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CFA Level I Exam · Yield and Yield Spread Measures for Floating-Rate Instruments

How to Price a Floating-Rate Note with Discount Margin

Updated 7 October 2026 · Fact-checked

To price a floating-rate note, project each coupon as (reference rate + quoted margin) ÷ periods per year, holding the reference rate constant. Discount those coupons and the principal at (reference rate + discount margin) ÷ periods per year. If the discount margin equals the quoted margin, price is par. If it is higher, price is below par.

Understand Pricing a Floating-Rate Note with Discount Margin

A floating-rate note (FRN) pays a coupon that resets to a reference rate plus a fixed spread. The fixed spread is the quoted margin. A coupon is set at the start of each period and paid at the end.

Because the coupon follows market rates, the FRN's price barely moves when rates change. What moves the price is credit risk. The market sets the required margin, also called the discount margin, which is the spread investors want over the reference rate for this issuer today.

Pricing is ordinary bond pricing with one change. You assume the reference rate stays at its current level for every period. The coupon is (reference rate + quoted margin) ÷ m. The discount rate is (reference rate + discount margin) ÷ m. Here m is the number of payments per year.

The two margins decide where the price sits. If the quoted margin equals the required margin, coupon and discount rate match, so the price is par on a reset date. If the required margin is higher than the quoted margin, the note pays too little for its risk and trades at a discount. If it is lower, the note pays more than required and trades at a premium.

The reference rate cancels out of the gap between price and par. Only the difference between the two margins matters. That is why you can often rank the answers without a full calculation.

Key formulas to remember

FRN price
PV = Σ [ (FV × (Index + QM) ÷ m) ÷ (1 + (Index + DM) ÷ m)^t ] + FV ÷ (1 + (Index + DM) ÷ m)^N
Sum from t = 1 to N. Index is the reference rate, QM the quoted margin, DM the discount (required) margin, m the payments per year, N the total periods. Assumes the index stays constant.
Periodic coupon
Coupon = FV × (Index + QM) ÷ m
Use the index rate that applies to the period. Margins are annual, so divide by m.
Periodic discount rate
r = (Index + DM) ÷ m
Use this as I/Y on the calculator.
Par, premium or discount rule
DM = QM → price = par; DM > QM → price < par; DM < QM → price > par
Exact par holds on a reset date with the index held constant and a flat projection. Between reset dates, accrued interest complicates the quoted price.
Price gap from par
Price − FV = FV × (QM − DM) ÷ m × annuity factor at r for N periods
Useful shortcut because the reference rate drops out of the numerator.

How to solve Pricing a Floating-Rate Note with Discount Margin questions

Use this method for any FRN pricing question. It works with the BA II Plus or HP 12C.

  1. 1List the inputs: face value, reference rate, quoted margin, discount (required) margin, payments per year and years to maturity.
  2. 2Convert to periods: N = years × m. Convert annual rates to periodic rates by dividing by m.
  3. 3Compute the periodic coupon = FV × (reference rate + quoted margin) ÷ m. Keep the reference rate constant for all periods.
  4. 4Compute the periodic discount rate = (reference rate + discount margin) ÷ m.
  5. 5Enter N, I/Y (as a percentage per period), PMT = coupon, FV = face value, then compute PV. On the BA II Plus press CPT PV; on the HP 12C press PV. The answer shows with a negative sign.
  6. 6Check the sign of the gap against the rule. If DM > QM, the price must be below FV. If DM < QM, it must be above FV. If they are equal, it must equal FV.
  7. 7Answer in the form asked: price per 100 of face value or in currency terms for the stated face value.

Quickest way: Compare margins first, then size the gap

When to use it: Use when options are widely spaced or you only need to know whether the price is above or below par. Always use it as a sanity check.

  1. Compare required (discount) margin with quoted margin. This tells you premium, par or discount at once.
  2. Often one option is exactly par. If margins are equal, choose it and skip all calculation.
  3. Otherwise, compute the per-period margin gap: (QM − DM) ÷ m, in percent of face value.
  4. Multiply the gap by the annuity factor for N periods at the periodic discount rate. Add the result to par (negative if DM > QM).
  5. Eliminate any option on the wrong side of par before doing more work.

Common mistakes in Pricing a Floating-Rate Note with Discount Margin

  • Using the annual margin or annual rate as the periodic rate

    Candidates forget that the margin and index are quoted per year while coupons are paid more often.

    Fix: Divide both the coupon rate and the discount rate by m, and set N = years × m.

  • Choosing a premium when the required margin is above the quoted margin

    Candidates mix up the direction, thinking a higher required margin means a higher price.

    Fix: A higher required margin means a higher discount rate relative to the coupon, so the price falls below par. Remember: DM > QM gives a discount.

  • Discounting at the quoted margin or at the coupon rate

    Candidates copy the coupon rate into I/Y out of habit from fixed-rate bonds.

    Fix: The coupon uses the quoted margin. The discount rate uses the required (discount) margin. Write them on separate lines.

  • Letting the reference rate change across periods

    Candidates try to forecast future index resets.

    Fix: For this method, hold the current reference rate constant for all future coupons unless the question gives a forward curve.

  • Expecting large price swings when the reference rate rises

    Candidates apply fixed-rate bond duration logic.

    Fix: An FRN's coupon resets with the index, so the price stays close to par. Credit spread changes, not index changes, drive the price.

  • Forgetting the principal in the FV register or entering the wrong sign

    Rushing under time pressure.

    Fix: Always set FV to face value and PMT to the coupon, both positive. Read PV as the absolute value.

Worked examples

Example 1

A 2-year floating-rate note has a face value of 100 and pays semiannual coupons at the 6-month reference rate plus a quoted margin of 0.50%. The reference rate is 4.00% and is assumed to stay constant. The required margin is 0.80%. What is the price per 100 of face value? A. 98.86 B. 99.43 C. 100.57

Show the solution
  1. Periods: N = 2 × 2 = 4.
  2. Coupon = 100 × (4.00% + 0.50%) ÷ 2 = 2.25.
  3. Discount rate per period = (4.00% + 0.80%) ÷ 2 = 2.40%.
  4. Quick check: required margin 0.80% is greater than quoted margin 0.50%, so the price is below par. This removes C.
  5. Calculator: N = 4, I/Y = 2.4, PMT = 2.25, FV = 100, CPT PV = −99.43.
  6. Cross-check: 1.024^4 = 1.099512, so the principal PV = 90.9495. The annuity factor = (1 − 0.909495) ÷ 0.024 = 3.7711. Coupon PV = 2.25 × 3.7711 = 8.4849. Total = 99.434.

Answer: B. The price is about 99.43 per 100 of face value, a discount to par.

Example 2

A 1-year FRN with face value 100 pays quarterly coupons at the 3-month reference rate plus a quoted margin of 1.00%. The reference rate is 5.00% and is assumed constant. The required margin is 0.60%. What is the price per 100 of face value? A. 99.614 B. 100.000 C. 100.386

Show the solution
  1. Periods: N = 1 × 4 = 4.
  2. Coupon = 100 × (5.00% + 1.00%) ÷ 4 = 1.50.
  3. Discount rate per period = (5.00% + 0.60%) ÷ 4 = 1.40%.
  4. Quick check: required margin 0.60% is below quoted margin 1.00%, so the price is above par. This removes A and B.
  5. Calculator: N = 4, I/Y = 1.4, PMT = 1.5, FV = 100, CPT PV = −100.386.
  6. Cross-check: the extra coupon per period = 1.50 − 1.40 = 0.10. Annuity factor at 1.4% for 4 periods = 3.8638. Premium = 0.10 × 3.8638 = 0.386. Price = 100.386.

Answer: C. The price is about 100.386 per 100 of face value, a premium to par.

Exam tips

  • Read which margin is the quoted margin and which is the required margin before doing any arithmetic. Questions often list them in a confusing order.
  • Settle premium, par or discount first. Often one option is on the wrong side of par and you can eliminate it in seconds.
  • Check the payment frequency. Quarterly and semiannual FRNs are both common, and the periodic rate and N change with m.
  • Numerical options are listed smallest to largest, so check whether your answer fits the order and sits near par. An FRN price far from par usually signals a setup error.
  • There is no penalty for wrong answers. If time runs short, use the margin comparison to cut three options to two and guess.

Practice questions from Yield and Yield Spread Measures for Floating-Rate Instruments

Pricing a Floating-Rate Note with Discount Margin: frequently asked questions

When does a floating-rate note trade at a discount?

It trades at a discount when the required (discount) margin is greater than the quoted margin. The coupon is too low for the credit risk investors see, so they pay less than par. This usually follows a deterioration in the issuer's credit quality.

Why does an FRN trade near par when interest rates change?

Its coupon resets to the reference rate, so cash flows move with market rates. The discount rate moves by the same amount, which leaves the price close to par on reset dates. Only a change in the required margin pushes the price away from par.

Do I need to forecast the reference rate to price an FRN?

Not in the standard method. You hold the current reference rate constant for all future coupons. Both the coupon and the discount rate use that same rate, so it has little effect on how far the price sits from par.

What is the difference between quoted margin and discount margin?

The quoted margin is the fixed spread over the reference rate set in the note's terms. The discount margin is the spread that makes the present value of projected cash flows equal the market price. Compare it with the quoted margin to judge whether the note trades at par, premium or discount.