company x wishes to borrow euros at a fixed rate of interest . company Y wishes to borrow Japanese yen at a fixed rate of interest. the amounts required by the two companies are roughly the same at the current exchange rate. the companies have been quoted the following interests rate , which have been adjusted for the impact of taxes:
Company X : Yen =6.0% euro=8.5%
company Y : Yen=7.5% euro=9.0%
design a swap that will net a bank , acting as intermediary , 50 basis points per annum. make the swap equally attractive to the two companies and ensure that all foreign exchange risk is assumed by the bank

To design an interest rate swap that meets the criteria, we'll need to ensure that both Company X and Company Y benefit from the swap while the bank earns 50 basis points (0.50%) per annum. The bank will assume all foreign exchange risk, so the swap will focus on interest rate differences.

### Initial Setup:
- **Company X** prefers to borrow euros but has a better rate in yen.
- **Company Y** prefers to borrow yen but has a better rate in euros.

### Interest Rates:
- **Company X**: 
  - Yen = 6.0%
  - Euro = 8.5%
- **Company Y**: 
  - Yen = 7.5%
  - Euro = 9.0%

### Step 1: Establish Comparative Advantages
- **Company X** has a comparative advantage in borrowing yen (6.0% vs. 7.5% for Company Y).
- **Company Y** has a comparative advantage in borrowing euros (9.0% vs. 8.5% for Company X).

### Step 2: Determine the Total Differential
- **Yen Differential**: 7.5% - 6.0% = 1.5%
- **Euro Differential**: 9.0% - 8.5% = 0.5%

### Step 3: Design the Swap
- The bank aims to earn 0.50% (50 basis points) per annum, so we'll split the total differential between the companies, considering the bank's fee.

1. **Company X** borrows yen directly at 6.0% and agrees to pay a fixed euro interest rate to Company Y via the swap.
2. **Company Y** borrows euros directly at 9.0% and agrees to pay a fixed yen interest rate to Company X via the swap.
3. The bank earns 0.50% per annum by adjusting the swap rates slightly in its favor.

#### Calculate Swap Rates:
- **Yen Swap Rate**: 
  - Company X pays Company Y at a rate higher than 6.0% but lower than 7.5% to make it attractive. 
  - Assume a mid-point rate: \(6.0\% + \frac{(7.5\% - 6.0\%) - 0.5\%}{2} = 6.75\%\).
- **Euro Swap Rate**: 
  - Company Y pays Company X at a rate lower than 9.0% but higher than 8.5%.
  - Assume a mid-point rate: \(8.5\% + \frac{(9.0\% - 8.5\%) - 0.5\%}{2} = 8.75\%\).

### Final Swap Structure:
- **Company X**:
  - Borrows yen at 6.0% (directly).
  - Pays 8.75% (euro rate) to the bank.
  - Receives 6.75% (yen rate) from Company Y.
  - Net cost in euros: \(8.75\% - 6.75\% = 2.0\%\) plus the initial 6.0% yen rate, totaling **8.0%** in euros.

- **Company Y**:
  - Borrows euros at 9.0% (directly).
  - Pays 6.75% (yen rate) to the bank.
  - Receives 8.75% (euro rate) from Company X.
  - Net cost in yen: \(9.0\% - 8.75\% = 0.25\%\) plus the initial 6.75% yen rate, totaling **7.0%** in yen.

### Bank's Position:
- The bank earns the 0.50% difference in both currencies:
  - Receives 8.75% from Company X and pays 8.75% to Company Y (in euros).
  - Receives 6.75% from Company Y and pays 6.25% to Company X (in yen).

This structure makes the swap equally attractive to both companies, with each benefiting slightly from their comparative advantage, and ensures that the bank earns its fee while taking on the foreign exchange risk.

### Relative Questions:
1. What is the impact on the companies if the exchange rate between euros and yen fluctuates?
2. How would the swap be structured if the bank's fee was reduced to 25 basis points instead of 50?
3. What are the potential risks for the bank if there is a significant economic change in either Europe or Japan?
4. How does the interest rate differential between the two currencies affect the overall swap agreement?
5. How could changes in tax laws impact the attractiveness of such a swap for the companies involved?

### Tip:
When designing swaps, it's crucial to ensure that both parties have enough incentive to engage in the swap, making it a win-win situation while adequately compensating the intermediary (bank) for the risks taken.

Explore how to design an interest rate swap between Company X and Company Y, ensuring equal attractiveness while the bank earns 50 basis points per annum. Includes detailed steps, interest rate differentials, and risk management.

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