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When I calculate “internal rate of return (IRR)”, should I include cash balance?
Both are correct depending on what you are really trying to evaluate. If you only want to understand how that particular investment you were taking money in and out of did by itself than you would ignore the cash.  You might use this if you were thinking of replacing that particular investment with another but keeping the in/out strategy. If you want to understand how the whole investment strategy worked (both the in/out motion and the choice of investment) than you would definitely want to include the cash component as that is necessary for the strategy and would be your final return if you implemented that strategy. As a side note, neither IRR or CAGR are not great ways to judge investment strategies as they have some odd timing issues and they don't take into account risk.