Sample ICM Math Calculation

If you are really into ICM calculations for your sit and go skill set, then you should do what this forum member has done and try specific scenarios layed out in basic math. You can even post it in our poker forum for evaluation.

Situation: $5 SnG on the bubble, hero is facing all in push by button....Action goes: Cutoff ( Chip leader) folds, Button ( fourth in chips..aka villain) pushes, Small blind ( Second in chips ) folds, Big blind (aka..hero..third in chips) Fold or call push?

Hero dealt: [Ad 5h]
Blinds: 100-200
Payouts: 1st- $25 2nd-$15 3rd-$10

The stacks are:
Cutoff- 5937
Button- 2286
Small blind- 4475
Hero (Big blind)- 2302

Before the hand, here is how equity is split up:
Players Chips Equity
cutoff 5937 $19.79
button 2286 $7.62
Small blind 4475 $14.92
Hero ( Big Blind) 2302 $7.67

Call push and lose ( -$7.61)
Player Chips Equity
cutoff 5937 $19.79
button 4672 $15.57
small blind 4375 $14.58
hero( big blind) 16 $0.06

Call push and win (+$7.96)
Player Chips Equity
cutoff 5937 $19.79
button 0 $0.00
small blind 4375 $14.58
hero (big blind) 4688 $15.63

So we are risking $7.67 to potentially win $7.96 and using the ratio of ( risk/winnings)/( total equity/winnings) to get the percentage needed by a hand to win against a random hand to make this call +$ev

So ($7.67/$7.96)/ ($15.63/7.96)
So (.963)/ (1.963)= 49.1%

This means are hand needs to win at least 49.1% of the time to make this call +$ev...

Ad 5h against any random hand has 57.697% equity is this making it a clear call....

I would like to know how my math is in this ICM question. I hope this makes sense and i am starting to get the hang of ICM...

Just to throw in a wrench, villain is playing semi passive and has been playing tight over the last maybe 10-12 hands....does this mean that we ignore the ICM calculation and put villain on a better opening range or do we still abide by ICM and call?

And if we do ignore ICM then were also ignoring a +$ev situation (provided my math is correct) which means were making a mistake, but since were on the bubble does that mean its ok to ignore this +$ev situation? Hope this is making sense and somebody can check the math and then determine what we would do in these other situations..