so: if the outer ring is at 46mm with a 113 bottom bracket, you can calculate where it will be with a 107mm bottom bracket. here's how:
subtract 107 from 113 to get the difference. the answer is 6.
divide 6 in half. you get 3. three millimeters. the reason you divide it in half is because you are taking length off from both sides of the spindle.
next, subtract 3 from 46. the answer is 43 millimeters.
next, subtract 42 from 43, and the answer is 1 millimeter.
so: how close is it to 42? 1 millimeter.