To calculate the discount on bonds payable, find the bond’s present value by discounting its future cash flows at the current market interest rate, then subtract that present value from the bond’s face value. The gap between the two is the discount, and it exists because the bond’s stated coupon rate is lower than what investors currently demand for comparable risk. After issuance, that discount is amortized as additional interest expense over the life of the bond until the carrying value climbs back to face value at maturity.
What You Need Before You Start
Four inputs drive the calculation. All of them come from the bond certificate or the offering memorandum.
- Face value (par value). The amount the issuer repays at maturity. Commonly $1,000 per bond for corporate issues, or $100,000 in textbook illustrations.
- Stated (coupon) interest rate. The percentage printed on the bond that determines each cash interest payment.
- Market interest rate (yield to maturity). The rate investors currently demand for bonds of similar risk and maturity. It reflects inflation expectations and the issuer’s creditworthiness. When perceived default risk rises, investors demand a higher yield, which pushes the bond price down.
- Number of periods to maturity. The total count of interest payment intervals until the bond matures.
If the bond pays interest semi-annually, which is the most common arrangement for U.S. corporate bonds, divide each annual rate by two and multiply the number of years by two. A 10-year bond paying twice a year has 20 periods, and a 6% annual market rate becomes 3% per period.
Calculating the Bond’s Present Value
A bond’s price is the sum of two present values: the lump-sum repayment of face value at maturity, and the annuity of coupon payments made along the way. Discount both streams at the market rate, not the coupon rate, because the market rate reflects what investors could earn on comparable alternatives.
Present Value of the Face Value
The face value is a single payment at the end of the bond’s life:
PV = Face Value ÷ (1 + r)n
where r is the market rate per period and n is the total number of periods.
Present Value of the Coupon Payments
The coupons form an ordinary annuity:
PV of Coupons = Payment × [(1 − (1 + r)−n) ÷ r]
The periodic payment equals the face value times the coupon rate per period. Add the two present values together to get the bond’s issue price.
Worked Example
A company issues a $100,000 bond with a 4% annual coupon, paying interest semi-annually, maturing in 10 years. The market rate for comparable bonds is 6%. Because the market rate exceeds the coupon rate, the bond will sell at a discount.
Adjust for semi-annual periods first. The coupon rate per period is 2%, the market rate per period is 3%, and the total number of periods is 20. Each semi-annual coupon payment is $2,000 ($100,000 × 2%).
Present value of the face value: $100,000 ÷ (1.03)20 = $100,000 ÷ 1.8061 = $55,368.
Present value of the coupons: $2,000 × [(1 − (1.03)−20) ÷ 0.03] = $2,000 × 14.8775 = $29,755.
Issue price: $55,368 + $29,755 = $85,123.
Finding the Discount and Recording It
The discount is simply the face value minus the price:
$100,000 − $85,123 = $14,877
That $14,877 is booked to a contra-liability account called Discount on Bonds Payable. On the balance sheet, it offsets the Bonds Payable account, so the net liability shown equals the $85,123 the company actually received.
The issuance entry uses three accounts:
- Debit Cash for $85,123, the amount actually received from investors.
- Debit Discount on Bonds Payable for $14,877, the gap between what was received and what must be repaid.
- Credit Bonds Payable for $100,000, the full face value the company must repay at maturity.
The balance sheet then shows Bonds Payable at $100,000 less the unamortized discount of $14,877, for a net carrying value of $85,123. As the discount is amortized each period, that carrying value climbs toward $100,000.
Amortizing the Discount
The $14,877 has to be allocated to interest expense across the 20 semi-annual periods. Two methods are available.
Straight-Line Method
Divide the discount evenly across all periods:
$14,877 ÷ 20 = $743.85 per period
Each period, total interest expense equals the $2,000 cash coupon plus $743.85 of amortization, for $2,743.85. The entry debits Interest Expense $2,743.85, credits Cash $2,000, and credits Discount on Bonds Payable $743.85.
The method is simple, but the constant dollar amount means the implied interest rate drifts as the carrying value changes. Under GAAP, straight-line is permitted only when its results do not differ materially from the effective interest method.
Effective Interest Method
The effective interest method is preferred under both GAAP and IFRS. It produces a constant interest rate rather than a constant dollar amount, which better reflects the economics of the borrowing.
Each period, three steps:
- Multiply the carrying value at the start of the period by the market rate per period. That is the interest expense.
- Subtract the cash coupon from the interest expense. The difference is the discount amortization.
- Add the amortization to the prior carrying value to get the new carrying value.
The first two periods of the example:
Period 1. Interest expense = $85,123 × 3% = $2,554. Cash coupon = $2,000. Amortization = $554. New carrying value = $85,677.
Period 2. Interest expense = $85,677 × 3% = $2,570. Cash coupon = $2,000. Amortization = $570. New carrying value = $86,247.
Both the interest expense and the amortization rise each period as the carrying value grows. By the last period, the carrying value equals the $100,000 face value and the entire discount has flowed through interest expense. The journal entry each period debits Interest Expense for the calculated amount, credits Cash $2,000, and credits Discount on Bonds Payable for the amortization.
A full amortization schedule listing every period’s opening carrying value, interest expense, coupon, amortization, and closing carrying value is the standard working paper for this, and it doubles as audit support.
Zero-Coupon Bonds
A zero-coupon bond pays no periodic interest. The entire return comes from buying below face value and receiving face value at maturity. With no coupons, the price formula collapses to the lump-sum piece:
Price = Face Value ÷ (1 + r)n
The discount on a zero-coupon bond is typically much larger than on a coupon-paying bond because the whole return is embedded in the price. All of it is amortized as interest expense using the effective interest method: each period, multiply the carrying value by the market rate, and add the full amount to the carrying value since no cash interest is paid.
Tax Treatment of the Discount
The Internal Revenue Code treats bond discounts differently for the issuer and the investor.
For the Issuer
An issuer that sells a bond at a discount can deduct the amortized discount as interest expense over the bond’s life. The IRS treats the discount as part of the cost of borrowing: the company received less cash than it must repay, and that gap functions as additional interest.
For the Investor
The difference between face value and issue price is classified as original issue discount (OID). Under IRC Section 1272, the bondholder must include a portion of the OID in gross income each year, even when no cash is received until maturity or a coupon date. The daily accrual is calculated using a constant-yield method based on the bond’s adjusted issue price and yield to maturity.1GovInfo. 26 USC 1272 – Current Inclusion in Income of Original Issue Discount
Issuers must file Form 1099-OID with the IRS and send a copy to the bondholder whenever the OID includible in gross income for the year is $10 or more.2Internal Revenue Service. About Form 1099-OID, Original Issue Discount
The De Minimis Exception
Not every discount triggers OID treatment. Under IRC Section 1273, if the total discount is less than one-quarter of one percent (0.25%) of the face value multiplied by the number of complete years to maturity, the discount is treated as zero for OID purposes.3Office of the Law Revision Counsel. 26 USC 1273 – Determination of Amount of Original Issue Discount The investor recognizes the small discount as a capital gain at maturity or sale, not as ordinary income accrued annually.
For a 10-year, $100,000 bond, the de minimis threshold is $2,500 (0.25% × $100,000 × 10 years). A $2,000 discount falls below that threshold and escapes annual OID inclusion.
Getting the Amortization Wrong
Improper amortization misstates interest expense and the carrying value on the balance sheet. For public companies, the SEC can take enforcement action when disclosure documents contain materially misleading financial information, including errors in how bond costs are calculated and reported.4U.S. Securities and Exchange Commission. Municipal Bond Participants – Public Officials and Obligated Persons Auditors look closely at amortization schedules, and switching between the effective interest and straight-line methods without justification will draw questions. A period-by-period schedule that reconciles to the general ledger is the cleanest defense.