new layer from calculations with fields of other layers in QGIS

I've two layers, both with the same fields: A, V, where A is the shape's area and V a value given by me. I want a new layer with shape created by the intersection of the other layers' shapes and a value given by the calculation: (A1*V1+A2*V2)/(A1+A2). Is there a command to make it automatically? Obviously in reality I have many layers with many shapes, otherwise I made it manually.