CFA Level I · CFA Level I Exam

Fixed-Income Instrument Features: formula sheet

Full chapter guide

Key formulas

Coupon per period: Coupon payment = Par value × Annual coupon rate ÷ Number of payments per year; The coupon is based on par value, never on the market price.
Annual coupon: Annual coupon = Par value × Coupon rate; Divide by frequency to get each payment.
Premium or discount: Price > Par: premium. Price < Par: discount. Price = Par: par bond.; Price is usually quoted as a percentage of par.
Tenor: Tenor = Maturity date − Settlement (valuation) date; Tenor is the remaining life, not the original maturity.
Current yield (link to pricing): Current yield = Annual coupon ÷ Bond price; Uses price, unlike coupon rate, which uses par.
Current yield: Current yield = annual coupon payment ÷ bond price; Use the flat (clean) price. Ignores capital gain or loss and time value.
Bond price from YTM: PV = Σ [PMT ÷ (1 + r)^t] + FV ÷ (1 + r)^N; r is the periodic yield. YTM is the r that makes PV equal the market price.
Periodic and annual yield (bond-equivalent basis): Annual YTM = periodic rate × number of periods per year; A semiannual bond quoted on a bond-equivalent basis: double the six-month rate. The result is a stated annual rate, not an effective annual rate.
Floating-rate note coupon: Coupon rate = reference rate + quoted margin; Reset date sets the rate. Coupon is usually paid in arrears, at the end of the period.
Zero-coupon bond price: Price = par ÷ (1 + r)^N; N is in periods. For semiannual compounding, N = years × 2 and r = annual rate ÷ 2.
Price relationships: Discount: coupon rate < current yield < YTM; Premium: coupon rate > current yield > YTM; At par all three are equal.
Interest in a period: Interest = Beginning balance × periodic rate; Applies to every structure. Use the periodic rate (annual rate ÷ payments per year).
Principal repaid in a period: Principal repaid = Total payment − Interest; For level-payment amortizing bonds, the total payment stays fixed while the interest part falls.
Ending balance: Ending balance = Beginning balance − Principal repaid; Carry this forward as the next period's beginning balance.
Level payment (fully amortizing): PMT = PV × r ÷ [1 − (1 + r)^−n]; r is the periodic rate and n is the number of periods. On a calculator, solve for PMT with FV = 0.
Balloon payment (partially amortizing): Balloon = Remaining balance at maturity after the last regular payment; On a calculator, set FV to 0 for full amortization. A nonzero balance means a partial structure.
Bullet bond cash flows: Coupon each period = Face value × coupon rate ÷ payments per year; principal = Face value at maturity; Principal does not change before maturity.
Callable bond value: Callable bond value = Straight bond value − Value of call option; The issuer owns the call, so the investor's bond is worth less.
Putable bond value: Putable bond value = Straight bond value + Value of put option; The investor owns the put, so the bond is worth more.
Convertible bond value: Convertible value = Straight bond value + Value of call option on the stock; The holder owns the conversion option.
Conversion price: Conversion price = Par value ÷ Conversion ratio; Price per share paid implicitly through conversion.
Conversion value: Conversion value = Share price × Conversion ratio; What the bond is worth if converted now.
Conversion premium: Conversion premium = Bond market price − Conversion value; Premium ÷ conversion value gives the premium ratio. Check the question for which form is asked.
Minimum convertible value: Floor = higher of (Straight bond value, Conversion value); The market price of a convertible normally sits at or above this floor.
Affirmative vs negative covenants: Affirmative = what the issuer MUST do; Negative = what the issuer must NOT do; Negative covenants restrict flexibility more and protect bondholders more.
Taxable-equivalent yield: Taxable-equivalent yield = tax-exempt yield ÷ (1 − tax rate); Use it to compare a tax-exempt municipal bond with a taxable bond. The tax rate is the investor's marginal rate, as a decimal.
After-tax yield: After-tax yield = taxable yield × (1 − tax rate); The reverse comparison: convert the taxable bond's yield to after-tax.
OID accretion (constant-yield method): Interest income for the period = beginning carrying value × yield per period; accretion = interest income − coupon; Rules differ by jurisdiction; some accrue the discount, others use straight-line. Follow the question.

Quick revision

A bond's contract sets issuer, maturity, par value, coupon rate and frequency, and currency.
Par value is the principal repaid at maturity; coupon payment = coupon rate × par value ÷ payments per year.
Floating-rate coupon = reference rate + spread; the cash flows move with the reference rate.
A zero-coupon bond pays no coupons and is issued at a discount to par.
A step-up coupon rises on a schedule set in advance.
A bullet bond repays all principal at maturity; an amortizing bond repays principal over its life.
A fully amortizing bond has zero balance at maturity; a partially amortizing bond leaves a balloon payment.
A call option benefits the issuer; a put option benefits the bondholder.
A conversion option lets the holder exchange the bond for shares, so the investor typically accepts a lower coupon.
Affirmative covenants require actions; negative covenants restrict actions; both protect lenders.
Features that favour the issuer usually require a higher yield; features that favour the investor allow a lower yield.
Always read who holds the option before judging its effect.

Common mistakes

Calculating the coupon on the market price instead of par. Fix: Coupon = par × coupon rate. Price only affects yield, not the coupon.
Paying the full annual coupon every period for a semiannual bond. Fix: Always divide the annual coupon by the number of payments per year.
Using current yield as if it were YTM. Fix: Current yield ignores the pull to par. Use it only when the question asks for it by name.
Forgetting to double N and halve the rate for semiannual bonds. Fix: Always write N = years × frequency and PMT = annual coupon ÷ frequency before keying in.
Treating coupon as constant in an amortizing bond Fix: In amortizing structures, interest falls as the balance falls. Always apply the rate to the beginning balance.
Using the annual rate on monthly or semiannual payments Fix: Divide the annual rate by payments per year and multiply years by payments per year before using PMT or interest calculations.
Saying a callable bond has a lower yield than an option-free bond. Fix: The investor is giving up something, so demands a higher yield and pays a lower price.
Treating conversion price as the current share price. Fix: Conversion price = par ÷ conversion ratio. It is a fixed contract term. Conversion value uses the market share price.
Calling a restriction on dividends an affirmative covenant. Fix: Classify by what the issuer does: if it restricts action, it is negative.
Thinking the trustee guarantees repayment. Fix: The trustee monitors and enforces the indenture on behalf of bondholders but does not repay the debt. The issuer owes the payments.

Exam tips

Questions are three-option MCQs, so identify the trap option that uses price instead of par or ignores frequency.
Read whether the rate is annual and how often it is paid before calculating.
Know definitions precisely: indenture, tenor, par, zero-coupon, dual-currency.
Numerical options run smallest to largest, so check whether your answer is the annual or periodic coupon.
There is no penalty for wrong answers, so never leave a question blank.
Questions often ask you to rank coupon rate, current yield and YTM. Check price against par first and you can answer without a calculator.
Read the coupon structure closely. Step-up (scheduled) and floating (reference rate + spread) are often placed side by side as distractors.
A zero-coupon bond always trades below par before maturity when yields are positive. Use that to remove wrong options.