Accretion of a Discount

Accretion of a discount is the gradual increase in the recorded value of a bond or other debt instrument that was bought for less than its face value, so that its book value reaches face value by the maturity date. Each period's increase is treated as additional interest income, because the investor will receive the full face amount at maturity even though they paid less. Holders of zero-coupon bonds, Treasury bills and bonds bought in the secondary market below par all deal with accretion.

Accretion is the mirror image of amortisation of a premium. When a bond is bought above face value, its book value is written down over time, as described under amortization of bond premium; when it is bought at a bond discount, its value is written up. Both adjustments make reported interest reflect the bond's true yield rather than just its coupon.

Imagine buying a voucher today for $95 that can be exchanged for $100 in two years. You have not lost or gained anything the day you buy it, but by the end you will have made $5. Accretion is the accounting habit of recognising that $5 bit by bit over the two years, rather than all at once at the end, so your records show the voucher growing steadily towards its full value.

For a bond the logic is the same. The gap between what you paid and what you will get back at maturity is part of your return, just like the regular interest payments, so it is spread across the life of the bond.

There are two common approaches. The straight-line method spreads the discount evenly over the remaining periods. The constant-yield method, also called the effective interest rate method, applies the bond's yield to maturity to its current carrying value each period:

• $\text{CV}_{t-1}$ is the carrying value at the start of the period.
• $y$ is the yield to maturity per period, set at purchase.
• $C$ is the cash coupon received in the period.

Suppose an investor pays $950 for a two-year bond with a face value of $1,000 and a 4% annual coupon ($40 a year). The yield that equates the price with the cash flows is about 6.75%. In year one, interest income is $950 × 6.75% = $64.13; subtracting the $40 coupon leaves $24.13 of accretion, so the carrying value rises to $974.13. In year two, interest income is $974.13 × 6.75% = $65.75, accretion is $25.75, and the carrying value reaches $1,000 after rounding. Under straight-line accretion the investor would instead add $25 in each year.

Under both US GAAP and IFRS, debt securities held at amortised cost, such as held-to-maturity securities, must use the effective interest method unless the result is not materially different from straight-line. Accreted amounts are added to the carrying value of the investment and recorded as interest income in the income statement. Issuers do the reverse on the liability side: a company that sells bonds below par records a discount on bonds payable and recognises the discount as extra interest expense over the bond's life. Banks and insurers with large bond portfolios report substantial accretion income, which analysts watch because it is non-cash until maturity.

Tax rules separate two kinds of discount. Original issue discount (OID) arises when a bond is first sold below its redemption price; US holders generally must include a portion of OID in taxable income every year, even though they receive no cash for it, which is why zero-coupon bonds are often held in tax-advantaged accounts. Market discount arises when an investor buys an existing bond below its adjusted value in the secondary market, usually because market interest rates have risen. In the United States, market discount is generally taxed as ordinary interest when the bond is sold or matures, unless the holder elects to include it annually. Amounts below a small de minimis threshold may be treated as capital gain instead. Rules differ between countries, so investors check local guidance.

Accretion makes the reported return on a discounted bond match its economic yield. Without it, an investor would show low income during the bond's life and a large one-off gain at maturity, which would misstate performance in every period. For bank and fund managers, accretion also explains why the book value of a bond portfolio can rise even when market prices are flat. In tokenised bond markets, where government debt is issued or represented on blockchains, the same accounting applies: the token price may sit below face value, and holders' books still need to accrete the difference over time.

Accretion is a book entry, not cash. If the issuer defaults, the accreted amount may never be collected, and the investor may have paid tax on income they never received. Accretion also assumes the bond is held to maturity; if it is sold early, the sale price may be above or below the accreted value, producing a gain or loss. Callable bonds add complexity, because the effective maturity can change, and some rules require accretion to the earliest likely call date rather than the final maturity.