Difficulty: Intermediate | Prerequisites: introductory accounting (debits/credits), time value of money basics (present value, future value, discounting)
Bonds are one of the main ways companies raise long-term capital, and accounting for them properly is a core skill in intermediate financial accounting. When a bond's stated (coupon) rate differs from the market rate at issuance, the bond sells at a premium or a discount, and the issuer must account for that difference over the bond's life. This topic sits at the intersection of finance (time value of money) and accounting (journal entries, amortisation schedules). You need to be comfortable with present value calculations before any of this will make sense.
When a bond's coupon rate is lower than the market rate, it sells at a discount (below face value). You price the bond by taking the present value of its future cash flows: the annuity of coupon payments plus the lump sum of the principal. The discount is then amortised over the bond's life, which increases interest expense above the cash coupon each period.
Face value (par value)
The amount printed on the bond that will be repaid at maturity. In simple terms, this is the "sticker price" the issuer promises to pay back.
Coupon rate (stated rate / nominal rate)
The annual interest rate stated on the bond, applied to face value to determine cash interest payments. Think of it as the rate the bond contract locks in.
Market rate (effective rate / yield)
The rate investors actually demand given current conditions. This is the rate used to discount the bond's cash flows and determine what investors will pay today.
Discount on bonds payable
The difference between face value and issue price when the bond sells below par (because the coupon rate is lower than the market rate). In simple terms, it is the "shortfall" the issuer received upfront and must make up through higher effective interest over the bond's life.
Present value of an ordinary annuity (PVA)
The current worth of a series of equal payments received at the end of each period. This is how you value the stream of coupon payments.
Present value of a single amount (PV factor)
The current worth of one lump sum to be received in the future. This is how you value the principal repayment at maturity.
Bond issue price
The total present value the bond sells for on the date of issuance: PV of coupon payments plus PV of the principal.
When the coupon rate (12% annual, or 6% per semi-annual period) is below the market rate (14% annual, or 7% per semi-annual period), investors will not pay full face value. The bond sells at a discount.
To find the issue price, split the bond's future cash flows into two pieces and discount each at the market rate per period:
Coupon payments (annuity component): Semi-annual coupon = $700,000 x 6% = $42,000. There are 6 periods (3 years x 2). Use the PVA factor: PVA(6 periods, 7%) = 4.76654. PV of coupons = $42,000 x 4.76654 = $200,195.
Principal repayment (lump sum component): Use the PV factor for a single amount: PV(6 periods, 7%) = 0.66634. PV of principal = $700,000 x 0.66634 = $466,438.
Total issue price: $200,195 + $466,438 = $666,633.
The bond sells for $666,633 against a face value of $700,000, creating a discount of $33,367.
On 1 January 2019, the issuer records:
Debit Cash: $666,633 (what was actually received)
Debit Discount on Bonds Payable: $33,367 (contra-liability, reduces the net carrying amount)
Credit Bonds Payable: $700,000 (the face value obligation)
The carrying amount on the balance sheet at issuance is $700,000 less $33,367 = $666,633. Over the life of the bond, the discount is amortised (reduced to zero), so the carrying amount climbs back up to $700,000 by maturity.
\text{Bond Issue Price} = (C \times \text{PVA}(n, r)) + (F \times \text{PV}(n, r))Where C = coupon payment per period, F = face value, n = number of periods, r = market rate per period.
\text{PVA}(n, r) = \frac{1 - (1 + r)^{-n}}{r}\text{PV}(n, r) = (1 + r)^{-n}\text{Discount on Bonds Payable} = F - \text{Issue Price}Corporations issue bonds at a discount when prevailing interest rates are higher than the coupon they set. This is routine in capital markets: a company might lock in a round-number coupon rate for simplicity, knowing the bond will price at a discount to reflect the higher yield investors require. Government bonds work the same way: when market rates rise after a bond's coupon is set, the bond trades below par.
Students often think the discount means the company "lost money" on issuance. It does not. The discount simply reflects that the coupon rate is below the market rate; investors pay less upfront and are compensated through higher effective interest.
Students confuse the coupon rate with the market rate. The coupon rate determines the cash payment each period. The market rate determines the present value (the price investors will pay).
Students sometimes use the annual rate directly in the PV formulas for a semi-annual bond. You must use the rate per period (annual rate divided by 2) and the total number of semi-annual periods (years times 2).
Students forget that Discount on Bonds Payable is a contra-liability, not an asset. It sits on the balance sheet as a reduction of Bonds Payable.
Bond valuation questions almost always require you to split the calculation into two PV components (annuity + lump sum). Show both steps.
Watch for semi-annual vs. annual: if the bond pays interest semi-annually, divide the annual rate by 2 and multiply the years by 2 before looking up PV factors.
You will likely be asked to record the issuance journal entry. The debit to Discount on Bonds Payable is the part students drop.
Carrying amount at issuance = Face Value minus Discount. Exams test whether you know this equals the issue price.
True or False: A bond sells at a discount when the coupon rate exceeds the market rate.
Fill in the blank: The issue price of a bond equals the PV of ______ plus the PV of ______.
True or False: Discount on Bonds Payable is an asset account.
Fill in the blank: For a 3-year bond paying interest semi-annually, you use ______ periods in the PV calculation.
True or False: At issuance, the carrying amount of a discounted bond equals its face value.
Answers: 1. False (it sells at a discount when the coupon rate is below the market rate). 2. coupon payments (annuity); the principal (lump sum). 3. False (it is a contra-liability). 4. 6. 5. False (it equals face value minus the discount).
Q: A company issues a $500,000, 10% (annual), 5-year bond when the market rate is 12%. Interest is paid semi-annually. What is the semi-annual coupon payment?
A: $500,000 x 5% = $25,000 per period (10% annual divided by 2 for semi-annual).
Q: In the example above, how many periods would you use to look up the PV annuity factor?
A: 10 periods (5 years x 2).
Q: A bond with face value $700,000 is issued for $666,633. What is the discount, and is it a debit or credit in the issuance entry?
A: The discount is $33,367 ($700,000 minus $666,633). It is debited (Discount on Bonds Payable is a contra-liability that reduces the net obligation).
Q: Why does a bond sell at a discount rather than at par?
A: Because the bond's coupon rate is lower than the prevailing market rate. Investors demand compensation for receiving below-market coupon payments, so they pay less than face value upfront.
This connects directly to the next topic, discount amortisation and interest expense accounting, where the effective interest method and straight-line method are used to allocate the discount over the bond's life. It also ties back to time value of money concepts from introductory finance: the PV annuity and PV single-amount formulas are the same ones used in capital budgeting (NPV analysis) and loan valuation.
Bond pricing, bond valuation, present value of bonds, discount on bonds payable, contra-liability, coupon rate vs market rate, stated rate vs effective rate, PV of annuity, PV of single amount, bond issuance journal entry, bonds issued at a discount, face value, par value, yield to maturity, semi-annual interest, FIN 301, intermediate accounting