What is accretion of discount (plain-language definition)
– Accretion of discount is the gradual increase in the book value (carrying value) of a bond that was bought below its face (par) value. As the bond moves toward its maturity date, its carrying value rises until it equals par at maturity.
Key terms (short definitions)
– Par value (face value): the amount repaid to the bondholder at maturity (e.g., $100 or $1,000).
– Coupon rate: the bond’s stated annual cash interest, usually expressed as a percent of par.
– Discount bond: a bond purchased for less than par.
– Yield to maturity (YTM): the single discount rate that makes the present value of the bond’s future cash flows equal to its current price; it’s the bond’s actual expected annual return if held to maturity.
– Constant-yield method: a way to spread the discount accretion so that the carrying value grows at the bond’s yield each period (this is the IRS-required method for many tax purposes).
– Straight-line method: a simple approach that spreads the total discount evenly across the remaining periods until maturity.
How accretion works (conceptual)
– All bonds mature at par. If you buy below par, you expect capital gain equal to (par − purchase price) by maturity.
– Under straight-line accretion, that gain is allocated equally each period.
– Under the constant-yield method, the bond’s carrying value increases by the period’s imputed interest (prior carrying value × YTM per period) and then is reduced by any coupon actually paid. The difference between imputed interest and coupon is the accretion for that period. Over time this produces an increasing accretion amount and a carrying value that compounds at the YTM.
Checklist — steps to account for accretion
1. Confirm whether the bond was purchased at a discount (purchase price < par).
2. Decide which method applies:
– For tax OID rules and many reporting situations use the constant-yield (effective interest) method.
– For simple accounting/informal tracking you might use straight-line (but check tax/GAAP requirements).
3. If using constant-yield:
– Solve for YTM using the bond price and cash flows (coupon payments and par at maturity).
– Build an amortization schedule: for each period compute imputed interest = prior carrying value × periodic YTM; accretion = imputed interest − coupon (if coupon is paid that period); new carrying value = prior carrying value + accretion.
4. Reconcile the carrying value at maturity to par (small rounding differences can occur).
5. Track tax reporting requirements (OID rules, reporting of interest income vs accretion) and any special features (callable, putable, tax-exempt).
6. If you sell before maturity, the realized gain/loss depends on sale price vs your adjusted carrying value.
Formula summary
– Bond price (present value) equation used to find YTM:
Price = Σ (Coupon_t / (1 + r)^t) + Par / (1 + r)^N
where r is the periodic yield and N is the number of periods.
– Constant-yield accretion (per period):
Imputed interest = Prior carrying value × r
Accretion = Imputed interest − Coupon_paid (if coupon is paid that period)
New carrying value = Prior carrying value + Accretion
– Straight-line accretion (per period):
Accretion_per_period = (Par − Purchase_price) / Remaining_periods
Worked numeric example (small, concrete)
Assumptions
– Par = $100
– Coupon = 2% annual → coupon payment = $2 per year
– Purchase price = $75
– Term = 10 years
– Assume annual compounding and annual coupon payments
Step A — approximate YTM
Use the price formula and solve for r (YTM). A simple approximate formula gives:
YTM ≈ [annual coupon + (Par − Price)/Years] / [(Par + Price)/2]
Plugging numbers:
YTM ≈ [2 + (100 − 75)/10] / [(100 + 75)/2] = (2 + 2.5) / 87.5 = 4.5 / 87.5 ≈ 0.0514 → about 5.14% (refine numerically; solving the exact present-value equation gives roughly 5.3% annual).
Step B — first-year constant-yield accretion (using r ≈ 5.30%)
– Starting carrying value = $75.00
– Imputed interest = 75.00 × 0.0530 ≈ $3.975
– Coupon actually paid = $2.00
– Accretion for year 1 = 3.975 − 2.00 = $1.975
– Carrying value at end of year 1 = 75.00 + 1.975 = $76.975
Year 2 (illustrates compounding)
– Imputed interest = 76.975 × 0.0530 ≈ $4.079
– Coupon = $2.00
– Accretion = 4.079 − 2.00 = $2.079
– Carrying value end of year 2 = 76.975 + 2.079 ≈ $79.054
Compare with straight-line for contrast
– Straight-line accretion per year = (100 − 75) / 10 = $2.50 each year (constant each year, no compounding).
Special considerations and common complications
– Tax rules: the IRS has specific treatments for Original Issue Discount (OID) and generally requires the constant-yield method for accrual to compute adjusted basis for tax purposes. Check IRS guidance when filing.
– Coupons vs imputed interest: coupon receipts are taxed as interest in the year received; OID accruals may be taxable as interest even if cash is not yet received.
– Secondary-market purchases: if you buy a bond between coupon dates you may pay accrued interest; the tax and basis adjustments differ depending on trade terms and local rules.
– Embedded options (callable, puttable) change expected cash flows and therefore the YTM and accretion pattern.
– Market price vs carrying value: market prices fluctuate; accretion tracks the contractual path to par if the bond is held to maturity, not market value.
Sources for further reading
– Investopedia — “Accretion of Discount” (overview)
https://www.investopedia.com/terms/a/accretion-of-discount.asp
– Internal Revenue Service — Tax Topic: Original Issue Discount (OID)
https://www.irs.gov/taxtopics/tc404
– U.S. Securities and Exchange Commission — Investor Bulletin: Bonds (basics)
https://www.investor.gov/introduction-investing/investing-basics/investment-products/bonds
– FINRA — Bonds: A Primer for Individual Investors (practical considerations)
https://www.finra.org/investors/learn-to-invest/types-investments/bonds
Educational disclaimer
This explainer is informational and educational only. It does not constitute personalized investment, tax, or accounting advice. For decisions that affect taxes, regulatory reporting, or significant capital allocation, consult a qualified tax advisor, accountant, or licensed financial professional.