Answer: -924,458

## Explanation To value the interest rate swap with 2.5 years remaining, we need to calculate the present value of the remaining fixed and floating payments. **Given:** - Original swap: Pay fixed 5%, receive LIBOR - Notional: $20,000,000 - Remaining life: 2.5 years - New 2-year swap rate: 2.96% - New 3-year swap rate: 3.075% - Risk-free rate: 3.6% (compounded quarterly) **Step 1: Calculate the 2.5-year swap rate using interpolation** Since we have 2-year (2.96%) and 3-year (3.075%) swap rates, we can linearly interpolate for 2.5 years: 2.5-year swap rate = 2.96% + (3.075% - 2.96%) × (2.5 - 2)/(3 - 2) = 2.96% + 0.115% × 0.5 = 3.0175% **Step 2: Calculate the value of the swap** The value of a swap where we pay fixed and receive floating is: Value = PV(floating payments) - PV(fixed payments) Since the floating leg resets to par at each payment date, PV(floating payments) = Notional Therefore, Value = Notional - PV(fixed payments at current market rate) **Step 3: Calculate present value of fixed payments** Quarterly payment = 20,000,000 × 5% × 0.25 = $250,000 Using the 3.6% risk-free rate compounded quarterly: Quarterly discount rate = 3.6%/4 = 0.9% There are 10 quarterly payments remaining (2.5 years × 4 quarters) PV(fixed payments) = 250,000 × [1 - (1 + 0.009)^(-10)] / 0.009 = 250,000 × 9.555 = $2,388,750 **Step 4: Calculate the value** Value = 20,000,000 - 2,388,750 = $17,611,250 However, this calculation doesn't account for the market swap rate difference. The correct approach is: Value = Notional × (Current swap rate - Original swap rate) × Annuity factor Annuity factor = [1 - (1 + r)^(-n)] / r Where r = quarterly discount rate = 0.9% n = number of quarters = 10 Annuity factor = [1 - (1.009)^(-10)] / 0.009 = 9.555 Value = 20,000,000 × (3.0175% - 5%) × 0.25 × 9.555 = 20,000,000 × (-1.9825%) × 0.25 × 9.555 = -$924,458 The negative value indicates that the party paying fixed 5% is at a disadvantage compared to current market rates of around 3.0175%.

Author: LeetQuiz .