FAR · Select balance sheet accounts · 5 practice questions
Effective Interest Method: Zero-Coupon Note Carrying Amount
A zero-interest note starts at present value and grows by the effective rate times its beginning carrying amount. Use the worked example and free practice to separate interest expense from cash paid.
Try one first
Hint
First determine the note's initial present value, then ask how one year of effective interest changes that carrying amount.
Answer A. At issuance the note is recorded at the present value: $100,000 × 0.7513 = $75,130. Accrete the discount for one year under the effective-interest method: $75,130 × 10% = $7,513. The carrying amount at December 31, 20X5 is $75,130 + $7,513 = $82,643.
Why not B: Tempting because it is the present value at issuance, but the question asks for the balance at December 31, 20X5 after one year of discount accretion under the effective-interest method.
Why not C: This amount reflects accreting the discount for two years (the carrying amount after two years), not one year; therefore it is the balance at a later date, not December 31, 20X5. (Small rounding differences may explain the exact cents shown.)
Why not D: This is the note's face amount payable at maturity. Under U.S. GAAP the liability is initially measured at present value and accretes toward face over time, so it will not equal $100,000 until maturity.
Worked example
Vale Co. issues a two-year, noninterest-bearing note for cash. Its $72,000 face amount is due at maturity. The market rate is 20%, compounded annually. There are no issuance costs or payments before maturity. Find the initial carrying amount and its balance at each year-end before repayment.
| 1 | Initial carrying amount$72,000 ÷ (1.20 × 1.20) | $50,000 |
| 2 | Year 1 interest expense$50,000 × 20% | $10,000 |
| 3 | Year 1 ending carrying amount$50,000 + $10,000 | $60,000 |
| 4 | Year 2 interest expense$60,000 × 20% | $12,000 |
| 5 | Year 2 balance before repayment$60,000 + $12,000 | $72,000 |
The note starts at $50,000, rises to $60,000 after Year 1, and reaches its $72,000 face amount immediately before repayment.
Check: No cash payments means no subtraction: $50,000 × 1.20 × 1.20 = $72,000 before repayment.
Key points
- Use a reliable equipment cash price to measure the note initially; otherwise, discount the future payment at the market rate.
- Debt issuance costs reduce initial carrying amount and affect the effective yield; their amortization increases carrying amount.
- Accrued coupon interest is a separate payable, not part of the debt's carrying amount.
- For premium debt, interest expense is less than cash interest paid, so carrying amount falls toward face.
How the exam traps you
- Reporting face value or the original present value at year-end. Start at present value, then add discount amortization for each elapsed period.
- Using the stated rate to compute interest expense. Use the effective rate on beginning carrying amount; use the stated rate only for cash interest.
- Spreading the discount evenly across the note's term. Apply the effective rate to each period's updated beginning balance.
Question 2
Hint
First determine the initial carrying amount (present value = proceeds), then apply the 10% market rate to that beginning carrying amount to compute Year 1 accretion.
Answer D. The note was issued at a significant financing discount and is initially measured at present value (proceeds = $400,000). Under the effective-interest method the discount is accreted at the market rate: Year 1 interest = $400,000 × 10% = $40,000. Thus the Dec 31, Year 1 carrying amount is $400,000 + $40,000 = $440,000.
Why not A: This choice appeals to the idea that no cash changes hands until maturity, so the carrying amount 'should' stay at proceeds. It is wrong because the effective-interest method requires periodic accretion of the discount, so the carrying amount increases each period before maturity.
Why not B: This distractor tempts because some practitioners simplify by spreading the total discount ($132,400) evenly over three years (≈ $44,133 per year), producing the shown amount. It fails because the stem requires the effective-interest method, which amortizes discount based on the beginning carrying amount and the market rate rather than straight-line allocation.
Why not C: This is attractive to those who equate the legal maturity amount with carrying value, especially when no cash interest is paid. It is incorrect because GAAP requires initial recognition at present value when a significant financing element exists and subsequent accretion of the discount even if cash interest is paid only at maturity.
Question 3
Hint
First determine the note's initial recorded amount, then accrete the discount for each full year through the balance sheet date.
Answer B. The note is initially recorded at the reliable cash price of $400,000. Under the effective interest method at 10%, accretion for Year 1 is $40,000 (carrying amount $440,000) and for Year 2 is $44,000 (10% of $440,000), yielding $484,000 at December 31, 20X6.
Why not A: This equals the carrying amount after one year of accretion (400,000 + 40,000) and is tempting, but the question asks for the balance after two full years (through 12/31/20X6).
Why not C: This is the result of straight-line amortizing the $132,400 discount over 3 years (~$44,133 per year). The stem specifies the effective interest method, so Year 2 accretion is based on the Year 1 carrying amount, producing $484,000 instead.
Why not D: This is the face amount due at maturity. Before maturity, a noninterest-bearing note is reported at amortized cost (initial value plus accreted discount), not at its undiscounted face amount.
Question 4
Hint
Start with how a noninterest-bearing long-term note is measured at issuance, then move forward one year using the method stated in the stem.
Answer A. Because the equipment's fair value is not readily determinable, the note is initially recorded at the present value of the amount due: $665,500 × 0.7513 = $499,990 (rounded). During X5, Huron recognizes interest expense using the effective interest method at 10% of the opening carrying amount, or about $49,999. The 12/31/X5 carrying amount is therefore approximately $499,990 + $49,999 = $549,989.
Why not B: This is the correct initial present value on 1/1/X5, but it is incorrect for 12/31/X5 because one year of accretion (discount amortization) must be recognized under the effective interest method.
Why not C: This amount results from straight-line amortization of the discount over three years. The stem specifies the effective interest method, so amortization should be based on the market rate applied to the carrying amount, not straight-line.
Why not D: This is the face amount payable at maturity. A noninterest-bearing note with a significant financing component is not recorded at face value at issuance; it is recorded at present value and accreted to face over the term.
Question 5
Hint
Start by identifying whether the bond was issued at a premium or a discount, then think about how that affects both amortization and the relationship between cash interest and interest expense.
Answer A. The bonds were issued at a premium because the issue price ($1,040,000) exceeds face ($1,000,000). Under the effective-interest method the premium is amortized, reducing the carrying amount toward face over time. Because the effective interest rate is less than the stated rate on a premium issue, interest expense (carrying amount × effective rate) is less than the cash interest paid.
Why not B: This describes a discount situation. For bonds issued at a discount the carrying amount increases and interest expense exceeds cash paid; here the bonds were issued at a premium, so the carrying amount decreases instead.
Why not C: This option mixes a correct direction for amortization with the wrong interest relationship. On a premium, amortization lowers the carrying amount and the effective interest (interest expense) is less than the stated cash interest.
Why not D: Interest expense equals cash interest only if the bond was issued at par. With a premium the effective rate is lower than the stated rate, so interest expense will not equal the cash interest paid.
Common questions
How do you calculate a zero-coupon note's carrying amount?
Discount the maturity payment at the market rate, then add each period's effective interest. With no payments, carrying amount equals initial present value × (1 + effective rate)^elapsed periods.
How do debt issuance costs affect the effective interest method?
They reduce the initial carrying amount and increase the effective yield. Apply that yield to the beginning carrying amount; amortization of the costs increases carrying amount.
Can I use straight-line amortization instead of effective interest?
Use effective interest when the question requires it. Straight-line is acceptable only when its results are not materially different from effective interest.
Watch it solved
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