Bond Discounts, Premiums, and Effective Interest Amortization

FAR treatment for debt carrying value, discount and premium amortization, effective interest expense, and early extinguishment.

Bond accounting in FAR is a carrying-value problem. The issuer receives proceeds, records a liability, recognizes interest expense over time, and eventually settles the debt. The exam usually tests whether the candidate can separate face amount, cash interest, market yield, unamortized discount or premium, debt issuance costs, and gain or loss on retirement.

The core idea is simple: the carrying amount moves toward the face amount by maturity. A discount increases over time toward face value. A premium decreases over time toward face value. The effective interest method explains why that movement is not arbitrary.

Issuance Price and Carrying Amount

A bond’s face amount is the principal due at maturity. The stated rate, or coupon rate, determines the cash interest paid. The market yield at issuance determines the price investors are willing to pay. When the stated rate and market yield differ, the bond is issued at a discount or premium.

Relationship at issuance Issue price Initial carrying amount Later carrying amount pattern
Stated rate equals market yield Face amount Face amount Usually stays near face amount
Stated rate is less than market yield Below face amount Discounted amount Increases toward face amount
Stated rate is greater than market yield Above face amount Premium amount Decreases toward face amount

Debt issuance costs related to a recognized debt liability are generally presented as a direct deduction from the carrying amount of the debt, consistent with the presentation of a debt discount. They are not a separate asset for ordinary balance sheet presentation. Their amortization is reported as interest expense.

    flowchart TD
	    A["Compare stated rate with market yield"] --> B{"Which rate is higher?"}
	    B -- "Stated rate lower" --> C["Issue at discount"]
	    B -- "Stated rate higher" --> D["Issue at premium"]
	    B -- "Rates equal" --> E["Issue near face amount"]
	    C --> F["Carrying amount accretes upward"]
	    D --> G["Carrying amount amortizes downward"]
	    E --> H["Carrying amount remains close to face"]

Effective Interest Method

The effective interest method recognizes interest expense at a constant effective yield on the beginning carrying amount of the debt. The method keeps the accounting aligned with the economic borrowing rate at issuance.

[ \text{Interest Expense} = \text{Beginning Carrying Amount} \times \text{Market Yield per Period} ]

[ \text{Cash Interest Paid} = \text{Face Amount} \times \text{Stated Rate per Period} ]

The difference between interest expense and cash interest is the discount or premium amortization.

Bond type Interest expense compared with cash interest Carrying amount effect
Discount bond Interest expense is greater than cash interest Discount amortization increases carrying amount
Premium bond Interest expense is less than cash interest Premium amortization decreases carrying amount
Par bond Interest expense usually equals cash interest Carrying amount remains near face amount

FAR questions often give annual rates but semiannual payments. In that case, divide the annual stated rate and annual market yield by two, and use the number of semiannual periods. Do not apply an annual rate to a six-month carrying amount unless the question explicitly uses annual periods.

Discount Example

Assume a company issues 5-year bonds with a face amount of $100,000, a stated annual rate of 6 percent, and annual interest payments. The market yield at issuance is 7 percent, so the bonds are issued at $95,842. The discount is $4,158.

Year 1 under the effective interest method:

[ \text{Interest Expense} = 95{,}842 \times 7% = 6{,}709 ]

[ \text{Cash Interest} = 100{,}000 \times 6% = 6{,}000 ]

[ \text{Discount Amortization} = 6{,}709 - 6{,}000 = 709 ]

The ending carrying amount is:

[ 95{,}842 + 709 = 96{,}551 ]

For a discount bond, the carrying amount increases because the issuer is recognizing more interest expense than it pays in cash. The unpaid portion is economically part of the borrowing cost embedded in the discount.

Premium Example

Assume instead that a company issues 5-year bonds with a face amount of $100,000, a stated annual rate of 8 percent, and annual interest payments. The market yield at issuance is 7 percent, so the bonds are issued at a premium for more than face amount.

In each period:

[ \text{Interest Expense} = \text{Beginning Carrying Amount} \times 7% ]

[ \text{Cash Interest} = 100{,}000 \times 8% ]

[ \text{Premium Amortization} = \text{Cash Interest} - \text{Interest Expense} ]

For a premium bond, cash paid is greater than interest expense. The excess reduces the carrying amount until the liability reaches face value at maturity.

Amortization Schedule Mechanics

An effective-interest schedule is a repeating five-column process. Once the beginning carrying amount, stated cash payment, and market yield are known, each period follows the same pattern.

Year Beginning carrying amount Interest expense at 7% Cash paid at 6% Discount amortization Ending carrying amount
1 $95,842 $6,709 $6,000 $709 $96,551
2 $96,551 $6,759 $6,000 $759 $97,310
3 $97,310 $6,812 $6,000 $812 $98,122
4 $98,122 $6,869 $6,000 $869 $98,991
5 $98,991 plug to maturity $6,000 plug to face $100,000

The final period is often adjusted by a small plug because of rounding. FAR questions may ask for the carrying amount after one interest payment, after several payments, or just before retirement. The process is the same: start with the beginning carrying amount and update it for amortization through the measurement date.

Straight-Line Amortization

Straight-line amortization spreads the total discount or premium evenly over the debt term. It is easier, but it does not produce a constant effective yield. Under U.S. GAAP, the interest method is the conceptual default, while another method may be acceptable only when the result is not materially different.

For example, a $4,000 discount amortized over four annual periods produces $1,000 of discount amortization each year under straight-line amortization. Interest expense equals cash interest plus $1,000. For a $4,000 premium over four years, interest expense equals cash interest minus $1,000.

The exam trap is assuming straight-line is always acceptable because it is easier. If a question asks for effective interest, use the beginning carrying amount and market yield. If it says straight-line and the fact pattern allows it, spread the total discount or premium evenly.

Journal Entry Effects

The entries follow the same logic as the formulas. For a discount bond, interest expense exceeds cash paid, and the carrying amount rises.

1Dr Interest expense
2    Cr Discount on bonds payable
3    Cr Cash

For a premium bond, cash paid exceeds interest expense, and the carrying amount falls.

1Dr Interest expense
2Dr Premium on bonds payable
3    Cr Cash

The discount account is a contra-liability. The premium account increases the carrying amount of the liability. Debt issuance costs reduce the carrying amount and are amortized into interest expense, similar to the effect of a discount.

Early Retirement and Extinguishment

When debt is retired before maturity, compare the debt’s net carrying amount with the reacquisition price. The net carrying amount includes the face amount adjusted for unamortized discount, premium, and related issuance-cost effects. The reacquisition price is the amount paid to settle the debt, including any call premium.

[ \text{Gain or Loss} = \text{Net Carrying Amount} - \text{Reacquisition Price} ]

Result Income statement effect
Carrying amount exceeds reacquisition price Gain on extinguishment
Reacquisition price exceeds carrying amount Loss on extinguishment
Carrying amount equals reacquisition price No gain or loss

Assume bonds with a $100,000 face amount have an unamortized discount of $2,000 when the issuer calls them at 102. The net carrying amount is $98,000. The reacquisition price is $102,000. The issuer recognizes a $4,000 loss because it paid more than the carrying amount to retire the liability.

1Dr Bonds payable                         100,000
2Dr Loss on extinguishment                  4,000
3    Cr Discount on bonds payable           2,000
4    Cr Cash                              102,000

Accrued interest should be handled separately if the retirement date falls between interest payment dates. Do not include ordinary accrued interest in the extinguishment gain or loss unless the question’s reacquisition price explicitly combines it and asks for that treatment.

Common FAR Traps

  • Using the stated rate to calculate interest expense under the effective interest method. The stated rate calculates cash interest; the market yield calculates interest expense.
  • Forgetting to adjust annual rates for semiannual periods.
  • Treating a discount as an asset or a premium as revenue. They are valuation adjustments to the debt carrying amount.
  • Ignoring debt issuance costs when computing carrying amount or effective interest.
  • Recording a gain on early retirement when the reacquisition price is higher than carrying amount.
  • Using the face amount as carrying amount before all discount or premium has been amortized.

Key Takeaways

Debt amortization questions become manageable when you separate cash interest from interest expense. Cash interest follows the stated rate and face amount. Interest expense follows the market yield and beginning carrying amount. Discounts increase carrying amount over time. Premiums decrease carrying amount over time. Early retirement requires a carrying amount versus reacquisition price comparison, with any difference recognized as gain or loss.

### A bond is issued at a discount when: - [ ] The stated rate is higher than the market yield. - [x] The stated rate is lower than the market yield. - [ ] The cash interest paid equals interest expense in every period. - [ ] The face amount is lower than the maturity amount. > **Explanation:** A discount arises because investors demand a market yield higher than the stated coupon rate, so they pay less than face amount. ### Under the effective interest method, interest expense is calculated using: - [ ] Face amount multiplied by the stated rate. - [ ] Face amount multiplied by the original coupon payment. - [x] Beginning carrying amount multiplied by the market yield at issuance. - [ ] Ending carrying amount multiplied by the stated rate. > **Explanation:** Effective interest expense uses the beginning carrying amount and the effective market yield established at issuance. ### For a discount bond, discount amortization equals: - [ ] Cash interest paid minus interest expense. - [x] Interest expense minus cash interest paid. - [ ] Face amount minus cash interest paid. - [ ] Market yield minus stated rate, with no carrying amount calculation. > **Explanation:** Interest expense exceeds cash interest for a discount bond, and the difference increases the carrying amount. ### For a premium bond accounted for under the effective interest method: - [x] The carrying amount decreases toward face amount. - [ ] The carrying amount increases toward face amount. - [ ] Interest expense is always greater than cash interest. - [ ] The premium is recognized as revenue immediately. > **Explanation:** A premium bond starts above face amount. Premium amortization reduces the carrying amount over the bond's life. ### Which statement best describes debt issuance costs for a recognized debt liability? - [ ] They are usually recorded as a separate long-term asset. - [x] They are generally presented as a direct deduction from the carrying amount of the debt. - [ ] They are ignored after issuance. - [ ] They are reported as revenue because they reduce cash proceeds. > **Explanation:** Debt issuance costs are presented as a direct deduction from the related debt liability and amortized to interest expense. ### A bond has a \$100,000 face amount and \$3,000 of unamortized discount. What is its carrying amount before considering any issuance costs? - [ ] \$103,000 - [x] \$97,000 - [ ] \$100,000 - [ ] \$3,000 > **Explanation:** A discount reduces the carrying amount: \$100,000 minus \$3,000 equals \$97,000. ### An issuer retires debt with a net carrying amount of \$98,000 for \$102,000. What is the result? - [ ] \$4,000 gain - [x] \$4,000 loss - [ ] No gain or loss - [ ] \$102,000 interest expense > **Explanation:** The issuer paid \$4,000 more than the carrying amount to extinguish the debt, so it recognizes a loss. ### When bonds pay interest semiannually, a FAR calculation normally requires the candidate to: - [x] Use the semiannual stated rate, semiannual market yield, and number of semiannual periods. - [ ] Use the annual stated rate for every six-month period. - [ ] Ignore the market yield and use only the coupon rate. - [ ] Record interest expense only at year-end. > **Explanation:** The rates and periods must match the payment interval used in the amortization schedule. ### Which item is most likely to be excluded from an extinguishment gain or loss calculation and handled separately? - [ ] Unamortized discount - [ ] Unamortized premium - [ ] Call premium included in the reacquisition price - [x] Ordinary accrued interest between payment dates > **Explanation:** Accrued interest is usually treated as interest for the current period rather than part of the debt's carrying amount versus reacquisition price comparison.
Revised on Monday, June 15, 2026