No, you would not need to change the cost basis every year because the exchange rate changes. Basically, in year one, when you started depreciated the property that is your cost basis. That is the basis you will depreciate until you sell the property. When you sell the property, you would use the exchange rate on that date to calculate your gain or loss on the sale. Just like a property in the US, you would only adjust your basis when you do something such as selling it or making a major improvement to it. Otherwise, what it started at is what it stays until you sell it.
If you have other expenses during other years, then yes, they would be calculated at the rate of exchange on the date of the expense.
Sale of foreign property
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