Answer: `-1.550 million`

The financial institution is the **fixed-rate payer** (pays 3.0% semi-annually, receives LIBOR) on a $400 million notional swap with 9 months (0.75 years) remaining. There are two payment dates left: in 0.25 years and in 0.75 years. ### Step 1: Value the payment due in 0.25 years - The LIBOR rate for this payment was fixed 0.25 years ago at **3.0%** (semi-annual compounding). - Fixed leg payment: 3.0% × 0.5 × $400m = +$6.0m (outflow for the institution). - Floating leg receipt: also 3.0% × 0.5 × $400m = +$6.0m (inflow). - **Net cash flow at t = 0.25**: **$0**. - Present value: **$0** (no discounting needed for a zero cash flow). ### Step 2: Value the payment due in 0.75 years - The floating leg will be based on the 6-month LIBOR rate set in 0.25 years (i.e., the forward rate F(0.25, 0.75)). - Given the flat LIBOR zero curve at 2.20% continuous compounding, the 6-month forward rate (semi-annual compounding) is given as: \[ 2 \times (e^{0.0220/2} - 1) = 2.2121\% \] - Fixed leg payment (outflow): 3.0% × 0.5 × $400m = $6.0m. - Expected floating receipt (based on forward): 2.2121% × 0.5 × $400m ≈ $4.4242m. - **Net cash flow at t = 0.75**: $4.4242m – $6.0m = **–$1.5758m** (net outflow). ### Step 3: Discount the net cash flow to today - Risk-free (LIBOR) zero rate = 2.20% continuous compounding. - Discount factor for t = 0.75 years: \( e^{-0.0220 \times 0.75} \). - PV of the net outflow ≈ **–$1.550 million**. ### Step 4: Total present value of the swap - PV = PV(at 0.25) + PV(at 0.75) = $0 + (–$1.550m) = **–$1.550 million**. The swap has **negative value** to the financial institution because it is locked into paying a fixed rate (3.0%) that is now higher than the prevailing forward LIBOR rate (≈2.2121%). It must make a net payment on the second exchange date, and the present value of that obligation is approximately $1.55 million. **Nearest answer: A: `-$1.550 million`**

Author: LeetQuiz .