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