Bonds payable is the topic where intermediate accounting stops being bookkeeping and starts being finance. A bond's price depends on the market interest rate on the day it is issued, and the difference between that price and face value has to be spread over the bond's life. This post covers how to price a bond, why bonds sell at a discount or a premium, and how to build the amortization table, using the effective-interest method and the straight-line shortcut.
Two Interest Rates, One Bond
Every bond question involves two rates, and confusing them is the root of most errors:
- The stated (coupon) rate is printed on the bond. It fixes the cash interest paid each period: face value × stated rate.
- The market (effective) rate is what investors demand on the day of issue. It sets the price, and it drives interest expense.
If the market rate is higher than the stated rate, the bond's coupons are unattractive, so investors pay less than face value: a discount. If the market rate is lower, they pay more: a premium. If the two are equal, the bond sells at face value.
Pricing the Bond
A bond's price is the present value of everything it pays, discounted at the market rate: the stream of coupons (an annuity) plus the face value at maturity (a lump sum).
Fairview Logistics issues $100,000 of 5-year, 8% bonds on January 1, paying interest semiannually. The market rate is 10%.
Semiannual payments mean 10 periods at 5% (half the annual market rate). Each coupon is $100,000 × 8% × 6/12 = $4,000.
PV of coupons: $4,000 × 7.72173 (PV of an annuity, 10 periods, 5%) = $30,887
PV of face value: $100,000 × 0.61391 (PV of $1, 10 periods, 5%) = $61,391
Issue price = $92,278, a discount of $7,722.
| Account | Debit | Credit |
|---|---|---|
| Cash | 92,278 | |
| Discount on Bonds Payable | 7,722 | |
| Bonds Payable | 100,000 |
Discount on Bonds Payable is a contra-liability. The balance sheet shows the bonds at their carrying value: $100,000 − $7,722 = $92,278. (Some intermediate texts record the bonds net, at $92,278, with no separate discount account. The interest figures are identical either way.)
Effective-Interest Amortization (Discount)
Each period:
- Interest expense = carrying value at the start of the period × market rate per period
- Cash paid = face value × stated rate per period
- Amortization = the difference, which raises the carrying value toward face value
| Period | Cash paid (4%) | Interest expense (5%) | Discount amortized | Carrying value |
|---|---|---|---|---|
| Issue | 92,278.00 | |||
| 1 | 4,000.00 | 4,613.90 | 613.90 | 92,891.90 |
| 2 | 4,000.00 | 4,644.60 | 644.60 | 93,536.50 |
| 3 | 4,000.00 | 4,676.83 | 676.83 | 94,213.33 |
| 4 | 4,000.00 | 4,710.67 | 710.67 | 94,924.00 |
The first interest payment, on June 30:
| Account | Debit | Credit |
|---|---|---|
| Interest Expense | 4,613.90 | |
| Discount on Bonds Payable | 613.90 | |
| Cash | 4,000.00 |
Notice the pattern: with a discount, the carrying value rises each period, so interest expense rises too. By period 10, the carrying value reaches exactly $100,000, ready for repayment. (Final-period rounding is absorbed in the last line.)
Effective-Interest Amortization (Premium)
Same bonds, but the market rate is 6% (3% per period). Price: $4,000 × 8.53020 + $100,000 × 0.74409 = $108,530, a premium of $8,530.
| Period | Cash paid (4%) | Interest expense (3%) | Premium amortized | Carrying value |
|---|---|---|---|---|
| Issue | 108,530.00 | |||
| 1 | 4,000.00 | 3,255.90 | 744.10 | 107,785.90 |
| 2 | 4,000.00 | 3,233.58 | 766.42 | 107,019.48 |
| Account | Debit | Credit |
|---|---|---|
| Interest Expense | 3,255.90 | |
| Premium on Bonds Payable | 744.10 | |
| Cash | 4,000.00 |
With a premium, interest expense is less than the cash paid, and the carrying value falls toward face value.
The Straight-Line Shortcut
Straight-line spreads the discount or premium evenly: $7,722 ÷ 10 = $772.20 per period, so interest expense is $4,772.20 every period. It is easier, but it gives a constant dollar expense on a changing balance, which makes the implied interest rate drift over time. US GAAP allows straight-line only when the result is not materially different from effective interest. IFRS does not allow it at all. Use effective interest unless the question says otherwise.
Common bond accounting mistakes
- Computing interest expense at the stated rate. Expense uses the market rate on the carrying value. The stated rate on face value gives only the cash payment.
- Using annual figures for semiannual bonds. Halve both rates and double the number of periods, in the pricing and in the table.
- Pricing at the stated rate. Discount the cash flows at the market rate. Pricing at the stated rate always gives face value.
- Amortizing in the wrong direction. Carrying value always moves toward face value: up for a discount, down for a premium.
- Treating Discount on Bonds Payable as an asset. It is a contra-liability that reduces the bonds' carrying value.
- Forgetting the accrual at year-end. If an interest date does not fall on the balance sheet date, accrue the interest and amortization up to year-end.
Build complete amortization schedules and journal entries on Accountely's bonds payable challenges, and see how bonds compare with other borrowing under bonds and long-term debt. The grader checks each period's interest, amortization and carrying value, so a wrong rate shows up in the first line.
Frequently Asked Questions
Why are bonds issued at a discount or a premium?
When the market interest rate is above the bond's stated rate, investors pay less than face value, so the bond sells at a discount. When the market rate is below the stated rate, they pay more, so it sells at a premium.
How is interest expense calculated under the effective interest method?
Multiply the bond's carrying value at the start of the period by the market rate. The cash paid is face value times the stated rate, and the difference is the amortization of the discount or premium.
When can the straight-line method be used?
Under US GAAP, only when the results are not materially different from the effective interest method. Straight-line spreads the discount or premium evenly over the bond's life.
Is a bond discount an asset?
No. Discount on Bonds Payable is a contra-liability that reduces the carrying value of the bonds. It is amortized to interest expense over the bond's life.