=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.