Please provide the formulas to be used. Exchange rate is USD$/$EUR: $1\mathrm{.}47.$ Suppose it is end of November $2007,$ and Porsche reviews its hedging strategy for the cash flows it expects to obtain from vehicle sales in North America during the calendar year $2009.$ Assume that Porsche entertains three scenarios: The expected volume of North American sales in $2009$ is $32,750$ vehicles. The low$-$sales scenario is $30\%$ lower than the expected sales volume, and the high$-$sales scenario is $30\%$ higher than the expected sales volume. Assume, in each scenario, that the average sales price per vehicle is $$90,000$ and that all sales are realized at the end of November $2009.$ All variable costs incurred by producing and shipping an additional vehicle to be sold in North America in $2009$ are billed in $$ and amount to $60,000$ per vehicle. Characterize how Porsche$$s $$ cash flows, net of variable costs, obtained from its North American sales depend on the spot exchange rate that prevails at the end of November $2009,$ if:

Porsche does not hedge its currency exposure at all.

Porsche hedges by selling forward US$ equal to the amount of expected $2009$ sales with a two$-$year forward contract.

Porsche hedges by buying two$-$year European at$-$the$-$money put options on US$ $($providing to Porsche the right to sell US$$,$ receiving $,$ at the strike exchange rate$)$ in sufficient quantity to have the right to sell an amount of US$ equal to expected $2009$ sales.