Question

A 2y (two-year) floater issued with a face value of $1,000 and maturity of 9/15/2021 has a quarterly coupon rate of 3mL + 60 bps. (3mL = 3-month Libor). It has a floor of 3% and a cap of 5% on the coupon. Compute the coupon rate and dollar amount of coupon for the 8 coupon dates. Make sure to align your coupon amount with the date on which it will occur. Note that the convention for the coupon is Act/360. 3mL reset date	3mL (%)
9/15/2019	2.13
12/15/2019	2.25
3/15/2020	2.70
6/15/2020	3.67
9/15/2020	3.28
12/15/2020	4.35
3/15/2021	4.82
6/15/2021	5.21
9/15/2021	3.78

Answer 1

Solution: Coupon Rate = 3 month LIBOR + 60bps = 3 month LIBOR + 0.6%

a) Coupon Rate on 15-12-2019 = 3 month LIBOR (15-09-2019) + 0.6%

Coupons are paid using the LIBOR rate at the beginning of the period. Hence, for the coupon paid on 15-12-2019, LIBOR stated on 15-09-2019 is used for calculations.

Thus, Coupon Rate on 15-12-2019 = 2.13% + 0.6% = 2.73%

Since the floater is having a floor rate of 3% hence the effective coupon rate would be 3%

Coupon amount = Effective coupon rate*(Number of days between dates/360)*Face value

Coupon amount on 15-12-2019 = 3%*91/360*1000 = $7.5833

b) Coupon Rate on 15-09-2020 = 3 month LIBOR (15-06-2020) + 0.6%

Coupons are paid using the LIBOR rate at the beginning of the period. Hence, for the coupon paid on 15-09-2020, LIBOR stated on 15-06-2020 is used for calculations.

Thus, Coupon Rate on 15-09-2020 = 3.67% + 0.6% = 4.27%

Coupon amount = Effective coupon rate*(Number of days between dates/360)*Face value

Since the coupon rate lies between the floor rate of 3% and the cap rate of 5%, thus, no adjustment is required.

Coupon amount on 15-12-2020 = 4.27%*92/360*1000 = $10.9122

c) Coupon Rate on 15-06-2021 = 3 month LIBOR (15-03-2021) + 0.6%

Coupons are paid using the LIBOR rate at the beginning of the period. Hence, for the coupon paid on 15-06-2021, LIBOR stated on 15-03-2021 is used for calculations.

Thus, Coupon Rate on 15-06-2021 = 4.82% + 0.6% = 5.42%

Since the coupon rate is greater than the cap rate of 5%, hence, the effective coupon rate = 5%

Coupon amount = Effective coupon rate*(Number of days between dates/360)*Face value

Coupon amount on 15-06-2021 = 5%*92/360*1000 = $12.7778

Similarly, the coupon rates and coupon amounts are calculated for the other periods.