Floating-Rate Note Yields:

EXAMPLE: Valuation of a floating-rate note

A $100,000 floating rate note is based on 180-day LIBOR (the reference rate) with a quoted margin of 120

basis points. On a reset date with 5 years remaining to maturity, 180-day LIBOR is quoted as 3.0%

(annualized) and the discount margin (based on the issuer’s current credit rating) is 4.5% (annualized).

What is the market value of the floating rate note?

Answer:

The current annualized coupon rate on the note is 3.0% + 1.2% = 4.2%, so the next semiannual coupon

payment will be 4.2% / 2 = 2.1% of face value. The required return in the market (discount margin) as an

effective 180-day discount rate is 4.5% / 2 = 2.25%.

Using a face value of 100%, 10 coupon payments of 2.1%, and a discount rate per period of 2.25%, we can

calculate the present value of the floating rate note as:

N = 10; I/Y = 2.25%; FV = 100; PMT = 2.1; CPT PV = 98.67

The current value of the note is 98.67% of its face value, or $98,670.

my thought: According to CFA book, the I/Y should be the reference rate+ Discount margin. so should be (3%+4.5%)/2=3.75%

Below from CFA book:

where:

*PV* = present value, or the price of the floating-rate note = 97

Index = reference rate, stated as an annual percentage rate = 0.01

*QM* = quoted margin, stated as an annual percentage rate = 0.0080

*FV* = future value paid at maturity, or the par value of the bond = 100

*m* = periodicity of the floating-rate note, the number of payment periods per year = 2

*DM* = discount margin, the required margin stated as an annual percentage rate

Could anybody explain this?