Excel formula for first day of previous month

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I'm trying to write a formula for the first day of the previous month.
I'm using: =DATE(YEAR(TODAY()),MONTH(TODAY())-1,1)

It works today, but I don't think it will work in January, because the formula would then return the year as 2016, and I need it to return the previous year in that case. Does anyone have a suggestion for how I can modify this so it will return Dec 1 of the previous year if the current date is sometime in January?

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