You invest euro-denominated funds in a property whose value and eventual sale proceeds are stated in another currency. A local price increase then explains only part of the outcome. For comparison with your euro outlay, converting at the relevant time also belongs in the calculation.
Consciously limit the international case
We use a fictitious currency X with no connection to any specific country. Purchase and sale costs, taxes, debts, rents and exchange fees are excluded from the model. The aim is solely to link two changes in value in a single correct calculation. For a real foreign investment, all legal and tax issues would need to be clarified separately.
At the start you buy in the example for 100.000 X. The assumed rate is explicitly: one X equals one euro. The original euro outlay therefore amounts to 100.000 euro.
Translate the local gain back into euros
Later the assumed net sale proceeds amount to 110.000 X. In X the amount has risen by ten per cent. The assumed exchange rate is now only 0,80 euro per X. For that reason 110.000 X become 88.000 euro.
Compared with the original 100.000 euro this results in a deficit of 12.000 euro or twelve per cent. The result arises from 1,10 times 0,80 = 0,88. Simply adding the two percentage changes as plus ten minus twenty equals minus ten would not correctly reflect the effect on the altered amount.
Keep the exchange-rate direction consistent
Always note whether euro per unit X or units X per euro are meant. For our calculation euro per X is used consistently. If you invert the quotation, the arithmetic operation must also match; a reciprocal must not unnoticedly appear as the same rate.
The two freely chosen rates are not actual reference or execution rates. For an actual sale, attainable exchange, costs and the timing of available euro payment are of interest. a property value in X is not yet a confirmed sale and not a receipt of money.
Check your objective in the correct currency
If the capital is needed for a later euro purchase, a justified exchange-rate scenario belongs in the personal affordability assessment. If, by contrast, it is needed for obligations in X, a different comparison may be relevant. Nothing here constitutes a recommendation for currency hedging or foreign-currency financing.
The learning example demonstrates a personal capital-investment question: local appreciation and the result from the perspective of the originally invested euro capital can have different signs. Both figures therefore need their own clearly labelled calculation.