A U$.$S$.$ auto dealer contracts on February $1,2023$ to take delivery of $10$ Mercedes cars at $75,000$ each on May $15,2023.$ The dealer must pay $750,000$ on delivery and wishes to immunize itself against any increase in the Euro. The current spot $$/=1\mathrm{.}3535.$ Euro futures for June $2023$ delivery are priced at $$/=1\mathrm{.}3933.$ There are $125,000$ per futures contract.

a$.$ What is the dealer$$s total exposure in Euros?

b$.$ What is his expected cost in $ at the present exchange rate?

c$.$ If the dealer decides to immunize himself and secure a futures contract, what action should he take? How many contracts should be buy$/$sell$?$

d$.$ Suppose that on May $15,2023,$ spot $$/=1\mathrm{.}4050$ and Euro futures price $($June delivery$)$ has risen to $$/=1\mathrm{.}4493.$ Compute the profit or loss on the dealer$$s hedge of his future Euro payables.