Is the NULL Budget the issue, or the Budget Year not == 2016?
Either way, a different approach to this might be ZN. Something this:
ZN(IF [BYear] == "2016"
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IF [BYear] == "2016"
THEN IFNULL([Budget], 0)
The calculation above is functioning as intended. Suppose BYear == "2017". Then your calculated field will not meet the condition [BYear] == "2016", so it will skip the THEN clause and look for an ELSE clause. Since you did not specify the ELSE clause, the value is NULL.