Sharepoint calculated field formula

Question

=IF(([ATP Type] = "Tin", DATE(YEAR([First Production Date]), MONTH([First Production Date] + 4), DAY(First Production Date))),
(IF([ATP Type] = "Film & Tray", DATE(YEAR([First Production Date]), MONTH([First Production Date] + 3), DAY(First Production Date))), 
DATE(YEAR([First Production Date]), MONTH([First Production Date] + 1), DAY(First Production Date))))

My requirement is simple. A dropdown with three string values that represent an integer to add months to a date field for the output of a new production date.

Can someone please help me correct my formula.

Answer 1

=IF([Target First Production Date]="","",IF([ATP Type]="Tin",DATE(YEAR([Target First Production Date]),MONTH([Target First Production Date])-4,DAY([Target First Production Date])),IF([ATP Type]="Film & Tray",DATE(YEAR([Target First Production Date]),MONTH([Target First Production Date])-3,DAY([Target First Production Date])),IF([ATP Type]="Case",DATE(YEAR([Target First Production Date]),MONTH([Target First Production Date])-1,DAY([Target First Production Date]))))))

That was my final formula @yevgeniy.chernobrivets, yes you were correct. Also I had to explicitly create the final IF case as opposed to relying on the implicit else which I find strange.