Damage conversions with hatred and infernal blow

I am wondering exactly how the damage conversion would work for the following scenario:

Infernal blow templar with hatred aura active.

As a simple example, lets say I do 100 physical damage base, 50% is converted to fire by infernal blow and 20% physical is added as cold by hatred. Say I also have passives adding up to 50% increased fire damage dealt.

My guess is that it would work out like this:

100 physical damage base
20% physical dmg is addeed as cold --> 100 x 0.2 = 20 cold damage added.
50% physical dmg converted to fire --> 100 x 0.5 = 50 fire damage
Fire damage increased by 50% --> 50 * 1.5 = 75 fire dmg after passives.
Total dmg = 50 physical + 20 cold + 75 fire.

Can anyone confirm whether this is the way it will work out?

Yes, that is correct.

Keep in mind the confusing behaviour, once you get %increased physical damage too.
So for you example i'll add a 30% increased phys damage:
We have:
100 base phys
50% phys converted to fire
20% phys added as cold
50% increased fire
30% increased phys

This makes for:
Fire: (100*0.5) * (1 + 0.5 + 0.3) = 90
Cold: (100*0.2) * (1 + 0.3) = 26
Phys: (100*0.5) * (1 + 0.3) = 65
Total: 181 dmg

Basically this means, that phys increase applies to converted damage,
however it does so AFTER the conversion, sharing it's increase with the corresponding
increases to the now elemental damage.