What is a bond discount?
A bond discount exists when a bond’s current market price is below its face (par) value—the amount the issuer repays at maturity, commonly $1,000 for many corporate and municipal issues. Buying a bond at a discount gives the investor two sources of return: the periodic coupon (interest) payments and the capital gain realized when the bond is repaid at par.
Key definitions
– Par value (face value): The amount the issuer promises to pay at maturity.
– Coupon rate: The annual interest rate stated on the bond, used to calculate periodic coupon payments.
– Market yield (market interest rate): The prevailing rate investors require for a bond of similar risk and maturity.
– Yield to maturity (YTM): The internal rate of return that equates the bond’s current price to the present value of its future coupon payments plus principal.
– Bond discount: Par value minus market price (if positive). Expressed in dollars or as a percentage of par.
Why bonds trade at a discount
– Market interest rates rise above the bond’s coupon rate. Existing bonds with lower coupons become less attractive; their prices drop until their effective yield matches the market yield.
– Credit deterioration. A downgrade or greater perceived default risk pushes price below par.
– Supply/demand imbalances and liquidity concerns can lower prices.
– Many zero-coupon bonds are issued at a deep discount because they pay no periodic coupons; the return comes entirely from the difference between purchase price and par.
How price is determined (basic formula)
A bond’s market price equals the present value (PV) of its expected future cash flows:
Price = sum_{t=1 to n} [Coupon_t / (1 + r)^t] + [Par / (1 + r)^n]
where:
– Coupon_t = cash coupon in period t (for level coupons, same each period)
– r = market yield per period (adjust annual rate for coupon frequency)
– n = total number of periods
Step-by-step checklist before buying a discounted bond
– Confirm par value and maturity date.
– Check the coupon rate and payment frequency (annual, semiannual, etc.).
– Determine the current market yield or the yield you require.
– Compute price via the PV formula or find market price quotes.
– Check credit rating and recent rating actions.
– Consider call provisions (issuer may redeem early) and tax treatment.
– Compare yield to maturity with relevant benchmark yields (e.g., Treasuries).
– Assess liquidity—how easily you can sell before maturity.
– Review total return drivers: coupons + expected price change to par.
Worked numeric example (semiannual coupons)
Scenario: A bond has
– Par value = $1,000
– Coupon rate = 3.5% annually, paid semiannually → coupon per period = (3.5%/2) × $1,000 = $17.50
– Time to maturity = 3 years → n = 3 × 2 = 6 periods
– Market annual yield = 5%, so yield per period r = 5%/2 = 2.5% = 0.025
1) Present value of principal:
PV_principal = 1000 / (1.025)^6 ≈ $862.30
2) Present value of coupons:
Compute each coupon’s PV and sum:
PV_coupon = 17.50/(1.025)^1 + 17.50/(1.025)^2 + … + 17.50/(1.025)^6
Evaluating the six terms gives approximately $96.39
3) Market price:
Price = PV_principal + PV_coupon ≈ 862.30 + 96.39 = $958.69
4) Discount and discount rate:
Dollar discount = Par − Price = 1,000 − 958.69 = $41.31
Discount as a percentage of par = 41.31 / 1,000 = 4.13%
Interpretation: Because the market yield (5%) exceeds the bond’s coupon rate (3.5%), the bond sells below par. An investor who buys at $958.69 will receive the same coupon payments as before plus the $41.31 capital gain at maturity (assuming no default).
Practical notes
– Yield to maturity gives the most complete single-number comparison between bonds with different coupons or prices; use a financial calculator or spreadsheet for YTM.
– If a bond is callable, the issuer could redeem it before maturity, which alters potential capital gain/loss.
– Taxes and transaction costs affect net return; check tax treatment for bond interest and capital gains.
Reputable references
– Investopedia — Bond Discount: https://www.investopedia.com/terms/b/bond-discount.asp
– U.S. Securities and Exchange Commission (SEC) — Investor Bulletin: Bonds: https://www.sec.gov/reportspubs/investor-publications/investorpub-bondshtm.html
– Financial Industry Regulatory Authority (FINRA) — Bond Basics: https://www.finra.org/investors/learn-to-invest/types-investments/bonds
Brief educational disclaimer
This explainer
Brief educational disclaimer This explainer is for educational purposes only and does not constitute investment, tax, or legal advice. Nothing here is a recommendation to buy or sell any security. Before acting, consult a licensed financial professional and read official prospectuses and tax guidance.
Quick practical checklist — evaluating a discount bond
– Confirm bond details: issuer, face value (par), coupon rate, coupon frequency, maturity date, call provisions.
– Compute current yield and approximate yield to maturity (YTM) to compare with alternatives (see formulas below).
– Check credit risk and recent ratings (S&P, Moody’s, Fitch) and any issuer news.
– Confirm liquidity: bid-ask spreads and typical trade sizes for that issue.
– Check tax treatment: is interest taxable at federal/state levels? Are there tax-exempt features (e.g., municipal bonds)?
– Check transaction costs and how they affect net yield.
– Consider reinvestment risk of coupons and, if callable, the possibility of early redemption.
Key formulas and how to compute YTM
– Current yield = annual coupon payment / market price.
– Approximate YTM (annual) — quick rule of thumb:
YTM ≈ [C + (F − P) / n] / [(F + P) / 2]
where C = annual coupon ($), F = face value, P = price paid, n = years to maturity.
This approximation is useful for a quick comparison but is not exact for coupons paid more than annually.
– Exact YTM (solving the present-value equation):
P = Σ (C_t / (1 + y)^{t}) + F / (1 + y)^{N}
where C_t are coupon payments at each period, F is face value at maturity, N is number of periods, and y is the periodic yield. Solve for y (usually numerically). Annualize y according to payment frequency.
Excel / spreadsheet and calculator tips
– Excel YIELD function (for bond priced between settlement and maturity):
=YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis])
Example inputs must use Excel date cells for settlement and maturity.
– Using RATE for periodic-yield solving:
For semiannual coupons: =RATE(nper, -pmt, -pv, fv) * periods_per_year
Example: face $1,000, 5% coupon (semiannual = $25 per period), price $950, maturity 5 years → nper = 10, pmt = 25, pv = -950, fv = 1000
Then =RATE(10,25,-950,1000)*2 returns the annual YTM.
Worked numeric example (approximation)
– Inputs: face F = $1,000; coupon = 5% → C = $50; price P = $950; years n = 5.
– Approximate YTM = [50 + (1000 − 950) / 5] / [(1000 + 950) / 2] = [50 + 10] / 975 = 60 / 975 = 6.15% (annual, approximate).
– Use Excel/financial calculator for the exact YTM — the exact annual YTM will be close but typically requires solving the PV equation.
Special considerations
– Callable bonds: issuer can redeem early (call). Use yield to worst (lower of YTM and yield to call) for conservative comparison.
– Accrued interest and settlement: bonds trade with accrued interest; price quotes may be clean (ex-accrued) versus dirty (including accrued interest). Confirm which price you’re using.
– Tax and after-tax yield: convert yields to after-tax equivalents if comparing taxable and tax-exempt bonds. After-tax yield = pre-tax yield × (1 − marginal tax rate). For municipal bonds, consider federal and state tax differences.
– Transaction costs and liquidity: wide bid-ask spreads reduce realized return, particularly for retail-sized trades in less liquid issues.
– Reinvestment risk: coupons received may be reinvested at different rates; this affects total return compared with YTM assumptions.
Where to look for authoritative information
– Investopedia — Bond Discount: https://www.investopedia.com/terms/b/bond-discount.asp
– U.S. Securities and Exchange Commission (SEC) — Bonds investor bulletin: https://www.sec.gov/reportspubs/investor-publications/investorpub-bondshtm.html
– Financial Industry Regulatory Authority (FINRA) — Bond basics: https://www.finra.org/investors/learn-to-invest/types-investments/bonds
– Internal Revenue Service (IRS) — Topic on capital gains, interest
– Internal Revenue Service (IRS) — Publications on original-issue discount (OID), market discount, and investment income: https://www.irs.gov/publications/p550
Practical checklist when evaluating a bond bought at a discount
1. Confirm type of discount
– Original-issue discount (OID): discount at initial issuance. Accrues and is taxed as interest as it accrues under IRS rules.
– Market discount: bought below par in the secondary market. Tax treatment differs from OID (see IRS guidance).
2. Determine cash flows you will actually
2. Determine cash flows you will actually receive
– List the scheduled coupon payments (amount, frequency, payment dates) and the maturity (face/par value returned at maturity).
– If the bond is callable, convertible, or has a sinking-fund provision, list the earliest dates and prices at which the issuer can redeem or change the bond — those change your expected cash flows.
– Note accrued interest at purchase: secondary‑market prices are quoted clean (without accrued interest) or dirty (including accrued interest). Confirm whether the price you pay includes accrued interest and how settlement date affects your first coupon receipt.
3. Compute basic yield measures (quick checks)
– Current yield = (annual coupon payment) / (purchase price). Use this to compare simple income rates across bonds.
– Approximate yield to maturity (YTM) for a fixed‑rate bond (annual coupons): YTM ≈ [C + (F − P)/n] / [(F + P)/2], where C = annual coupon, F = face value, P = purchase price, n = years to maturity. This is an approximation; use a financial calculator or spreadsheet for the exact internal-rate-of-return (IRR).
– Yield to worst = the lowest yield possible assuming issuer exercises options (calls, sinking fund). Always compute YTW for callable issues.
Worked numeric example
– Suppose face F = $1,000, annual coupon rate = 5% → C = $50. Purchase price P = $950. Time to maturity n = 5 years.
– Current yield = 50 / 950 = 5.263%.
– Approximate YTM = [50 + (1,000 − 950)/5] / [(1,000 + 950)/2] = [50 + 10] / 975 = 60 / 975 = 6.154% (approximate).
– Use Excel function =YIELD(settlement, maturity, rate, pr, redemption, frequency) or a financial calculator to get the precise YTM (solves the IRR of the bond cash flows).
4. Understand taxation (confirm classification first)
– Original-issue discount (OID): if the bond was issued below par, the untaxed portion generally accrues and is treated as ordinary interest income as it accrues under IRS rules. See IRS guidance for allocation.
– Market discount: if you buy an existing bond in the secondary market below par, that difference is generally treated differently from OID. Market discount may be taxed as ordinary income to the extent of accrued market discount when you sell or when the bond is redeemed (or you can elect to include market discount as it accrues). Check IRS Publication 550 for details and elections.
– State and local tax treatment can differ; confirm with state rules or a tax adviser.
5. Create an amortization schedule (cash-flow and tax tracking)
– Produce a schedule that shows each coupon, principal repayment (if amortizing), carrying value, and increase in accreted discount (if applicable) for each period until maturity or call.
– If you plan to hold until maturity, schedule helps project realized cash receipts and the capital gain at redemption. If you plan to sell sooner, track accrued market discount for tax purposes.
– Use spreadsheet templates or bond functions to generate exact periodic accruals (constant-yield method).
6. Check credit, liquidity, and covenant risk
– Rating agencies (Moody’s, S&P, Fitch) provide credit opinions. Read the rating rationale and any recent changes. Lower-rated bonds often offer higher yields but carry greater default risk.
– Liquidity: check average daily volume, bid–ask spreads, and dealers active in the issue. Wider spreads increase trading costs and execution risk.
– Covenants/indenture: for corporate and municipal bonds, read key covenants (restrictive clauses, events of default, collateral, seniority/subordination). These affect recovery if the issuer defaults.
7. Model interest-rate sensitivity and scenarios
– Compute duration and convexity to estimate how price would change for a given parallel shift in interest rates. Duration ≈ weighted average time to cash flows and is measured in years. Shorter duration → less price sensitivity.
– Run scenario analyses: rising-rate scenario, call scenario (issuer calls if rates fall), issuer stress (rating downgrade), and early-sale scenario (liquidity spread widens). Quantify cash-flow and price implications for each.
8. Account for transaction and operational details
– Confirm settlement date and whether you’ll receive the next coupon (buyer vs seller of record rules).
– Include trading fees, dealer markups, and any custody or platform charges in your total-cost calculation.
– Verify tax lot and cost basis reporting procedures with your broker for accurate future tax reporting.
9. Monitor and review
– After purchase, monitor issuer news, interest‑rate environment, and any upcoming call dates or covenant triggers.
– Recompute yields-to-worst and scenario P&L periodically or when material news occurs.
– Keep detailed records of purchase price, accrued interest paid, and any elections (e.g., market-discount accrual election) for tax reporting.
Quick practical checklist (summary)
– Confirm discount type: OID vs market discount.
– Verify actual cash flows: coupons
– Verify actual cash flows: coupons (amount, frequency), final principal repayment, and whether any principal‑repayment schedule, sinking‑fund, or amortizing feature applies.
– Check embedded options: call dates/prices, put features, conversion terms, and any step‑up coupon provisions that change future cash flows.
– Confirm accrued interest handling: who pays it (buyer or seller), how it’s calculated (day‑count convention), and the settlement date.
– Determine day‑count convention used (e.g., actual/actual, 30/360) — this affects accrued interest and yield calculations. Ask your broker or read the prospectus if unsure.
– Tax classification: confirm whether the discount originates at issuance (original issue discount, OID) or arises in the secondary market (market discount). Each has different tax timing rules.
– Recordkeeping: save trade confirmations showing clean price, accrued interest paid, trade date, settlement date, and the broker’s cost‑basis report format.
– Reconcile total cash outlay: clean price + accrued interest + commissions/fees = cash paid at settlement.
– Post‑trade monitoring: track issuer credit news, interest‑rate shifts, and nearing call or maturity dates; update yield‑to‑worst and scenario P&L when facts change.
Worked numeric example (simple, illustrative)
Assumptions
– Face value (F) = $1,000.
– Annual coupon rate = 5% (C = $50 per year).
– Years to maturity (n) = 5.
– Market clean price (P) = $950.
– Annual coupons, no embedded options.
Step 1 — current yield
Current yield = annual coupon / price = 50 / 950 = 0.05263 = 5.263%.
Step 2 — approximate yield to maturity (YTM)
A simple approximation for YTM:
YTM ≈ [C + (F − P)/n] / [(F + P)/2]
Plugging the numbers:
YTM ≈ [50 + (1,000 − 950)/5] / [(1,000 + 950)/2]
YTM ≈ [50 + 10] / 975 = 60 / 975 = 0.06154 = 6.154%.
Interpretation: YTM is higher than the coupon because you bought at a discount. Exact YTM requires solving the bond‑price equation numerically.
Step 3 — rough annual discount amortization (for bookkeeping)
Total discount = F − P = $50. Over 5 years, a straight‑line approximation would be $10 per year added to cost basis (note: tax rules typically require a constant‑yield method, not straight‑line; this is for quick bookkeeping only).
Key formulas (reference)
– Clean bond price (present value of cash flows):
P = Σ_{t=1..n} [C_t / (1 + y)^t] + F / (1 + y)^n
where C_t = coupon at time t, y = yield per period, F = face value.
– Accrued interest (general concept):
Accrued interest = coupon_amount × (days_since_last_coupon / days_in_coupon_period)
Note: Use the bond’s day‑count convention; the numeric denominator depends on that convention.
– Approximate YTM (as used above):
YTM ≈ [C + (F − P)/n] / [(F + P)/2]
Use this only as a quick estimate; solve the price equation for exact YTM.
Tax and reporting summary (practical points)
– Original Issue Discount (OID): If the bond was issued at a discount to par at original issuance, the issuer’s prospectus and the IRS OID rules determine how that discount is accrued and taxed over time (typically as ordinary income recognized
over the life of the issue using the issuer’s stated accrual method (commonly the constant‑yield or “effective interest” method). The issuer and your broker normally report OID on Form 1099‑OID; you must include the accrued OID in income as reported.
Market discount (secondary‑market discount): if you buy a bond in the secondary market for less than its adjusted issue price (usually less than face value when the bond was not originally issued at a discount), the difference is “market discount.” By default, market discount is treated as ordinary income when realized — that is, when you sell the bond or it is redeemed — to the extent of the recognized gain. You can, however, elect to currently include market discount in income as it accrues; that election generally changes timing and character of recognition, so check IRS rules or a tax advisor before choosing it.
Accrued interest and the “dirty” versus “clean” price: when bonds trade between coupon dates, the buyer pays the seller the quoted clean price plus accrued interest (the “dirty” price). The buyer receives the full next coupon from the issuer. For tax purposes, the accrued interest paid to the seller is not taxable interest to the buyer at purchase — instead, it is treated as a basis adjustment (or as a deduction against the coupon when received, depending on circumstances and the bond type). Brokers normally report coupon interest received on Form 1099‑INT and OID on Form 1099‑OID; sales and redemptions appear on Form 1099‑B.
Practical checklist for recordkeeping and reporting
– Save trade confirmations showing: trade date, settlement date, clean price, accrued interest paid, and settlement amount (dirty price).
– Track each coupon receipt (