CFA Level I Exam · Topics in Long-Term Liabilities and Equity

Bond Issuance and Accounting for Bonds

Q: Why is a bond issued at a discount when the market rate is higher than the coupon rate?

Investors demand the market yield. If the coupon is lower than that yield, they pay less than face value so that their return rises to the market rate. The lower price is the present value of the fixed cash flows at the higher rate.

Q: What is the difference between the effective interest rate method and straight-line amortization?

The effective interest rate method sets interest expense as a constant percentage of the opening carrying amount, so the expense changes each period. Straight-line spreads the discount or premium equally. IFRS requires the effective interest rate method for liabilities at amortized cost.

Q: Does the carrying amount of a bond ever reach face value?

Yes, for a bond held to maturity. Discount amortization raises the carrying amount, and premium amortization lowers it, until it equals face value at maturity. Then the principal repayment extinguishes the liability.

Q: How are bond issuance costs treated under IFRS?

They are deducted from the initial fair value, so the liability starts lower. This increases the effective interest rate, which you must use for interest expense. The costs are therefore spread over the bond's life through interest expense.

Updated 7 October 2026 · Fact-checked

A bond is recorded at its issue price, the present value of its cash flows at the market rate. It is issued at par, at a discount or at a premium depending on market rate versus coupon rate. Each period, interest expense equals opening carrying amount times the market rate. The carrying amount then moves toward face value.

Understand Bond Issuance and Accounting for Bonds

A company that issues a bond promises two things: periodic coupons and the face value at maturity. The coupon rate is fixed in the contract. The market rate (the yield investors demand) moves with conditions. The issue price is the present value of those promised cash flows discounted at the market rate.

Three cases follow. If the market rate equals the coupon rate, the bond is issued at par. If the market rate is higher than the coupon rate, investors pay less than face value, so the bond sells at a discount. If the market rate is lower than the coupon rate, investors pay more than face value, so the bond sells at a premium.

Under IFRS, a bond liability is normally measured at amortized cost. It starts at fair value at issuance, less directly attributable transaction costs. After that, the effective interest rate method applies. Interest expense each period = opening carrying amount × the effective (market) rate at issuance. The cash coupon = face value × coupon rate. The difference between the two is the amortization of the discount or premium.

For a discount bond, interest expense is greater than the coupon. The shortfall is added to the carrying amount, so the liability rises toward face value. For a premium bond, interest expense is less than the coupon. The excess coupon reduces the carrying amount, so the liability falls toward face value. At maturity the carrying amount equals face value in both cases.

The cash received at issuance is a financing inflow. Repayment of principal is a financing outflow under both IFRS and US GAAP. Under US GAAP, interest paid is an operating cash flow. Under IFRS, interest paid may be classified as either operating or financing. The issue price is not income. The discount or premium only changes how total interest expense is spread over the bond's life.

Key formulas to remember

Issue price: Price = Σ [Coupon ÷ (1 + r)^t] + Face value ÷ (1 + r)^n; r is the market rate per period at issuance. Coupon = face value × coupon rate per period.
Interest expense (effective interest method): Interest expense = Opening carrying amount × market rate per period; The market rate is the one set at issuance. It does not change over the life of a fixed-rate bond.
Cash coupon: Coupon paid = Face value × coupon rate per period; Fixed by the contract. It does not depend on the issue price.
Amortization: Discount: amortization = interest expense − coupon. Premium: amortization = coupon − interest expense; Discount amortization increases the carrying amount. Premium amortization decreases it.
Ending carrying amount: Discount: ending = opening + amortization. Premium: ending = opening − amortization; Equivalent: ending = opening + interest expense − coupon paid.
Total interest expense over the life: Total interest expense = total coupons + discount (or − premium); Equivalently: total cash repaid (coupons + face value) − cash received at issuance.
Gain or loss on early extinguishment: Gain (loss) = Carrying amount − Repurchase price; A positive result is a gain. Repurchase price above carrying amount is a loss.
Par, discount, premium rule: Market rate = coupon rate: par. Market rate > coupon rate: discount. Market rate < coupon rate: premium; Compare the rates on the same periodic basis.

How to solve Bond Issuance and Accounting for Bonds questions

Use this sequence for any question on bond issuance, amortization or reporting.

1Identify the face value, coupon rate, payment frequency, term and market rate at issuance. Convert rates and periods to the payment frequency (for semiannual: halve the rates, double the periods).
2Compare the market rate with the coupon rate to decide whether the bond is at par, a discount or a premium. Do this before any calculation.
3Compute the issue price as the present value of coupons plus the present value of face value at the market rate. Use N, I/Y, PMT and FV on your calculator.
4Compute period 1 interest expense = issue price × market rate. Compute the cash coupon = face value × coupon rate.
5Find amortization as the difference between interest expense and coupon. Update the carrying amount: add it for a discount, subtract it for a premium.
6Repeat for later periods using the new opening carrying amount. Check that the final carrying amount equals face value.
7Read the question for what is asked: carrying amount, interest expense, cash flow classification or gain or loss on repurchase. Then eliminate the options that fail the direction check.

Quickest way: Direction check, then one period

When to use it: Use this when the question asks for one period's interest expense or the carrying amount after one period, and the issue price is given or easy to compute.

Discount (market rate above coupon rate): interest expense is greater than the coupon, and the carrying amount rises. Premium: interest expense is less than the coupon, and the carrying amount falls.
Opening carrying amount × market rate gives interest expense directly. Do not use face value.
Carrying amount after the period = opening + interest expense − coupon paid.
Use the direction check to remove two of the three options. Compute only if both remaining options are close.
If the issue price is not given, compute it once with the calculator (N, I/Y, PMT, FV, CPT PV). Ignore the negative sign.

Common mistakes in Bond Issuance and Accounting for Bonds

Calculating interest expense as face value × market rate.
The coupon is calculated on face value, so students apply the same base to the market rate.
Fix: Interest expense uses the opening carrying amount. Coupon uses face value. Keep the two bases separate.
Using the coupon rate to discount the cash flows.
The coupon rate is the number printed on the bond, so it looks like the rate to use.
Fix: Always discount at the market rate at issuance. Discounting at the coupon rate always gives par.
Moving the carrying amount in the wrong direction.
Students mix up discount and premium behavior.
Fix: Both converge to face value. Discount: starts below face and rises. Premium: starts above face and falls.
Forgetting to halve the rates and double the periods for semiannual bonds.
Annual figures are quoted in the stem, and students rush into the calculator.
Fix: Write periods and rate per period first. A 10-year semiannual bond has N = 20 and the rate is half the annual rate.
Treating the discount or premium as a gain, loss or separate asset.
Students think cash received below face value means a loss at issuance.
Fix: Under IFRS the liability is initially recognised at fair value net of transaction costs, then carried at amortized cost. The discount or premium adjusts interest expense over time. Nothing hits income at issuance.
Ignoring issuance costs.
Costs look like a separate expense to be taken immediately.
Fix: Under IFRS, costs reduce the initial carrying amount of the liability. This raises the effective interest rate. The costs are then spread through interest expense.

Worked examples

Example 1

A company issues a 3-year bond with face value $1,000,000 and a 5% annual coupon when the market rate is 6%. Under the effective interest rate method, what is interest expense in Year 1? A. $50,000 B. $58,396 C. $60,000

Show the solution

The market rate (6%) is higher than the coupon rate (5%), so the bond is issued at a discount. Interest expense must be greater than the $50,000 coupon.
Compute the issue price. Calculator: N = 3, I/Y = 6, PMT = 50,000, FV = 1,000,000, CPT PV = −973,270 (about). The price is $973,270.
Check by hand: PV of coupons = 50,000 × 2.673012 = 133,651. PV of face = 1,000,000 ÷ 1.06³ = 839,619. Sum = 973,270.
Year 1 interest expense = 973,270 × 6% = 58,396.
Check: amortization = 58,396 − 50,000 = 8,396. The Year 1 ending carrying amount is about 981,666, still below face value.

Answer: B. Year 1 interest expense is about $58,396. Option A is the coupon, and option C is face value × 6%.

Example 2

A company issues a 2-year bond with face value €1,000,000 and a 6% annual coupon when the market rate is 5%. What is interest expense in Year 2? A. €50,476 B. €50,930 C. €60,000

Show the solution

The market rate (5%) is below the coupon rate (6%), so the bond is issued at a premium. Interest expense is less than the €60,000 coupon, and the carrying amount falls.
Issue price: N = 2, I/Y = 5, PMT = 60,000, FV = 1,000,000, CPT PV = −1,018,594 (about).
Year 1 interest expense = 1,018,594 × 5% = 50,930. Coupon = 60,000.
Premium amortization in Year 1 = 60,000 − 50,930 = 9,070. Carrying amount at end of Year 1 = 1,018,594 − 9,070 = 1,009,524.
Year 2 interest expense = 1,009,524 × 5% = 50,476.
Check: Year 2 amortization = 60,000 − 50,476 = 9,524. Carrying amount = 1,009,524 − 9,524 = 1,000,000 = face value.

Answer: A. Year 2 interest expense is about €50,476. Option B is the Year 1 figure, and option C is the coupon.

Exam tips

Do the direction check first. Many questions can be answered by noting that a discount bond has interest expense above the coupon, and a premium bond below it.
Watch the base. Questions often put face value and carrying amount side by side to tempt you into the wrong base.
Read the periods carefully. A semiannual bond needs half the rate and double the periods, and each coupon is half the annual coupon.
Expect conceptual items too. Typical points: discount carrying amount rises, premium carrying amount falls, principal repayment is financing, and total interest expense equals total cash repaid minus cash received.
Remember that IFRS requires amortized cost with the effective interest method for most issued bonds. Items state US GAAP when it matters.

Practice questions from Topics in Long-Term Liabilities and Equity