Covered interest parity

Borrowing in euros, converting at spot, investing at the local rate and locking a rate to convert back should earn exactly what investing in euros would have earned. If it did not, there would be a riskless profit available, so the forward rate adjusts until it does.

The consequence is that the forward exchange rate is not a forecast in any interesting sense. It is arithmetic on two interest rates. A currency with higher interest rates trades at a forward discount, meaning the market rate for exchanging it later is worse than the rate today, by about the interest differential.

For valuation this is what makes the two cross currency DCF routes reconcile. Discounting local cash flows at a local rate and converting once at spot gives the same answer as converting each cash flow at the forward implied rate and discounting at the home rate, because the same interest differential appears in both places. If your two builds disagree, you have used an exchange rate path inconsistent with your two discount rates, and one of the two is wrong.

Covered interest parity is a market relationship rather than an economic theory, which is why it holds far more tightly than purchasing power parity does. It can drift, and the gap that opens when it does is known as the cross currency basis, but the drift is small next to the error of assuming no currency movement at all.