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My understanding is that the standard solution for consolidation in v11 is to select multiple companies in the Financial Reports (e.g. P&L).

This works well if they are all in the same base currency, but if not then the current exchange rate is used to convert to the base currency of the company (could be the parent but doesn't have to be).

This does not seem to be correct.  I believe that it should either use the actual rate at the time of the transaction or some other fixed rate (e.g. average rate for the period).

Does anyone have experience of doing consolidation in a multi-company environment with different base currencies?  Any good ideas?

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The rate used is the rate on the day that the conversion takes place.  This means you are seeing unrealized gains or losses on your reports, always using the latest daily exchange rate.

If it used the rate of the date of the transaction, you would not see the potential value of assets as if you sold them "today".  If you want to see how much of the other currency you hold in your bank, switch to that company's currency.

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