American Airlines has just signed a contract to purchase an A340-600 aircraft fr

Question

American Airlines has just signed a contract to purchase an A340-600 aircraft from Airbus for 250,000,000 euros. The payment is due six months later. As the Lead Risk Analyst of American Airlines, you are considering how best to hedge the exchange rate risk arising from the purchase, and need to make a recommendation to the Treasurer based on your analysis. You have gathered the following information:

The spot exchange rate is $1.2000/€

The six month forward rate is $1.1950/€

The cost of capital of American Airlines is 12% per annum.

The premium on a six-month call option on the euro with strike price $1.2000 is 2%.

You are trying to help decide between the following two alternatives:

Hedging with a forward contract

Hedging using a call option on the euro

a) Suppose that you strongly expect the euro to appreciate. In that case, which of the hedging alternatives would you recommend? Justify your recommendation. (No calculations are necessary.) (5 points)

b) Suppose that you strongly expect the euro to depreciate. In that case, which of the hedging alternatives would you recommend? Justify your recommendation (No calculations are necessary.) (5 points)

c) Suppose that you expect the euro to depreciate. By how much does the euro need to depreciate in order to make the call option a better alternative than the forward contract? In other words, how low does the euro have to go in value to make total cash outflow under the call option be less than that under the forward contract? Support your answer with calculations. (5 points)

Explanation / Answer

Call Option Strike Price = Spot Rate of Underlying (Euro) 1.2$ per Euro.

Option Premium = 2% of 1.2$ = 0.02 x 1.2 =0.024$.

Cost of Capital = 12% per annum. Maturity of Contract = 6 months or 0.5 years

Therefore, effective exchange rate under call option for hedger = Call Premium + Strike Price = 1.2+0.024 = $1.224 per Euro.

Spot Price after 6 months = Current Spot Price x e^(0.12 x 0.5) = 1.2 x e^(.12x0.5) = $1.2742 per Euro

Forward Contract Price = 1.195 $ per Euro.

(a) If appreciation is strongly expected then one can buy less euro per dollar. In other words the dollar value of the payables of 250 million Euros go up. Hence, the forward contract is a better option as it essentially locks in a cheaper rate of $1.195 per Euro. However, the hedger will face a loss if the euro depreciates against expectations as a forward contract is binding unlike a call option.

(b) If depreciation is strongly expected then one can buy more euro per dollar. In other words the dollar value of the payables worth 250 million Euros go down. Let the spot price after depreciation be S

Therefore, in case of forward contract : Hegder Loss = (1.195 - S) $ per Euro ( as the hedger has to purchase euros at the forward price of 1.195 $ per Euro)

Call Option: Hedger Loss = (Strike Price + Option premium -S) = (1.224 - S) $ per Euro

Hence, even in case of depreciation hedge using forward is better.

NOTE: If currency is expected to depreciate then no hedging is required as dollar value of 250 million euros payable goes down in this case. Even if hedge is used, call option though incurring higher losses would be better because option sare non binding whereas forwards are binding. From a purely loss minimising persective forwards is better but from the perspective of practical application a call is better.

(c) Call Option : Let spot price be K and Option Premium = 2% of the spot price K = 0.02 x K

Therefore, total cash outflow in call option = K + Option premium ( as the euro is depreciating the hedger will not exercise the option and purchase euros at the spot rate. However, the premium as a percentage of spot price of the underlying asset will already have been paid)

K + 0.02K = cash outflow under forward contract ( so as to make these two alternative equivalent)

K+0.02K= 1.195 $ per Euro. Solving for K = $1.171 per Euro.

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