Effect Interest Rate and Collar

The current interest rate on ABC’s floating rate notes, based on 6-month LIBOR plus 150bp, is 5.5%. To hedge its interest rate risk, ABC has decided to enter into a long interest collar. The cap and the floor of the collar have maturities of two years, with settlement dates in arrears every six months. The strike rate for the cap is 5.5% and for the floor is 4.5%, based on 6-month LIBOR, which is forecast to be 5.2%,6.1%,4.1% and 3.8%, in 6,12,18 and 24 months, respectively. Each settlement period consists of 180 days.

  1. what is the payoff on ABC’s collar 24 months from now. Answer: ABC will make a payment of 0.002 per dollar.

  2. what is the effective interest rate that ABC will pay 18 months from now assuming the notional principal of the collar is equal to the outstanding principal on the firm’s floating rate notes? Answer: 3.5%

Could somebody kindly tell me the logic and calculations for these two questions?

Many thanks!!!

We need to know the prinicipal amount.

assuming the notional principal of the collar is equal to the outstanding principal on the firm’s floating rate notes

1st question: you were long a collar, so you sold call, bought put.

payments in arrears, and assuming all times are 180 days between periods

caplet expired worthless. Max(0, LIBOR 4.1% - 5.5%) * 180/360 = 0.

You sold caplet - so no gain for you.

Floorlet => max (0, 4.5% - LIBOR 4.1%) * 180/360 = 0.2% = 0.002 per dollar

since you bought floorlet - you pay the amount.

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in 18 months you would use the 12 month rate.

interest paid = (6.1% + 150 bps) * 180 / 360 = -3.8%

Caplet = max (0, 6.1% - 5.5% ) * 180 / 360 = +0.3% (gain sold call)

Floorlet = max (0, 4.1% - 6.1%) * 180 / 360 = 0

Net = -3.8% + 0.3% = -3.5%

Because of the payment in arrear, so we must use the LIBOR in previous period for reference in the calcualtion for cap/floor payoff and effective interest rate? right?

Much appreciated for your detailed explaination!