What it means
A bond promises fixed cash flows: periodic coupon payments at a stated rate on the face value, and repayment of the face value at maturity. Its price is what investors will pay for those cash flows, which depends on the return they require.
If the coupon rate equals the market rate the bond sells at par, if the market rate is higher, whether because rates rose between the bond's design and its issue or because the issuer set a low coupon deliberately, it sells at a discount, and if the market rate is lower it sells at a premium. The discount adjusts the investor's yield to the market rate: an investor who pays $919 for a $1,000 bond paying 6% earns 8%, because the coupons are a larger percentage of what was paid and there is an $81 gain at maturity.
For the issuer, the discount is a cost, since it has received less than it must repay, and the difference is in substance interest paid at maturity instead of in coupons. Accounting standards record the liability at the proceeds received, not at face value, and increase it each period by an interest expense calculated at the effective rate (the market rate at issue) on the carrying amount.
Because the effective rate exceeds the coupon rate, the interest expense exceeds the cash coupon, and the excess is added to the liability. Over the life of the bond the carrying amount rises from the proceeds to the face value, and the total interest expense equals the total coupons plus the discount.
The unamortised discount is presented as a deduction from the face value of the bonds on the balance sheet, so that the bonds are shown at their carrying amount. The effective interest method produces an interest expense that rises slightly each period as the carrying amount grows.
The straight-line method spreads the discount evenly, which is simpler and gives a similar answer for small discounts and short terms but understates interest early and overstates it later, so international standards require the effective interest method and United States standards permit straight-line only where the difference is immaterial. Issue costs, such as underwriting and legal fees, are treated like a discount: deducted from the proceeds and amortised through the effective rate.
The discount also affects the reported cost of debt. A company that describes its borrowing as "6% bonds" when it issued them to yield 8% is understating its cost of debt by a quarter, and analysts calculating interest cover or the weighted average cost of capital use the effective rate.
Where bonds are repurchased before maturity, the difference between the price paid and the carrying amount, including any unamortised discount, is a gain or loss on extinguishment. Zero-coupon bonds are the extreme case: no coupons at all, issued at a deep discount, with the entire return delivered at maturity, so the whole of the interest expense arises from amortising the discount.
The tax treatment of discounts varies by jurisdiction, and many systems allow the issuer to deduct the amortised discount as interest and require the investor to accrue it as income.
In practice
Real-world examples
Example 1
A utility designs a bond with a 5% coupon, but rates rise before the launch and investors require 5.6%, so the $200,000,000 issue prices at 97.4 and the company records a $5,200,000 discount to amortise over ten years.
Example 2
A company issues zero-coupon notes with a face value of $50,000,000 for $31,000,000, repayable in ten years, and records interest expense each year at the 4.9% effective rate with no cash coupon until maturity.
Example 3
A company buys back bonds with a carrying amount of $9,500,000 (face $10,000,000 less unamortised discount $500,000) for $9,700,000 and records a $200,000 loss on extinguishment.
Think of it
Bond discount is selling bonds for less than face value-the difference is extra interest cost over time.
Formula
Calculation
Issue price = Present value of coupons at the market rate + Present value of face value at the market rate
Discount on bonds payable = Face value minus Issue price
Interest expense for a period = Opening carrying amount x Effective rate per period
Discount amortisation for the period = Interest expense minus Cash coupon
Closing carrying amount = Opening carrying amount + Discount amortisation
Total interest cost over the life = Total coupons + Discount (+ Issue costs)
Worked example. A company issues $10,000,000 of five-year bonds with a 6% coupon paid semi-annually ($300,000 every six months) when the market rate for similar bonds is 8% (4% per half-year). There are ten half-year periods.
- Present value of coupons = $300,000 x annuity factor at 4% for 10 periods (8.1109) = $2,433,270
- Present value of face value = $10,000,000 / 1.04 to the power of 10 = $10,000,000 x 0.6756 = $6,755,640
- Issue price = $2,433,270 + $6,755,640 = $9,188,910; discount = $10,000,000 minus $9,188,910 = $811,090
- Entry at issue: debit cash $9,188,910; debit discount on bonds payable $811,090; credit bonds payable $10,000,000
Effective interest method, first two periods.
- Period 1: interest expense = $9,188,910 x 4% = $367,556; cash coupon $300,000; amortisation $67,556; carrying amount $9,256,466
- Period 2: interest expense = $9,256,466 x 4% = $370,259; coupon $300,000; amortisation $70,259; carrying amount $9,326,725
- The pattern continues; by period 10 the carrying amount reaches $10,000,000 and the final interest expense is about $396,200
- Total interest cost over five years = 10 x $300,000 + $811,090 = $3,811,090, an effective 8% a year on the amount actually borrowed, not the 6% coupon
Straight-line comparison. Amortisation of $811,090 / 10 = $81,109 a period, giving interest expense of $381,109 in every period: higher than the effective method early, lower later, with the same total. The effective method is the required one.Case study
Seen in the real world
This is a fictional, illustrative scenario. A manufacturing company's board approved $10,000,000 of five-year bonds with a 6% coupon, on the finance director's advice that 6% was cheaper than the bank's 7.5% term loan. By the time the bonds were issued, market rates for the company's credit quality had moved to 8%, and the bonds sold at $9,188,910, a discount of $811,090. The finance director reported the bonds as placed "at 6%", but the first year's interest expense came to about $738,000, not the $600,000 the board expected. The answer was the discount: the bonds cost 8% a year on the $9,188,910 actually borrowed, and the difference between that and the 6% coupon, about $138,000 in the first year, was being added to the liability.
The bank loan at 7.5%, passed over in favour of the bonds, would have cost less than their effective 8%. The board adopted two rules: borrowing proposals must be evaluated and reported on their effective rate, including discounts, premiums and issue costs, and board papers must show the total cash cost of a financing over its life alongside its headline rate. The finance director's note observed that the bonds had not been a bad decision, since rates had moved after the decision was made, but that describing 8% money as 6% money had been a bad report. The discount on bonds payable was the accounting entry that eventually told the board the truth.
Watch out
Common mistakes
- Describing the cost of discounted bonds by their coupon rate; the effective rate, which includes the amortisation of the discount and issue costs, is the true cost of borrowing.
- Recording the bonds at face value with the discount as an expense at issue, or amortising it straight-line when the effective interest method is required.
- Presenting the discount as an asset rather than as a deduction from the face value of the bonds, so that the liability is overstated and an asset with no value is shown.
Questions
People also ask
Why would a company issue bonds at a discount?
Usually because market rates rose between setting the coupon and issuing the bonds, or because the company set a round-number coupon slightly below the market. Sometimes deliberately, as with zero-coupon bonds, to defer the cash cost of borrowing to maturity.
What is the difference between a discount and a premium on bonds payable?
A discount arises when the coupon is below the market rate and the bonds sell below face value; it is amortised as additional interest expense. A premium arises when the coupon is above the market rate and the bonds sell above face value; it is amortised as a reduction of interest expense. In both cases the carrying amount converges on the face value at maturity.
How does the discount affect cash flow?
The proceeds at issue are lower than face value, which appears in financing cash flows. The periodic cash coupons are unaffected by the discount. At maturity the full face value is repaid. The amortisation of the discount is a non-cash component of interest expense, added back in the operating section of the cash flow statement.
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