I think you need to mention that the Analysis ToolPak Add-In needs to be installed before the EOMONTH() function is available.
If not sure that the Analysis ToolPak Add-In is installed, then the safest formula to use is your second one:
=DATE(YEAR(TODAY()),MONTH(TODAY())+num_mths,0) where num_mths = 0 for the end of month for the current month and num_mths = 1 for the end of the month for the next month, etc.
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