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Answer: -43,824.76
## Explanation This is a currency swap valuation problem where we need to calculate the value from the perspective of the party paying pounds and receiving euros. ### Key Information: - **Pounds paid**: 3% semi-annual on £1,000,000 - **Euros received**: 2% semi-annual on €1,100,000 - **Remaining periods**: 4 (0.5, 1, 1.5, 2 years) - **Risk-free rate (pounds)**: 2.5% semi-annual - **Forward exchange rates**: 1.1443, 1.1387, 1.1330, 1.1275 €/£ ### Calculation Steps: 1. **Calculate Pound Cash Flows (Outflows)**: - Semi-annual interest: £1,000,000 × 3%/2 = £15,000 - Final principal: £1,000,000 2. **Calculate Euro Cash Flows (Inflows)**: - Semi-annual interest: €1,100,000 × 2%/2 = €11,000 - Final principal: €1,100,000 3. **Convert Euro Cash Flows to Pounds using Forward Rates**: - Period 0.5: €11,000 / 1.1443 = £9,613.21 - Period 1: €11,000 / 1.1387 = £9,659.26 - Period 1.5: €11,000 / 1.1330 = £9,708.74 - Period 2: €11,000 / 1.1275 = £9,756.10 - Final principal: €1,100,000 / 1.1275 = £975,610.20 4. **Calculate Present Value using Pound Risk-Free Rate (2.5% semi-annual)**: - Discount factor = 1/(1 + 2.5%/2)^(2×t) - PV of Pound outflows: £15,000 × (DF₁ + DF₂ + DF₃ + DF₄) + £1,000,000 × DF₄ - PV of Euro inflows (converted): Sum of PV of converted cash flows 5. **Swap Value = PV(Inflows) - PV(Outflows)**: - The calculation yields approximately **-£43,824.76** ### Interpretation: The negative value (-£43,824.76) means the swap has negative value for the party paying pounds, indicating they are paying more than the current market rate for this swap arrangement.
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Consider a currency swap where interest on British pounds at the rate of 3% is paid and interest on euros at 2% is received. The British pound principal is 1.0 million pounds and the euro principal is 1.1 million euros. The most recent exchange has just occurred and the interest is exchanged every six months. There are two years are remaining in the life of the swap. The current exchange rate is 1.15 (1.15 euro per pound). Suppose that the forward exchange rates (euro per pound) for year 0.5, 1, 1.5 and 2 are 1.1443, 1.1387, 1.1330 and 1.1275 respectively. The risk-free rates in pounds are 2.5%. All rates are compounded semi-annually. What is the value of the swap (Pounds Paid) in pounds?
A
-43,824.76
B
+43,824.76
C
-29,591.90
D
+29,591.90