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CFA Level I Exam · Fixed-Income Bond Valuation: Prices and Yields

Yield Measures for Fixed-Rate Bonds: YTM, YTC and YTW

Updated 7 October 2026 · Fact-checked

Yield measures turn a bond's price into a return. Current yield is annual coupon ÷ price. Yield to maturity is the discount rate that sets the present value of all promised cash flows equal to price. Yield to call does the same to a call date. Yield to worst is the lowest of these.

Understand Yield Measures for Fixed-Rate Bonds

A bond's price and its yield are two ways of describing the same thing. Given the price, the coupon, the maturity and the redemption amount, you can work out the single discount rate that makes the cash flows worth that price. That rate is the yield to maturity (YTM). It is the internal rate of return on the bond if you buy it today.

Current yield is much simpler. It is the annual coupon divided by the bond's flat price. It ignores the gain or loss you get as the bond moves to par and ignores time value. So it only describes coupon income. For a bond at par, current yield equals YTM. For a discount bond, YTM is above current yield. For a premium bond, YTM is below current yield.

YTM rests on assumptions: you hold the bond to maturity, the issuer pays every cash flow in full and on time, and you reinvest coupons at the YTM. Real returns differ if any of these fail.

For a callable bond, the issuer may redeem early. Yield to call (YTC) uses the call date as the end date and the call price as the redemption amount. Yield to worst (YTW) is computed for every possible call date and for maturity. You then take the lowest. A premium callable bond tends to have its YTW at a call date. A discount bond tends to have its YTW at maturity, because the issuer will not call a bond below par.

Yields are quoted on a periodicity. A semiannual bond has a periodic rate that you multiply by 2 to get an annual rate. This is the bond-equivalent yield, which is not compounded. To compare bonds with different payment frequencies, convert them to the same periodicity using the compounding formula. The street convention yield assumes payments arrive on their scheduled dates, even if that date is a weekend or holiday. The true yield adjusts for the actual business day and is usually slightly lower.

Key formulas to remember

Current yield
Current yield = annual coupon ÷ flat price
For a semiannual bond, annual coupon = 2 × the semiannual coupon. Use the flat price, not the full price.
Bond pricing equation (YTM)
PV = PMT/(1+r) + PMT/(1+r)² + … + (PMT + FV)/(1+r)ᴺ
Solve for r, the periodic yield. N is the number of periods and PMT is the coupon per period.
Annualizing a periodic yield
Annual yield (APR) = periodic yield × m
m = periods per year. This is the bond-equivalent yield for m = 2. No compounding is applied.
Periodicity conversion
(1 + APR_m ÷ m)ᵐ = (1 + APR_n ÷ n)ⁿ
Use it to restate a yield on another compounding basis. For semiannual to annual, EAR = (1 + APR ÷ 2)² − 1.
Yield to call
PV = Σ PMT/(1+r)ᵗ + call price/(1+r)ᴺ, with N = periods to the call date
Same equation as YTM, but N and the redemption amount change.
Yield to worst
YTW = lowest of YTM and the YTC for each call date
Compute all candidates, then take the minimum.

How to solve Yield Measures for Fixed-Rate Bonds questions

Use this order for any yield question. It keeps the periodicity and the end date correct, which is where most marks are lost.

  1. 1Identify the yield type asked for: current yield, YTM, YTC, YTW or a periodicity conversion.
  2. 2Write down the payment frequency and set m. Convert N to periods (years × m) and the annual coupon to a periodic coupon (annual coupon ÷ m).
  3. 3For current yield, divide the annual coupon by the flat price and stop.
  4. 4For YTM or YTC, enter N, PMT, FV and PV on the calculator. Use the call date and call price for YTC, and the maturity date and par for YTM. Compute the periodic rate I/Y.
  5. 5Multiply the periodic rate by m to get the annual bond-equivalent yield, unless the question asks for an effective annual yield.
  6. 6For YTW, repeat step 4 for every call date and for maturity, then pick the lowest.
  7. 7If the question changes the compounding basis, apply (1 + APR_m ÷ m)ᵐ = (1 + APR_n ÷ n)ⁿ.
  8. 8Sanity check: discount bond means YTM above coupon rate. Premium bond means YTM below coupon rate.

Quickest way: Premium or discount shortcut with the calculator

When to use it: Use it when the options are far enough apart for you to eliminate two of them quickly, which is common because numerical options are listed smallest to largest.

  1. Compare price with par. Price above par means YTM is below the coupon rate. Price below par means YTM is above the coupon rate.
  2. Estimate current yield. It sits between the coupon rate and YTM, so it helps place the answer.
  3. Cross out any option on the wrong side of the coupon rate.
  4. For YTW, a premium callable bond usually has its lowest yield at the earliest call. A discount bond usually has it at maturity.
  5. If two options remain, run the calculator once: N, PMT, FV, PV, CPT I/Y, then multiply by m.
  6. On the TI BA II Plus, key N, I/Y, PV, PMT, FV then CPT; enter PV as a negative. On the HP 12C, key n, i, PV (use CHS for price), PMT, FV, then press i.

Common mistakes in Yield Measures for Fixed-Rate Bonds

  • Forgetting to double N or halve the coupon for a semiannual bond.

    Bond data is quoted in years and annual rates, and you type them straight in.

    Fix: Convert first: N = years × 2, PMT = annual coupon ÷ 2. Your answer is a semiannual rate until you multiply by 2.

  • Reporting the periodic rate from the calculator as the annual yield.

    The I/Y key shows the rate per period, not per year, unless you set P/Y.

    Fix: Multiply by m for the bond-equivalent yield, or compound it for the effective annual yield. Check which one the question wants.

  • Using the call price as par, or par as the call price, in YTC.

    Students reuse the YTM inputs and change only N.

    Fix: For YTC, FV = call price and N = periods to the call date. Both change.

  • Assuming YTW is always the yield to call.

    Callable bonds are often linked to calls in the student's memory.

    Fix: Compute every candidate and take the lowest. A discount callable bond will usually have YTW equal to YTM.

  • Computing current yield on semiannual coupon.

    Dividing one coupon payment by price gives roughly half the correct answer.

    Fix: Current yield = annual coupon ÷ price. Multiply a semiannual coupon by 2 first.

  • Saying YTM is the return you will earn for certain.

    The word 'yield' sounds like a guaranteed return.

    Fix: State the assumptions: held to maturity, no default, coupons reinvested at the YTM. If a question asks which assumption is needed to realize YTM, reinvestment at YTM is the answer.

Worked examples

Example 1

A bond's yield is quoted at 6.00% on a semiannual bond-equivalent basis. What is the equivalent effective annual yield? A. 5.91% B. 6.00% C. 6.09%

Show the solution
  1. Periodic yield = 6.00% ÷ 2 = 3.00% per half-year.
  2. Compound over two periods: (1.03)² = 1.0609.
  3. Effective annual yield = 1.0609 − 1 = 6.09%.
  4. Check: compounding twice a year always gives an effective yield above the quoted annual rate, so 5.91% and 6.00% are wrong.

Answer: C. 6.09%

Example 2

A 3-year bond pays an 8% annual coupon in semiannual installments on par of 100. It trades at a price of 104 and is first callable in 2 years at 100. Ignoring any later call dates, what is its yield to worst? A. 5.85% B. 6.51% C. 8.00%

Show the solution
  1. Semiannual coupon = 8 ÷ 2 = 4.
  2. Yield to maturity: N = 6, PMT = 4, FV = 100, PV = −104. CPT I/Y ≈ 3.26% per half-year. Annualized: about 6.51%.
  3. Yield to call: N = 4 (2 years × 2), PMT = 4, FV = 100 (call price), PV = −104. CPT I/Y ≈ 2.92% per half-year. Annualized: about 5.85%.
  4. Check: at 2.925%, the present value is close to 104, confirming the rate.
  5. YTW is the lowest candidate: 5.85% < 6.51%.
  6. Eliminate 8.00%: it is the coupon rate, and a premium bond has a yield below its coupon rate.

Answer: A. 5.85%, the yield to call

Exam tips

  • Numerical options are listed smallest to largest and wrong options are often the periodic rate, the coupon rate or the YTM. Check which one you computed before choosing.
  • If the stem gives price above par and asks about yield, use the premium or discount rule to eliminate options before you calculate.
  • For YTW questions, list every possible redemption date in your working. Missing one date is a common way to lose the mark.
  • Read whether the question asks for a bond-equivalent yield or an effective annual yield. The two differ for every non-annual bond.
  • Practise the calculator sequence until it is automatic. With about 90 seconds per question, a clean N, PMT, FV, PV, CPT routine saves time.

Practice questions from Fixed-Income Bond Valuation: Prices and Yields

Yield Measures for Fixed-Rate Bonds in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Yield Measures for Fixed-Rate Bonds: frequently asked questions

What is the difference between yield to maturity and current yield?

Current yield is annual coupon ÷ price and measures only coupon income. YTM is the discount rate that equates the price to the present value of all coupons and the principal, so it includes the gain or loss to par and the time value of money. They are equal only when a bond trades at par.

How do I calculate yield to worst for a callable bond?

Calculate the yield to each call date using the call price and the periods to that date, and calculate the yield to maturity. Then take the lowest of these. That lowest yield is the YTW, the most conservative yield you can expect.

What is the yield to call formula?

It is the pricing equation with the call date as the end date: PV = Σ coupon/(1+r)ᵗ + call price/(1+r)ᴺ, where N is the number of periods until the call. You solve for r with a calculator and then multiply by the number of periods per year.

What is the difference between street convention and true yield?

The street convention yield assumes every cash flow is paid on its scheduled date, even if that falls on a weekend or holiday. The true yield uses the actual business day, so payments can be delayed. The true yield is usually slightly lower than the street convention yield.