# Calculating the Discount Margin for a Floating-Rate Note

I am struggling a bit with the coupon payments for the simplified FRN pricing (the rest is clear to me). The formula is given by:

PV=num/denom+…

num=(Index+QM)/m*FV

denom=(1+Index+DM/m)^N

Now in the numerator we are simply computing the coupon payments of each period, by dividing the annual percentage rate by the number of payment periods per year. Say I have a 5% FRN that is paying semiannually, my coupon payments each period would be \$2.5.

But in all of the examples given in the curriculum use non-annual rates for the index. Below is an example:

A four-year French floating-rate note pays three-month Euribor (Euro Interbank Offered Rate, an index produced by the European Banking Federation) plus 1.25%. The floater is priced at 98 per 100 of par value. Calculate the discount margin for the floater assuming that three-month Euribor is constant at 2%. Assume the 30/360 day-count convention and evenly spaced periods.

Solution:

By assumption, the interest payment each period is 0.8125 per 100 of par value:

(0.02+0.0125)*100/4=0.8125

If this FRN is paying 3-month Euribor, plus1.25%, then the coupon payments should be 3.25 4 times a year, right?

Interest rates are always – _ always! _ – quoted as annual rates.

3.25% is the annual (nominal) interest rate. The quarterly interest rate is ¼ of that: 0.8125%.

I can’t believe I missed that so far, then it all makes sense of course. Thanks for clarifying that S2000!!!

You’re quite welcome.

It can be overwhelming at times; I understand.