Question

Consider a semiannual payment floating-rate security whose coupon rate is determined as:

reference rate + 75 basis points

Assume its term to maturity is 10 years and current price is 99.25. What is the discount margin of the floater if the initial reference rate is 5%?

Answer 1

no of periods = 10 years * 2 = 20 semi annual periods

Coupon rate = Reference rate + 75 basis points

Coupon rate = 5% + 0.75%

Coupon rate = 5.75%

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (5.75% / 2) * $100

Coupon per period = $2.875

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

99.25 = $2.875 / (1 + YTM% / 2)¹ + $2.875 / (1 + YTM% / 2)² + ...+ $2.875 / (1 + YTM%/ 2)²⁰ + $100 / (1 + YTM% / 2)²⁰

Using Texas Instruments BA 2 plus calculator

SET N = 20, PMT = 2.875, FV =100, PV = -99.25

CPT --> I/Y = 2.9251

YTM / 2= * I/Y

YTM = 2 * 2.9251

YTM = 5.8501%

YTM = reference rate + discount(required) margin

5.85% = 5% + discount(required) margin

discount(required) margin = 85 bps