How do the following item crafting speedups stack?

Question

So, let's say we've got a level 10 dwarf, Rodney, who first took a level in wizard, making it his favored class. At that point in time, he chose a Valet Familiar. Then he took 5 levels in Cleric, as a Forgemaster. This gives him Craft Magic Arms and Armor and Master Smith (Ex). He then took a four more levels in Wizard, to pick up his Racial Favored Class Bonus. (Only once though!) He chooses Craft Magic Arms and Armor to gain the extra 200 gp/day. He also got a Bonus Feat, at Wizard 5, which he used to apply pickup Arcane Builder, also applied against Craft Magic Arms and Armor.

Master Smith (Ex):

At 5th level, a forgemaster can craft mundane metal items quickly, using half their gp value to determine progress, and can craft magical metal items in half the normal amount of time.

The Racial Favored Class Bonus for Dwarf Wizards:

Select one item creation feat known by the wizard. Whenever crafting an item using that feat, the amount of progress made in an 8-hour period increases by 200 gp (50 gp if crafting while adventuring). This does not reduce the cost of the item; it just increases the rate at which the item is crafted.

Arcane Builder:

Select one type of magic item (potions, wondrous items, and so on). You create items of this type 25% faster than normal, and gain a +4 bonus on Spellcraft checks (or other checks, as appropriate) to craft items of this type.

Rodney is a fan of getting things done fast, so he also always adds +5 to the DC of the craft check to get the items done in half the time.

Okay, so we've got some things going on here:

For Magical Arms and Armor, we've got a straight +200 boost.

For Metal magical items, crafting now takes 1/2 the time.

For a Valet Familiar, we can now craft twice as much per day.

For the +5 DC boost, we can craft in 1/2 the time.

For Arcane Builder, we can craft 25% faster.

So how much can we craft per day?

Does this reduce the total crafting time, ie, for a theoretical 15000 gp metal sword, will it still take 15 days, or will it take less?

My guesses are 1000 gp * (2x->3x->4x)*5/4 + 200 = 5200 gp/day, or (1000gp + 200)*2 *2 *2 * 5/4= 12000 gp per day.

And I'm not sure how much actual time is saved, as I think that the total time needed isn't reduced in all cases.

Answer 1

You get the full amount of reduction

So:

1) X2 X2 is usually only X3 in Pathfinder, because most of the time multipliers stack additively.

2) This doesn't apply here because there's no rolling involved, luckily. It would apply to crafting mundane items, and that gets weird fast, but we'll ignore that.

So:

1,000 a day, base.

1/2 time from Master Smith is effectively X2

Valet Familiar is X2

+5 DC is effectively X2

Arcane Builder is 25% faster, which is effectively X1.25

Altogether that's 10,000 gp/day.

Now, we still need to figure out that favored class bonus. I left it til now because when you apply it might seem like it matters. Obviously, if you apply it first then you make an extra 2000 gp/day, but it seems at first like if you apply it last you'd only make an extra 200 gp/day. Fortunately, this is not the case. All of the abilities you are using to multiply things increase or decrease stuff with no reference to the base amount produced. This means that all gp crafting stuff needs to be modified this way, so that 200 gp would need to be modified by each wealth increasing thing, resulting in the 12,000 gp total.