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I am making an artificer that is optimized for making items. I currently have Extraordinary Artisan (-25% price), apprenticeship(-10% price) and mercantile background(-25% price, DM allowed me to buy materials as a single item).

The DM and I got into a discussion as to how discounts would stack. He is saying that it makes sense for discounts to stack multiplicatively (.75*.75*.9 = .506), but I told him that like any multipliers in 3.5 they stack additively ( 1 + (.75 - 1) + (.75 - 1) + (.9 - 1) = .40)

Which one is right?

UPDATE

As stated by SevenSidedDie, real-world values are subject to real math, so the question falls to whether discounts apply all to the same value (like in simple interest):

if something costs 1k, I would get 25% off of 1k, then 25% off of 1k, then 10% off of 1k = 1k - 250 - 250 - 100 = 400

or if they apply one at a time (like in compound interest):

if something costs 1k, I would get 25% off of (25% off of (10% off of 1k)) = 1k * .75 * .75 * .9 = 506

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  • \$\begingroup\$ Non-related to the question (that's why it is on the comments), but remember that if your DM allow it, you can craft an item restricted to race or class or alignment for an extra 30% discount on price: d20srd.org/srd/magicItems/… \$\endgroup\$ – Nibelung Sep 13 '15 at 4:46
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Your DM is right. The special additive combining of multipliers in D&D is only for abstract mechanical values such as dice rolls or modifiers. Under “The Basics: Multiplying” it says this clearly:

When applying multipliers to real-world values (such as weight or distance), normal rules of math apply instead.

This would include prices.

But doesn't additive multiplying apply to modifiers?

Yes, but that's not what you're doing here. Your modifiers aren't modifying another modifier or a dice roll, they're modifying a price, so the additive multipliers rule therefore doesn't apply and you use normal math instead.

Per the example provided in the link, it is explicitly the case that multipliers to things like a price are applied all at once together, not applied to the base number individually and then the individual results added together to find the total effect of the multipliers. Besides — that would make it identical to the additive method, which would defeat the point of saying to use normal math instead. That makes it work kind of like your compound interest example (although that's misleading, because interest involves the time dimension in a way that discounts to a given price do not).

If for some reason you're applying your discounts separately to separate costs, then this doesn't matter and how to combine them together is irrelevant, because they're obviously not being combined. How to combine multipliers is only relevant when one price has multiple discounts that apply to it at once.

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    \$\begingroup\$ The Complete Cost Reduction Handbook agrees with this answer, saying: "Furthermore, please note that as cost is a real world value, cost reductions are not added together but multiplied by the total, one after another so that two 25 percent reductions lead to a total reduction of 43.75 percent. PHB 304 is where that rule comes from." Otherwise, I could see a situation where you could eventually get merchants to give you money and the item... \$\endgroup\$ – phyrfox Sep 12 '15 at 18:35
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    \$\begingroup\$ Would XP cost reductions be computed as this answer suggests as an XP cost is part of the real-world cost of constructing an item or would XP cost reductions be computed in a lump sum as (presumably? probably?) real-world folks don't have XP? \$\endgroup\$ – Hey I Can Chan Oct 12 '15 at 17:01
  • \$\begingroup\$ @Hey I'm not sure, but I'd lean strongly toward normal math. Additive multipliers is for "When two or more multipliers apply to any abstract value (such as a modifier or a die roll)", which doesn't sound like XP. XP seems more like a quantity, a measurement. It's a real quantity to our out-of-game management of the character, if you will. But I think it's easier to define what XP isn't—a die roll or modifier—and take that as deciding that it doesn't get the exception of weird math. \$\endgroup\$ – SevenSidedDie Oct 12 '15 at 17:32
  • \$\begingroup\$ Sounds fair. If you'd like examples to update your answer, when creating a magic item a creature that successfully uses the feat Extract Demonic Essence (Fiendish Codex I 86) pays 50% XP and a creature with the feat Legendary Artisan (Eberron Campaign Setting 56) pays 75% XP. \$\endgroup\$ – Hey I Can Chan Oct 12 '15 at 17:47
  • \$\begingroup\$ so can someone clarify? Does this mean it's done like this? 5000−((5000/100)*25)=3750) 3750-((3750/100)*10)= 3,375 \$\endgroup\$ – Zakier Jun 25 '16 at 19:39
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As stated earlier, costs are real-world values, so always add does not apply to them.

The problem with adding the discounts is that each of them applies to a different value, so they don't actually stack.

Extraordinary Artisan gives you a discount on the base price, so you take base * .75, which equals the new "base" price.

Then, when you are purchasing materials (which is the base price times .75 from the previous discount times 0.5, which is the base discount for crafting materials), you get a 10% discount on the materials from apprentice(craftsman), so you now have (base * .75 *.5) * .9.

Finally, you get a 25% discount at the end of your purchase, so you get ( (base * .75 * .5) * .9) * .75

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