You are the CFO of a U.S.-based multinational firm. You need to borrow $1 million for six months to meet some working capital needs. You can borrow in the following currencies at the following rates which were quoted to you earlier today by your bank:
Dollars at 5.5%
Euros at 9.7%
Mexican Pesos at 11.6%
One dollar is currently worth 13.5 Mexican pesos and one dollar is also worth 0.75 euros.
You realize that the cost of borrowing in a currency other than your home currency involves exchanging your dollars into that currency when it is time to repay the loan in six months. With this in mind, at what future €/$ and Peso/$ exchange rates will you be indifferent between borrowing in all three currencies? That is, what do those exchange rates need to be in six months in order for the cost of borrowing in all three countries to have been exactly the same?