bonds issued below par, effective interest rate method, straight-line amortization, bond amortization schedule, discount on bonds payable, contra-liability, carrying amount, book value of bonds, bond pricing, present value of annuity, PVA factor, early extinguishment of debt, loss on early extinguishment, bond redemption, call price, market yield, yield to maturity, stated rate vs market rate, coupon rate, semiannual interest, intermediate financial accounting, bonds payable journal entries