Why bonds almost never sell at face value
A bond promises two things: a fixed coupon every period and the face amount at maturity. The stated rate that fixes the coupon is printed months before the bonds reach investors, and the yield investors actually demand on the day of issuance is whatever the market says that day. The two rates agree only by coincidence. When they disagree, the price adjusts until the promised cash flows, discounted at the market yield, are worth exactly what an investor will pay.
If the stated rate is below the market yield, investors will not pay face for a below-market coupon, so the bonds sell at a discount. If the stated rate is above the market yield, the coupon is worth more than the market requires and the bonds sell at a premium. Either way the issuer records bonds payable at the proceeds — the discount or premium is not a separate gain or loss, it is a rate adjustment spread over the life of the issue.
That spreading is amortisation, and under ASC 835-30 the required method is the effective-interest method. It produces an interest expense that is a constant percentage of the carrying value rather than a constant dollar amount, which is the whole point: the issuer’s real cost of the borrowing is the market yield it accepted at issuance, and the schedule reports exactly that in every period.
How the schedule is built, line by line
Everything starts with the proceeds. Discount each coupon and the maturity value at the market yield per period and add them up. The coupon stream is an ordinary annuity, so its present value is C × (1 − (1+y)−n) ÷ y, and the face is a single sum worth F × (1+y)−n. Note which rate does which job: the stated rate sizes C, and the market yield does all of the discounting.
From there each period repeats four operations. Interest expense is the beginning carrying value multiplied by the yield per period — not by the stated rate, and not by the face. Cash coupon is the face multiplied by the stated rate per period, and it never changes. Amortisation is the difference between the two. Ending carrying value is the beginning value plus that difference.
Write the amortisation as expense minus coupon and the sign takes care of itself. On a discount bond the expense exceeds the coupon, the difference is positive, and the carrying value is written up toward face. On a premium bond the expense is smaller than the coupon, the difference is negative, and the carrying value is written down toward face. In both cases the carrying value arrives at exactly the face amount on the last line, which is the arithmetic check that the schedule is right.
One identity is worth memorising because it makes the whole schedule self-checking: total interest expense over the life equals the total cash coupons plus the discount, or minus the premium. You never have to add up a column to know the answer.
Worked example: $100,000 of 10% five-year bonds yielding 12%
An issuer sells $100,000 of five-year bonds with a 10% stated rate paying semiannually, at a time when the market demands 12% on comparable debt. There are n = 5 × 2 = 10 periods, the coupon is C = $100,000 × 10% ÷ 2 = $5,000, and the yield per period is y = 12% ÷ 2 = 6%.
- Discount the coupons. (1 − 1.06−10) ÷ 0.06 = (1 − 0.5583948) ÷ 0.06 = 7.3600871. Times $5,000 gives $36,800.44.
- Discount the face. $100,000 × 0.5583948 = $55,839.48.
- Add them. $36,800.44 + $55,839.48 = $92,639.92 of proceeds. The discount is $92,639.92 − $100,000 = −$7,360.08.
- Period 1 interest expense. $92,639.92 × 6% = $5,558.40.
- Period 1 amortisation. $5,558.40 − $5,000 = $558.40, and the carrying value rises to $92,639.92 + $558.40 = $93,198.32.
- Period 2. $93,198.32 × 6% = $5,591.90 of expense, $591.90 of amortisation, carrying value $93,790.22. The expense grows every period because the base it is charged on grows.
- Total interest expense. Ten coupons of $5,000 is $50,000, plus the $7,360.08 discount, giving $57,360.08 over the life.
The period-1 journal entry is a debit to interest expense of $5,558.40, a credit to cash of $5,000, and a credit to discount on bonds payable (or directly to bonds payable, under the net presentation ASC 835-30 requires) of $558.40.
Compare that with straight-line. The discount is $7,360.08 over 10 periods, so straight-line would charge $736.01 of amortisation and $5,736.01 of expense in every period, including the first. Effective interest charges $558.40 in period 1 and $989.24 in period 10 — a difference of $177.61 in the first period alone, on a schedule where the ten-period total is identical.
Reading the schedule and the numbers it produces
Start with the direction. A negative premium/discount output means the bonds were issued at a discount, the coupon is below market, and every line of the schedule shows expense above the cash coupon with the carrying value climbing. A positive figure means a premium, expense below the cash coupon, and a carrying value falling. If the output is zero, the coupon matched the market and there is nothing to amortise — expense equals the coupon in every period, forever.
Then look at the shape of the expense column. Under effective interest, a discount bond’s interest expense increases every period and a premium bond’s decreases every period, because expense is a fixed percentage of a carrying value that is moving toward face from one side or the other. That is exactly the pattern examiners test, and it is the opposite of straight-line, which is flat by construction.
The straight-line figure is shown for comparison only. ASC 835-30 permits straight-line only when the result is not materially different from the effective-interest result; the gap widens with the size of the discount or premium and with the length of the issue, so a deep-discount 30-year bond is precisely the case where the shortcut is not available. On the worked example the first-period difference is $177.61 on a $5,558.40 expense — 3.2% — while the ten-period totals agree to the cent.
Finally, check the last line. The ending carrying value must be the face amount. If it is not, the yield, the term or the frequency in the inputs do not describe the same bond the proceeds were computed from.
Issue price of $100,000 of 8% five-year semiannual bonds at different market yields
| Market yield | Yield per period | PV of coupons | PV of face | Issue proceeds | Premium / (discount) |
|---|---|---|---|---|---|
| 6% | 3.0% | $34,120.81 | $74,409.39 | $108,530.20 | $8,530.20 |
| 7% | 3.5% | $33,266.42 | $70,891.88 | $104,158.30 | $4,158.30 |
| 8% | 4.0% | $32,443.58 | $67,556.42 | $100,000.00 | $0.00 |
| 9% | 4.5% | $31,650.87 | $64,392.77 | $96,043.64 | ($3,956.36) |
| 10% | 5.0% | $30,886.94 | $61,391.33 | $92,278.27 | ($7,721.73) |
| 12% | 6.0% | $29,440.35 | $55,839.48 | $85,279.83 | ($14,720.17) |
The 8% row is the par case: when the market yield equals the stated rate the proceeds are exactly face. Prices move inversely to yield, and the move is not symmetric — a two-point fall in yield adds $8,530 while a two-point rise removes $7,722.
What ASC 835-30 requires
The FASB codification treats a discount or premium as an inseparable part of the debt rather than as an asset or liability of its own, so it is presented net against the bonds payable on the balance sheet, not as a separate line. Amortisation runs through interest expense, not through a gain or loss. The interest method — the effective-interest method — is the required approach, with straight-line permitted only where the difference is immaterial.
Debt issuance costs follow the same logic under ASC 835-30 as amended by ASU 2015-03: they are presented as a direct deduction from the carrying amount of the debt and amortised as interest expense. This calculator prices the bond from the coupon and yield alone; if you have issuance costs, subtract them from the proceeds and re-solve for the yield that equates the reduced proceeds to the same cash flows, which is the effective rate the standard requires you to use. Under IFRS the equivalent requirement is the effective interest method defined in IFRS 9.
Errors that cost marks on FAR and points in review
- Discounting at the stated rate. The proceeds are the present value at the market yield. Using the coupon rate to discount always returns face value and hides the entire question.
- Charging interest expense on the face amount. Expense is the carrying value times the yield. Face times the coupon rate is the cash payment, which is a different line.
- Forgetting to halve both rate and term. Semiannual bonds use y ÷ 2 and n × 2. Halving one and not the other is the single most common arithmetic slip on this topic.
- Reversing the amortisation sign. Write amortisation as expense minus coupon and let the sign fall out; deciding the direction by intuition inverts premium and discount about half the time.
- Using straight-line by default. It is an exception permitted on materiality grounds, not the method. Examiners test the interest method.
- Treating a premium as income. It is a reduction of future interest expense, recognised over the life, not a gain at issuance.
- Applying this schedule to a bond retired early. On extinguishment you derecognise the remaining carrying value and record a gain or loss against the reacquisition price; the remaining schedule is discarded.
Where this fits with the other present-value calculations
Bond amortisation is one member of a family. The same present-value machinery, run on a different set of promised cash flows, produces the right-of-use asset and lease liability that ASC 842 requires — the lease liability is amortised with exactly this effective-interest pattern, which is why the two topics are examined together. On the investing side, the pricing step alone is a net present value calculation with the market yield as the discount rate, and solving for the yield that makes the proceeds equal the cash flows is an internal rate of return problem.
Elsewhere in FAR, the schedule interacts with the tax provision: because tax law and GAAP amortise differently in some jurisdictions, a bond issued at a discount can create a temporary difference of the kind a deferred tax liability calculator quantifies. And revenue-side questions on long-term contracts use their own allocation logic through percentage of completion.
If you are on the investor’s side rather than the issuer’s, the same schedule runs with the signs reversed: interest revenue instead of interest expense, and amortisation of a premium or discount on an investment in debt securities. The numbers are identical; only the accounts change.