CFA Level I · CFA Level I Exam

Fixed-Income Cash Flows and Types: formula sheet

Full chapter guide

Key formulas

Periodic coupon payment: Coupon per period = (coupon rate × par value) ÷ m; m is the number of coupon payments per year. Coupon rate is annual and quoted on par, not on price.
Annual coupon income: Annual coupon = coupon rate × par value; Use par value, never market price.
Number of remaining payments: Remaining payments = years to maturity × m; Check that the time is in years before multiplying.
Premium, par, discount: Price > par: premium. Price = par: par. Price < par: discount.; Price is quoted as a percentage of par, so 98.50 means 98.50% of par.
Current yield: Current yield = annual coupon ÷ bond price; Shows that coupon rate and yield differ unless price equals par.
Current yield: Current yield = Annual coupon ÷ Bond price; Use the annual coupon in currency terms. Use the price paid, not par. Ignores capital gain or loss.
Price-yield link to par: Price < par ⇒ YTM > current yield > coupon rate; Price > par ⇒ YTM < current yield < coupon rate; This ordering holds for a bond with a positive coupon and a remaining life of more than one period. At par all three are equal.
Bond price from YTM: PV = Σ [PMT ÷ (1 + r)^t] + FV ÷ (1 + r)^N; YTM is the r that makes PV equal the market price. r is per period; double a semiannual YTM for the bond-equivalent annual yield.
Investment grade cut-off: Investment grade: BBB- or higher (S&P, Fitch) or Baa3 or higher (Moody's); high yield: below; High yield is also called speculative grade or junk.
Tax on coupon interest: After-tax coupon = coupon × (1 − tax rate); Use when interest is taxed as ordinary income.
OID accretion (constant-yield method): Interest income for the period = beginning carrying value × yield at issue; accretion = interest income − coupon paid; Carrying value rises toward par. Taxable interest is the full interest income, not just the cash coupon, under a constant-yield rule.
Capital gain or loss on sale: Gain or loss = sale price − tax basis; Tax basis includes accreted OID for an issue-discount bond.
Covenant types: Affirmative = must do; Negative = must not do; Negative covenants restrict issuer actions and protect lenders.
Interest in a period: Interest = beginning balance × periodic rate; Use the rate per period. For semiannual payments, divide the annual rate by 2.
Principal repaid in a payment: Principal repaid = payment − interest; For a fully amortizing loan, the principal portions sum to the original principal.
Ending balance: Ending balance = beginning balance − principal repaid; Next period's interest is based on this balance.
Level payment (fully amortizing): Payment = PV × r ÷ [1 − (1 + r)^−n]; r is the rate per period and n the number of periods. On a calculator, use PV, N, I/Y and CPT PMT.
Balloon payment: Balloon = remaining balance after the last regular payment; Equals the future value of the loan less the future value of the payments made.
Bullet bond cash flows: Coupons = rate × principal each period; principal repaid once at maturity; No amortization before maturity.
FRN coupon rate: Coupon rate = reference rate + quoted margin; Use the annual rate, then divide by periods per year for the period coupon.
FRN coupon payment: Coupon = par × (reference rate + quoted margin) ÷ periods per year; Check whether the reference rate is quoted annually. A 6-month rate stated as annual still needs ÷ 2.
Fixed coupon payment: Coupon = par × coupon rate ÷ periods per year; Semiannual is the common exam case.
Zero-coupon bond price: Price = par ÷ (1 + r)^n; r is the periodic yield and n the number of periods. Return comes only from the discount. The return itself is r = (par ÷ price)^(1/n) − 1.
Capital-indexed bond: Adjusted principal = par × (1 + inflation); coupon = coupon rate × adjusted principal; Principal and coupon both rise with inflation when the coupon rate is fixed.
Interest-indexed bond: Coupon = (coupon rate + inflation adjustment) × original par; Principal repaid is the original par, unchanged.
PIK principal growth: New principal = old principal × (1 + coupon rate ÷ periods per year); Applies when the coupon is paid in additional bonds.
Callable bond value: Callable bond = Option-free bond − Call option; Issuer owns the call, so the investor's bond is worth less. Yield is higher.
Putable bond value: Putable bond = Option-free bond + Put option; Investor owns the put, so the bond is worth more. Yield is lower.
Convertible bond value (floor and option): Convertible bond = Straight bond value + Conversion option value; Price is at least the higher of the straight bond value and the conversion value.
Conversion price: Conversion price = Par value ÷ Conversion ratio; Share price at which par value equals conversion value.
Conversion value: Conversion value = Share price × Conversion ratio; What the bond is worth if converted now.
Market conversion price: Market conversion price = Convertible bond price ÷ Conversion ratio; Effective price paid per share if you buy the bond and convert.
Conversion premium: Conversion premium per share = Market conversion price − Current share price; premium % = that ÷ Current share price; Extra cost of buying shares through the bond versus buying shares directly.
Effect of interest rate changes on options: Rates fall: call more valuable to issuer; put less valuable to holder. Rates rise: put more valuable to holder; call less valuable to issuer; When rates fall, the issuer is more likely to call and the put is less likely to be exercised. When rates rise, the put is more likely to be exercised and the call is less likely to be exercised.

Quick revision

A bond's basic features are issuer, maturity, par value, coupon rate and frequency, and currency.
A bullet bond repays all principal at maturity; an amortising bond repays principal over its life.
A fully amortising bond has a balance of zero at maturity; a partially amortising bond leaves a balloon payment.
A sinking fund provision requires the issuer to retire part of the issue on a schedule.
A floating-rate note pays a reference rate plus a spread.
A step-up coupon rises on a preset schedule; a zero-coupon bond is issued at a discount and pays par at maturity.
A payment-in-kind coupon pays interest with additional bonds rather than cash.
A callable bond gives the option to the issuer, so investors require a higher yield.
A putable bond gives the option to the investor, so it is worth more than an otherwise identical straight bond.
A convertible bond lets the investor swap into the issuer's shares; a warrant is a separate right to buy shares.
Affirmative covenants require actions; negative covenants restrict actions.
The bond indenture or trust deed is the legal contract between issuer and bondholders.

Common mistakes

Calculating the coupon from the market price instead of par value. Fix: Coupon = coupon rate × par value. Price never enters the coupon calculation.
Forgetting to divide by the payment frequency. Fix: Always ask how many payments a year, then divide the annual coupon by that number.
Dividing the coupon by par to get current yield. Fix: Current yield uses the market price in the denominator. Coupon rate uses par.
Thinking current yield equals total return. Fix: Remember it ignores the gain or loss at maturity and the time value of money. Only YTM captures them (under its assumptions).
Calling a restriction on dividends an affirmative covenant. Fix: Restrictions and limits are negative covenants. Obligations to do something are affirmative.
Thinking the trustee works for the issuer. Fix: The trustee acts for bondholders and monitors the issuer's compliance.
Treating a balloon payment as an extra payment on top of full repayment. Fix: The balloon is the remaining balance due at maturity. Regular payments plus the balloon repay the loan.
Computing interest on the original principal in every period of an amortizing loan. Fix: Always use the beginning balance of that period. Interest falls as the balance falls.
Forgetting to divide the annual FRN rate by the number of periods. Fix: Always write the periods per year and divide before multiplying by par.
Using the reference rate from the payment date instead of the reset date. Fix: The coupon uses the reference rate set at the beginning of the period (in advance) and is paid at the end of the period (in arrears). Use the rate set at the start of the period, not the rate on the payment date.

Exam tips

Expect straightforward items: identify a feature from a description or compute a coupon. Read the stem once for features and a second time for what is asked.
Quoted prices are percentages of par. Convert to currency amounts only if the question asks for it.
Wrong options are often built from the common errors: using price instead of par, or skipping the frequency division. Match your answer against these traps.
Know that par, coupon rate, frequency and maturity are fixed by contract, while price and yield change. Many conceptual items test this split.
There is no penalty for a wrong answer, so if time is short, eliminate the option that uses price for the coupon and pick from the rest.
Questions often test only the direction of the relationship between coupon rate, current yield and YTM. Use the par rule and skip the calculator.
Learn the rating boundary exactly: BBB-/Baa3 is the lowest investment grade.
Read for hidden clues in the stem: issuer name, currency and maturity tell you the segment.