MINICASE: AIRBUS' DOLLAR EXPOSURE

Airbus sold an aircraft, A$400,$ to Delta Airlines, a U$.$S$.$ company, and billed $$30$ million payable in six months. Airbus is concerned with the euro proceeds from international sales and would like to control exchange risk. The current spot exchange rate is $$1\mathrm{.}05i$ and six$-$month forward exchange rate is $$\frac{1\mathrm{.}10}{}$ at the moment. Airbus can buy a six$-$month put option on U$.$S$.$ dollars with a strike price of $\frac{0\mathrm{.}95}{S}$ for a premium of $0\mathrm{.}02$ per U$.$S$.$ dollar. Currently, six$-$month interest rate is $2\mathrm{.}5\%$ in the euro zone and $3\mathrm{.}0\%$ in the U$.$S

a$.$ Compute the guaranteed euro proceeds from the American sale if Airbus decides to hedge using a forward contract

b$.$ If Airbus decides to hedge using money market instruments, what action does Airbus need to take? What would be the guaranteed euro proceeds from the American sale in this case?

c$.$ If Airbus decides to hedge using put options on U$.$S$.$ dollars, what would be the 'expected' euro proceeds from the American sale? Assume that Airbus regards the current forward exchange rate as an unbiased predictor of the future spot exchange rate.

d$.$ At what future spot exchange rate do you think Airbus will be indifferent between the option and money market hedge? Solution:

a$.$ Airbus will sell $$30$ million forward for $27,272,727=\frac{\text{\$}30,000,000}{\text{\$}\frac{1\mathrm{.}10}{}}.$

b$.$ Airbus will: $($a$)$ borrow the present value of the dollar receivable, i$.$e$.,$ $$29,126,214=$$$30,000,\frac{000}{1\mathrm{.}03},$ and $($b$)$ sell the dollar proceeds at the current spot for euros receiving: $27,739,251(-$ $$29,126,\frac{214}{\text{\$}}\frac{1\mathrm{.}05}{}$lon $)$ This is the euro amount that Airbus is going to keep.

c$.$ Since the expected future spot rate is less than the strike price of the put option, i$.$e Airbus expects to exercise the put option on $S$ and receive $28,500,000-($ $$30,00n,000.$ This is gross proceeds. Airbus spent $600,000(-0\mathrm{.}0230,000,000)$ upfront for the option and its total cost $($including the opportunity cost of earning interest on the put option premium$)$ is equal to $615,000-600,0001\mathrm{.}025.$ Ihus the net euro proceeds from the American sale is $27,885,000,$ which is the difference between the gross proceeds and the option costs $-615,000$

d$.$ At the indifferent future spot rate, the following will hold

$lon28,432,732-S_7(30,000,000)-lon615,000.$

Note that $28,432,73$ is the future value of the proceeds under money market hedging: $28,432,732-(27,739,251)$

$(1\mathrm{.}025)$ which is the accumulation value of investing the $in$ proceeds from the money maiket hedge at the $f$ interest rate Solving for $S_T,$ we obtain the "indifference" future spot exchange rate, i$.$e$.,\frac{0\mathrm{.}9683}{S},$ or $$\frac{1\mathrm{.}0327}{}$lon$(\frac{1}{}$lon$\frac{0\mathrm{.}9683}{S})$