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Sagot :
Let's solve the given problem using both a forward market hedge and a money market hedge step-by-step.
### Forward Market Hedge
Step 1: Calculate the amount in Euros that will be equivalent to [tex]$350,000 at the forward rate. The six-month forward rate given is 1.155 ($[/tex]/€).
[tex]\[ \text{Euro equivalent forward} = \frac{\$350,000}{\text{Forward rate}} = \frac{350,000}{1.155} \][/tex]
[tex]\[ \text{Euro equivalent forward} \approx 303,030.30 \, \text{Euros} \][/tex]
### Money Market Hedge
Step 1: Calculate the present value of the Euros needed to be borrowed now.
The annual borrowing interest rate for Euros is 14%.
[tex]\[ \text{Monthly interest rate for Euros} = \frac{0.14}{12} \approx 0.01167 \, \text{(or 1.167% per month)} \][/tex]
For a 6-month period, the interest rate would be:
[tex]\[ \text{Interest rate for 6 months} = 1 + (0.14 \times \frac{6}{12}) = 1 + 0.07 = 1.07 \][/tex]
Thus, the present value of Euros to be borrowed now:
[tex]\[ \text{Euro present value} = \frac{303,030.30 \, \text{Euros}}{1.07} \approx 283,205.89 \, \text{Euros} \][/tex]
Step 2: Convert this amount of Euros to USD at the spot rate.
The spot rate given is 1.166 ([tex]$/€). \[ \text{USD equivalent of present value} = 283,205.89 \, \text{Euros} \times 1.166 = 330,218.07 \, \text{USD} \] Step 3: Invest this amount in the USD market at the deposit rate. The annual deposit interest rate for USD is 4%. \[ \text{Monthly interest rate for USD} = \frac{0.04}{12} \approx 0.00333 \, \text{(or 0.333% per month)} \] For a 6-month period, the interest rate would be: \[ \text{Interest rate for 6 months} = 1 + (0.04 \times \frac{6}{12}) = 1 + 0.02 = 1.02 \] \[ \text{Future value of USD investment} = 330,218.07 \, \text{USD} \times 1.02 \approx 336,822.43 \, \text{USD} \] By following these steps, the firm can hedge its currency exposure through both the forward market and the money market. The results show: 1. For the Forward Market Hedge, the firm would need to have €303,030.30 in six months. 2. For the Money Market Hedge, the firm would borrow approximately €283,205.89 now, convert that to $[/tex]330,218.07 using the spot rate, and invest this amount in USD to get approximately [tex]$336,822.43 in six months. Both methods would ensure that the firm is protected against currency fluctuation risks for its payable amount of $[/tex]350,000 due in six months.
### Forward Market Hedge
Step 1: Calculate the amount in Euros that will be equivalent to [tex]$350,000 at the forward rate. The six-month forward rate given is 1.155 ($[/tex]/€).
[tex]\[ \text{Euro equivalent forward} = \frac{\$350,000}{\text{Forward rate}} = \frac{350,000}{1.155} \][/tex]
[tex]\[ \text{Euro equivalent forward} \approx 303,030.30 \, \text{Euros} \][/tex]
### Money Market Hedge
Step 1: Calculate the present value of the Euros needed to be borrowed now.
The annual borrowing interest rate for Euros is 14%.
[tex]\[ \text{Monthly interest rate for Euros} = \frac{0.14}{12} \approx 0.01167 \, \text{(or 1.167% per month)} \][/tex]
For a 6-month period, the interest rate would be:
[tex]\[ \text{Interest rate for 6 months} = 1 + (0.14 \times \frac{6}{12}) = 1 + 0.07 = 1.07 \][/tex]
Thus, the present value of Euros to be borrowed now:
[tex]\[ \text{Euro present value} = \frac{303,030.30 \, \text{Euros}}{1.07} \approx 283,205.89 \, \text{Euros} \][/tex]
Step 2: Convert this amount of Euros to USD at the spot rate.
The spot rate given is 1.166 ([tex]$/€). \[ \text{USD equivalent of present value} = 283,205.89 \, \text{Euros} \times 1.166 = 330,218.07 \, \text{USD} \] Step 3: Invest this amount in the USD market at the deposit rate. The annual deposit interest rate for USD is 4%. \[ \text{Monthly interest rate for USD} = \frac{0.04}{12} \approx 0.00333 \, \text{(or 0.333% per month)} \] For a 6-month period, the interest rate would be: \[ \text{Interest rate for 6 months} = 1 + (0.04 \times \frac{6}{12}) = 1 + 0.02 = 1.02 \] \[ \text{Future value of USD investment} = 330,218.07 \, \text{USD} \times 1.02 \approx 336,822.43 \, \text{USD} \] By following these steps, the firm can hedge its currency exposure through both the forward market and the money market. The results show: 1. For the Forward Market Hedge, the firm would need to have €303,030.30 in six months. 2. For the Money Market Hedge, the firm would borrow approximately €283,205.89 now, convert that to $[/tex]330,218.07 using the spot rate, and invest this amount in USD to get approximately [tex]$336,822.43 in six months. Both methods would ensure that the firm is protected against currency fluctuation risks for its payable amount of $[/tex]350,000 due in six months.
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