Apologoes if this has been covered already.

In terms of determining if a refi is worth it, a common test that I hear a lot of is to divide the closing costs by the monthly payment saving to determine a pay-back period.

My question is: Part of the monthly saving is a reduction in principal payment and the rest is a reduction in interst payment. Can the reduction in principal payment really be considered a "saving"? A percentage of my "saving" was going towards reducing my principal and is now staying in my wallet - how is that a saving? Should the payback period be determined by dividing by the saving in interest only?

Thanks in advance!