It’s clear from Reading 23 to use the historical rate at which the common stock was issued. But questions from Schweser QBank seem to indicate that the beginning rate (the exchange rate from the previous year) should be used. I assume, then, it depends on which rate(s) we’re given in the question?
Common stock and dividends are translated at the historic rate when they were issued under both methods. I’m guessing the question has a caveat that says firm was created January 1st of last year.
All components of equity other than retained earnings are to be translated at historical rates in both the methods. For retained earnings you will: Take the beginning value of retained earnings + Net Income (whatever value has come from the I/S) - Dividends translated at historical rates. I would go for historical rates first if mentioned in the question and if not mentioned, then go for the rate mentioned in the question.