Final answer:
To compute the U.S. firm's exchange exposure, you sum the future dollar values of the asset in each state multiplied by their probability, which gives an expected value. The exchange exposure is the difference between this expected value and the current dollar value of the asset.
Step-by-step explanation:
To calculate the exchange exposure faced by a U.S. firm with an asset in France, we must look at the potential changes in the dollar value of the asset due to changes in the exchange rate. This firm has equal probabilities for four different future states of the world, each with a different spot exchange rate and corresponding euro and dollar prices for the asset (P* for the euro price and P for the dollar price).
The firm's exchange exposure is its potential financial loss or gain resulting from the changes in the exchange rate. Since there are equal probabilities for each state, the expected value of the asset in dollars can be computed by summing the dollar values of the asset in each state multiplied by their respective probabilities and then subtracting the asset's current dollar value (P). The current dollar value can be considered as the weighted average of the four possible future dollar values (since the probabilities are equal).
Expected value of the asset in dollars: (0.25 * $1,800) + (0.25 * $1,540) + (0.25 * $1,300) + (0.25 * $1,080) = $450 + $385 + $325 + $270 = $1,430
The exchange exposure is the difference between this expected value and the current dollar value of the asset, if we consider the current dollar value to be the weighted average of the four states. However, if the firm has a specific dollar value for the current asset (say, based on the current spot rate), we would subtract that specific value instead.