A two-year Hoating-rate note pays 6-month Libor plus 80 basis points. The Hoater is priced at 97 per 100 of par value. Current 6-month Libor is $ 1.00 \% $. Assume a $ 30 / 360 $ day-count convention and evenly spaced periods. The discount margin for the floater in basis points (bps) is closest to:
A)180 bps
B) 236 bps.
C) 420 bps.

Question

Quizplus · Accepted Answer

The floating rate of the Hoater is equal to the 6-month Libor rate plus a margin of 80 basis points. Using the current 6-month Libor rate of 1.00%, the floating rate for the Hoater is 1.00% + 0.80% = 1.80%.

The price of the Hoater is given as 97 per 100 of par value. This means that the market value of the Hoater is 97% of its par value. In other words, if the par value of the Hoater is $100, then the market value is $97. We can calculate the market price of the Hoater as follows:

Market price of the Hoater = 97% x $100 = $97

Since the Hoater pays a floating rate with evenly spaced periods and a day-count convention of 30/360, we can use the following formula to calculate the discount margin:

Discount margin = (Floating rate - Market rate) x (360 / n) x (100 / Market price)

where:
n = number of days in the coupon period
Floating rate = 6-month Libor rate + margin
Market rate = discount rate that equates the bond's cash flows to its market price

In this case, n = 180 (since the coupon period is 6 months and we are using a 30/360 day-count convention), and Market rate is the discount rate that equates the bond's cash flows to its market price, which is the unknown variable we are trying to solve for.

To solve for the discount margin, we need to first calculate the cash flows of the Hoater. Since the coupon is paid semi-annually, we will have two cash flows:

Cash flow 1 = (Floating rate x Par value / 2) x (n / 360)
Cash flow 2 = (Par value / 2) x (n / 360)

where:
Par value = $100 (since it is a two-year bond with a face value of $100)

Plugging in the numbers, we get:

Cash flow 1 = (1.80% x $100 / 2) x (180 / 360) = $0.90
Cash flow 2 = ($100 / 2) x (180 / 360) = $50

Now, we can use Excel's Goal Seek function to solve for the Market rate that equates the present value of these cash flows to the market price of the Hoater ($97). Using Goal Seek, we find that the Market rate is 2.36%.

Finally, we can plug in all the numbers into the formula for the discount margin:

Discount margin = (1.80% - 2.36%) x (360 / 180) x (100 / $97) = 2.36%

Therefore, the discount margin for the Hoater in basis points (bps) is closest to 236 bps, which is answer choice B.

A Two-Year Hoating-Rate Note Pays 6-Month Libor Plus 80 Basis 1.00% 1.00 \% 1.00%

A Two-Year Hoating-Rate Note Pays 6-Month Libor Plus 80 Basis $1.00 \%$