Question

1. A 3-year maturity semiannual floating rate note is priced at 102.50 per 100 par value. Its coupon payments are based on LIBOR + 100 bps. Payment is made semiannually. The current LIBOR is 3%.

a) Calculate the discount margin on this FRN.

b) What would be the price of the FRN if the discount margin becomes 200 bps?

Answer 1

1)

No of periods = 3 years * 2 = 6 semi-annual periods

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

Coupon per period = (LIBOR + 100 bps / 2) * $100

Coupon per period = ((3% + 1%) / 2) * $100

Coupon per period = $2

We assume all the coupon in the future to be based on LIBOR + 100 bps

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

$102.5 = $2 / (1 + YTM / 2)¹ + $2 / (1 + YTM / 2)² + ...+ $2 / (1 + YTM / 2)⁶ + $100 / (1 + YTM / 2)⁶

Using Texas Instruments BA 2 plus calculator

SET N = 6, PMT = 2, FV = 100, PV = -102.5

CPT --> I/Y = 1.56

YTM = 2 * I/Y

YTM = 2 * 1.56%

YTM = 3.1206%

YTM = LIBOR + Discount margin

3.1206% = 3% + Discount margin

Discount margin = 0.1206% or 12.06 bps

2)

YTM = LIBOR + Discount margin

YTM = LIBOR + 200 bps

YTM = 3% + 2%

YTM = 5%

We assume all the coupon in the future to be based on LIBOR + 100 bps

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

Bond Price = $2 / (1 + 5% / 2)¹ + $2 / (1 + 5% / 2)² + ...+ $2 / (1 + 5% / 2)⁶ + $100 / (1 + 5% / 2)⁶

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $2 * (1 - (1 + 5% / 2)^-6) / (5% / 2) + $100 / (1 + 5% / 2)⁶

Bond Price = $11.0163 + $86.2297

Bond Price = $97.2459 per $100 par or $97.25 per $100 par