General Electric Co (GE) is scheduled to deliver GE aircraft engines to Airbus for the A380s at the end of each year for the next five years, starting in 2014. GE expects to receive €45,000,000 from Airbus on December 31 of each year for five years, starting in 2014. GE wants to enter into a fixed-for-fixed currency swap agreement with you a (a swap bank) in order to hedge the currency risk associated with these euro receivables by locking in an exchange rate at which it can convert the expected annual euro receivables to dollars.
The current spot exchange rate is $1.37/€. The fixed rate on a currency swap in euros is 4.5% per year and the fixed rate on a currency swap in dollars is 2.5%.
a. Determine what the notional principal in euros and dollars should be for the swap to achieve its objective.
b. Determine the annual cash flow payments between GE and you (bank).
c. Determine the implied exchange rate that GE would lock in if it enters into the swap agreement.
d. How does this implied exchange rate compare to the current spot exchange rate? Explain the difference.
To determine the notional principal in euros and dollars for the swap to achieve its objective, we need to calculate the present value of the expected annual euro receivables of €45,000,000 for five years, starting in 2014. We’ll discount these future cash flows to today’s value using the fixed euro and dollar swap rates.
First, we’ll calculate the present value of the euro receivables:
PV of Euro Receivables = Σ (Cash Flow / (1 + Euro Swap Rate)^t)
Where:
PV of Euro Receivables = €45,000,000 / (1 + 0.045)^0 + €45,000,000 / (1 + 0.045)^1 + €45,000,000 / (1 + 0.045)^2 + €45,000,000 / (1 + 0.045)^3 + €45,000,000 / (1 + 0.045)^4
PV of Euro Receivables = €45,000,000 + €43,181,818.18 + €41,431,685.39 + €39,744,703.68 + €38,115,002.05 PV of Euro Receivables ≈ €207,472,209.30
Now, we need to determine the notional principal in dollars. We can use the current spot exchange rate to convert the present value of euro receivables into dollars:
Notional Principal in Dollars = PV of Euro Receivables × Current Spot Exchange Rate
Notional Principal in Dollars = €207,472,209.30 × $1.37/€ ≈ $284,372,729.16
So, the notional principal in euros is approximately €207,472,209.30, and the notional principal in dollars is approximately $284,372,729.16.
b. To determine the annual cash flow payments between GE and the bank, we’ll calculate the fixed interest payments in euros and dollars based on the notional principals and swap rates.
For Euros: Annual Euro Payment = Notional Principal in Euros × Euro Swap Rate Annual Euro Payment = €207,472,209.30 × 4.5% ≈ €9,334,249.42
For Dollars: Annual Dollar Payment = Notional Principal in Dollars × Dollar Swap Rate Annual Dollar Payment = $284,372,729.16 × 2.5% ≈ $7,109,318.23
So, the annual cash flow payments are approximately €9,334,249.42 from GE to the bank in euros and approximately $7,109,318.23 from the bank to GE in dollars.
c. To determine the implied exchange rate that GE would lock in if it enters into the swap agreement, we can calculate it using the annual cash flow payments and the notional principals:
Implied Exchange Rate = Annual Dollar Payment / Annual Euro Payment Implied Exchange Rate = $7,109,318.23 / €9,334,249.42 ≈ $0.76/€
d. The implied exchange rate of $0.76/€ is lower than the current spot exchange rate of $1.37/€. This means that by entering into the swap agreement, GE would be locking in a more favorable exchange rate than the current spot rate. In other words, GE would be able to convert its euros to dollars at a better rate through the swap agreement, which helps hedge the currency risk associated with its euro receivables. The difference between the implied exchange rate and the current spot exchange rate represents a potential cost savings for GE in terms of currency conversion. This is a common objective of currency swaps, allowing businesses to manage and mitigate currency risk effectively.
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