Question

Suppose that a four-year FRN (floating-rate note) pays three-month Libor plus a quoted margin of 1.00% on a quarterly basis. Currently, three-month Libor is 1.65%. The discount margin is currently 0.90%. Calculate the price of the bond (DM < QM):

Answer 1

No of periods = 4 years * 4 = 16 quarterly periods

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

Coupon per period = ((LIBOR + 1%) / 4) * $1000

Coupon per period = ((1.65% + 1%) / 4) * $1000

Coupon per period = $6.625

Yield to Maturity(YTM) = LIBOR + Discount margin

YTM = 1.65% + 0.90%

YTM = 2.55%

Bond Price = Coupon / (1 + YTM / 4)^period + Face value / (1 + YTM / 4)^period

Bond Price = $6.625 / (1 + 2.55% / 4)¹ + $6.625 / (1 + 2.55% / 4)² + ...+ $6.625 / (1 + 2.55% / 4)¹⁶ + $1,000 / (1 + 2.55% / 4)¹⁶

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

Bond Price = $6.625 * (1 - (1 + 2.55% / 4)^-16) / (2.55% / 4) + $1,000 / (1 + 2.55% / 4)¹⁶

Bond Price = $100.47 + $903.32

Bond Price = $1003.79