Source: Bonds Examples, Journal Entries, Amortization Schedules & Calculations
Tags: bonds, bond pricing, discount bonds, effective interest method, straight-line amortization, journal entries, amortization schedule, bond redemption, carrying value, present value
Difficulty: Intermediate | Prerequisites: Time value of money (present value of lump sums and annuities), basic journal entry mechanics, understanding of debits and credits.
Bonds sit at the centre of long-term liability accounting and show up repeatedly in Intermediate Accounting II. The core idea: a bond's price is not its face value. It is the present value of its future cash flows, discounted at the market rate. When the coupon rate differs from the market rate, the bond sells at a premium or a discount, and the issuer must amortise that difference over the bond's life. If you are comfortable with present-value arithmetic and T-accounts, you have the tools you need. If those feel shaky, revisit Chapter 6 (time value of money) before going further.
A bond's issue price equals the present value of its interest payments plus the present value of the face amount returned at maturity, both discounted at the market (yield) rate. When the market rate exceeds the coupon rate, the bond sells below face value (at a discount), and the discount is amortised upward each period so the carrying value reaches face value by maturity. Two amortisation methods exist: the effective interest method (GAAP-preferred, interest expense = carrying value × market rate) and the straight-line method (equal amortisation each period).
Face value (par value / maturity value)
The amount printed on the bond certificate that the issuer promises to repay at maturity. In simple terms, this is the principal the bondholder gets back at the end.
Coupon rate (stated rate / nominal rate)
The interest rate stated on the bond, applied to face value to calculate the periodic cash interest payment. Think of it as the rate the bond "promises" to pay, regardless of what the market demands.
Market rate (yield rate / effective rate)
The rate of return investors require for bonds of similar risk and maturity. This is the discount rate used to price the bond. When it differs from the coupon rate, the bond sells at a premium or discount.
Discount on bonds payable
A contra-liability account that arises when a bond is issued below face value (market rate > coupon rate). It represents the extra interest cost the issuer will bear over the bond's life. In simple terms, the issuer received less cash than it must repay, and the discount captures that gap.
Carrying value (carrying amount / book value of bond)
Face value minus unamortised discount (or plus unamortised premium). This is the net liability on the balance sheet at any point in time. It moves toward face value as the discount or premium is amortised.
Effective interest method
The GAAP-preferred amortisation method. Interest expense each period equals the carrying value at the start of the period multiplied by the market rate. The difference between interest expense and the cash interest payment is the amortisation of the discount or premium.
Straight-line method
An alternative (simpler) amortisation method that spreads the total discount or premium evenly across all interest periods. Acceptable under GAAP only when results are not materially different from the effective interest method.
Early extinguishment (redemption / calling a bond)
Retiring a bond before its scheduled maturity, typically by paying a call price. Any difference between the call price and the carrying value at the redemption date produces a gain or loss on redemption.
The price of a bond is always the present value of its two future cash flow streams, both discounted at the market rate per period:
PV of the interest annuity: periodic cash interest payment × PV ordinary annuity factor
PV of the face value: face value × PV single-sum factor
Bond price = PV of interest annuity + PV of face value
Worked example (discount bond):
Face value = $700,000. Coupon rate = 12% annually, paid semiannually. Market rate = 14% annually. Maturity = 3 years.
Because interest is semiannual, convert everything to per-period terms:
Cash interest per period = $700,000 × 6% = $42,000
Market rate per period = 14% / 2 = 7%
Number of periods = 3 × 2 = 6
PV of interest payments = $42,000 × PV annuity factor (7%, 6 periods) = $42,000 × 4.76654 = $200,195
PV of face value = $700,000 × PV factor (7%, 6 periods) = $700,000 × 0.66634 = $466,438
Bond issue price = $200,195 + $466,438 = $666,633
The bond sells for $666,633 against a face value of $700,000, so there is a discount of $33,367. The market rate (14%) exceeds the coupon rate (12%), so investors pay less than face value to bring the effective yield up to 14%.
At issuance, debit Cash for the proceeds, debit Discount on Bonds Payable for the difference, and credit Bonds Payable for the face amount:
Dr. Cash: $666,633
Dr. Discount on Bonds Payable: $33,367
Cr. Bonds Payable: $700,000
The discount is a contra-liability. On the balance sheet, Bonds Payable of $700,000 less Discount of $33,367 gives a net carrying value of $666,633.
Under the effective interest method, each period's interest expense = beginning carrying value × market rate per period (7%). The difference between interest expense and the $42,000 cash payment is the discount amortisation, which increases the carrying value.
Period | Carrying Value (start) | Interest Expense (CV × 7%) | Cash Paid | Discount Amortised | Carrying Value (end) |
|---|---|---|---|---|---|
1 | $666,633 | $46,664 | $42,000 | $4,664 | $671,297 |
2 | $671,297 | $46,991 | $42,000 | $4,991 | $676,288 |
3 | $676,288 | $47,340 | $42,000 | $5,340 | $681,628 |
4 | $681,628 | $47,714 | $42,000 | $5,714 | $687,342 |
5 | $687,342 | $48,114 | $42,000 | $6,114 | $693,456 |
6 | $693,456 | $48,544* | $42,000 | $6,544 | $700,000 |
*Period 6 is adjusted so the carrying value reaches exactly $700,000 at maturity.
Notice that interest expense increases each period. This is the hallmark of the effective interest method for a discount bond: as the carrying value rises, a larger base is multiplied by the same 7% rate.
Total interest expense over 6 periods = $285,367, which equals total cash interest paid ($252,000) plus the total discount amortised ($33,367).
Under the straight-line method, the total discount ($33,367) is divided equally across all 6 periods:
Discount amortised per period = $33,367 / 6 = $5,561 (with rounding adjustment in the final period)
Interest expense per period = cash interest + discount amortisation = $42,000 + $5,561 = $47,561
Period | Carrying Value (start) | Interest Expense | Cash Paid | Discount Amortised | Carrying Value (end) |
|---|---|---|---|---|---|
1 | $666,633 | $47,561 | $42,000 | $5,561 | $672,194 |
2 | $672,194 | $47,561 | $42,000 | $5,561 | $677,755 |
3 | $677,755 | $47,561 | $42,000 | $5,561 | $683,316 |
4 | $683,316 | $47,561 | $42,000 | $5,561 | $688,877 |
5 | $688,877 | $47,561 | $42,000 | $5,561 | $694,438 |
6 | $694,438 | $47,562* | $42,000 | $5,562 | $700,000 |
*Adjusted for rounding so the carrying value reaches $700,000.
Notice that interest expense is constant each period. This is simpler but does not reflect the economic reality as precisely as the effective interest method.
Two interest payments occur in 2019 (June 30 and December 31). The entries differ by method.
Effective interest method, June 30, 2019 (Period 1):
Dr. Interest Expense: $46,664
Cr. Discount on Bonds Payable: $4,664
Cr. Cash: $42,000
Effective interest method, December 31, 2019 (Period 2):
Dr. Interest Expense: $46,991
Cr. Discount on Bonds Payable: $4,991
Cr. Cash: $42,000
Straight-line method, June 30, 2019 (Period 1):
Dr. Interest Expense: $47,561
Cr. Discount on Bonds Payable: $5,561
Cr. Cash: $42,000
Straight-line method, December 31, 2019 (Period 2):
The entry is identical to Period 1 under straight-line, because the amortisation is the same each period.
Masterwear calls the bonds on January 1, 2020, at a call price of $685,000. By this date, two periods of amortisation have passed (the two interest payments in 2019).
Under the effective interest method:
Carrying value after Period 2 = $676,288 (from the schedule above).
Remaining discount = $700,000 - $676,288 = $23,712.
The call price ($685,000) exceeds the carrying value ($676,288), so the issuer records a loss of $8,712.
Dr. Bonds Payable: $700,000
Dr. Loss on Bond Redemption: $8,712
Cr. Discount on Bonds Payable: $23,712
Cr. Cash: $685,000
Under the straight-line method:
Carrying value after Period 2 = $677,755 (from the straight-line schedule).
Remaining discount = $700,000 - $677,755 = $22,245.
Loss = $685,000 - $677,755 = $7,245.
Dr. Bonds Payable: $700,000
Dr. Loss on Bond Redemption: $7,245
Cr. Discount on Bonds Payable: $22,245
Cr. Cash: $685,000
Bond price:
\text{Price} = C \times \frac{1 - (1 + r)^{-n}}{r} + FV \times (1 + r)^{-n}Where C = cash interest per period, r = market rate per period, n = total number of periods, FV = face value.
Effective interest method (per period):
\text{Interest Expense} = \text{Carrying Value}_{\text{beginning}} \times r\text{Discount Amortisation} = \text{Interest Expense} - \text{Cash Interest Paid}Straight-line method (per period):
\text{Discount Amortisation} = \frac{\text{Total Discount}}{\text{Number of Periods}}\text{Interest Expense} = \text{Cash Interest Paid} + \text{Discount Amortisation}Gain or loss on early redemption:
\text{Gain (Loss)} = \text{Carrying Value at Redemption} - \text{Call Price}Positive = gain (issuer pays less than carrying value). Negative = loss (issuer pays more than carrying value).
Students often confuse the coupon rate with the market rate when calculating interest expense. The cash payment always uses the coupon rate (applied to face value). Interest expense under the effective method uses the market rate (applied to carrying value). Mixing these up will produce incorrect amortisation figures.
Students frequently forget to convert annual rates and years to semiannual figures. If interest is paid semiannually, you must halve the annual rate and double the number of years before looking up PV factors. Using annual rates with semiannual periods is one of the most common errors on exams.
A discount does not mean the issuer is losing money. It simply means the coupon rate is below the market rate, so investors demand a lower price to achieve the market yield. The discount is additional interest cost spread over the bond's life.
When recording early redemption, students sometimes compare the call price to the face value instead of the carrying value. The gain or loss is always call price versus carrying value at the date of redemption, not face value.
⚠️ Bond pricing calculations appear on nearly every Intermediate Accounting II exam. You will almost certainly be asked to compute a bond's issue price given face value, coupon rate, market rate, and maturity.
⚠️ Expect at least one question requiring you to prepare an amortisation schedule or compute interest expense for a specific period under the effective interest method.
⚠️ Early redemption journal entries are a common exam topic. Remember: the gain or loss is the difference between the carrying value and the call price, and any unamortised discount must be removed from the books.
⚠️ Know the difference between the two amortisation methods cold. The effective interest method produces increasing interest expense for discount bonds. The straight-line method produces constant interest expense. Exams often ask you to identify which method is being used from a given schedule.
Corporate treasurers use these exact calculations when deciding whether to issue bonds. If market rates have risen above the coupon rate they can offer, they know the bonds will sell at a discount and must plan for the higher effective interest cost. Conversely, when a company calls its bonds early, the gain or loss on redemption flows through the income statement, affecting reported earnings.
True or false: A bond sells at a discount when the coupon rate exceeds the market rate.
False. A bond sells at a discount when the market rate exceeds the coupon rate.
Fill in the blank: Under the effective interest method, interest expense each period equals ______ multiplied by the ______.
Beginning carrying value; market rate per period.
True or false: Under the straight-line method for a discount bond, interest expense increases each period.
False. Straight-line produces constant interest expense each period.
Fill in the blank: When a bond is redeemed early, a loss is recorded if the call price exceeds the ______.
Carrying value at the date of redemption.
True or false: Discount on Bonds Payable is a contra-liability account.
True.
Q: A company issues $500,000 of 10% bonds (interest paid semiannually) when the market rate is 12%. The bonds mature in 5 years. Will the bonds sell at a premium or a discount, and why?
A: At a discount. The market rate (12%) exceeds the coupon rate (10%), so investors will not pay full face value. They demand a lower price to achieve the 12% yield.
Q: Using the effective interest method, how do you calculate interest expense for the third period of a discount bond?
A: Multiply the carrying value at the beginning of Period 3 by the market rate per period. For a semiannual bond, use the semiannual market rate. Interest expense = CV at start of Period 3 × (market rate / 2).
Q: A bond has a face value of $700,000. After two periods of effective interest amortisation, the carrying value is $676,288. The company calls the bonds at $685,000. What is the gain or loss?
A: Loss of $8,712. The call price ($685,000) exceeds the carrying value ($676,288), so the issuer pays more than the book value of the liability. The journal entry includes a debit to Loss on Bond Redemption for $8,712.
Q: Under straight-line amortisation, a $33,367 discount is spread over 6 semiannual periods. What is the interest expense per period if the cash interest payment is $42,000?
A: Discount amortised per period = $33,367 / 6 = $5,561 (approximately). Interest expense = $42,000 + $5,561 = $47,561.
Q: Why does GAAP prefer the effective interest method over the straight-line method?
A: The effective interest method ties interest expense to the actual outstanding liability each period, reflecting the economic cost of borrowing more accurately. It produces a constant rate of interest relative to the carrying value, rather than a constant dollar amount of interest expense.
This material connects directly to premium bonds (the mirror case: coupon rate > market rate, bond sells above face value, premium is amortised downward). The mechanics are identical, only the direction reverses. It also links to installment notes, which use the same present-value annuity concepts but with equal total payments rather than equal interest-only payments.
The time value of money fundamentals from earlier chapters (PV of a lump sum, PV of an ordinary annuity) are the mathematical engine behind every calculation here. If bond pricing feels opaque, revisiting those foundations will clarify it.
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