Floating-Rate Note (FRN) Discount Margin Calculation
A two-year floating-rate note with USD 1,000 face value is priced at USD 1002.95. A USD 13.00 coupon is paid annually. Assuming that the coupon rate is 25 bps over the market reference rate (MRR), and the required rate is 1.15%, the note's discount margin is _closest_ to:
Incorrect.
This answer is a calculation of the floating-rate note's discount margin when the reference rate is not adjusted by the given basis points.
Incorrect.
This answer choice is a calculation of the discount margin for a semiannual fixed-rate note with all other conditions being equal to that of the given note.
Correct.
The floating-rate note's discount margin can be determined using the following formula:
$$\displaystyle 1+r=1+\frac{(R+DM)}{m}$$,
where _r_ is the note's discount rate, _R_ is the reference rate, _DM_ is the discount margin, and _m_ represents periodicity.
$$\displaystyle r=0.0115$$
The market reference rate, _R_, in this scenario is derived from the coupon rate and given basis points.
$$\displaystyle \mbox{Coupon Rate} = \mbox{MRR + Basis Points}$$
$$\displaystyle \mbox{MRR}=\frac{13}{1{,}000}-0.0025=0.0105\times 100= 1.05\%$$
The periodicity, denoted _m_, is equal to 1 since the note is an annual one. Solve for the fixed-rate note's discount margin _DM_.
$$\displaystyle 1+0.0115=1+\frac{0.0105+DM}{1}$$
$$\displaystyle DM=0.0115-0.0105=0.001$$,
or 0.10%.
-0.15%.
0.10%.
1.25%.
