Just to back you up on this, the savings should more than triple. 3x the compensation probably more than offsets the 3x in costs, so your savings may be more like 5x or more compared to low COL areas.
3 * income - 3 * cost = 3 * ( cost + savings ) - 3 * cost = 3 savings
Is my assumption wrong? Otherwise it's 3x and not 5x.