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Yes, basement insulation needs a vapor barrier due to its susceptibility to moisture seeping in from the outside of the house. You should install a moisture barrier before you install insulation or purchase insulation that comes prebuilt with a moisture barrier to avoid water damage in your insulation and costly mold and water remediation expenses. 

Heat lost through uninsulated basement walls can account for up to 30% of the total energy lost through heat transfer to the outdoors. While homes in mild climates won't gain as much benefit from having an insulated basement as those in cold climates, the effects are still noticeable on your energy bill.

Costs depend on area size, material thickness, and site preparation needs.

If you plan on heating your garage, you must install a vapor barrier when drywalling the garage. A vapor barrier protects your garage from frost and mold that can occur through condensation. If your garage is unheated, you don't need to install a vapor barrier. The only exception is if you regularly crank the heat in your car before getting in it. In this case, you may still want to install a vapor barrier, as your car can heat your garage.