You can spend $125,000 to produce a customized machine and enter a bid to sell it for 100,000 Euro. The bid process is one month long during which you must hold your price. Today's spot is 1.35 $/Euro. The US one month interest rate is 1% and the Euro 1 month rate is 2%. Assume a volatility of 20% and that the Black-Scholes assumptions hold, i.e. the exchange rate is log-normally distrusted with mean equal to the forward rate. Answer the following questions assuming that you will win the bid. Use the spreadsheet option calculator to answer part (c). All interest rates are quoted on an annual basis.
a. What is your profit in US$ if today's spot exchange does not change?
b. What exchange rate in one month time would create a loss of $10,000?
c. You want to evaluate the cost of buying a put on the Euro to hedge your FX risk. What is the value a one month put on 100,000 Euro struck at 1.35 $/Euro priced at 20% volatility?
d. What is the probability that an exchange rate move creates a loss greater than $10,000?