I have a basic crafters book, so I can craft a dagger by paying 1sp spending 4 days downtime and a DC 14 crafting check. Finally finishing it off for another 1sp in materials.
For a cold iron (or silver) dagger I need to use at least 20sp+2sp per bulk in cold iron, yeah? So I can pay 11sp in materials up front 4 days downtime and a DC 16 expert crafting check. Finishing off with the remaining 11sp in cold iron.
Is this correct? Did I miss something? Do I need to purchase a level 2 formula for a cold iron dagger?
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So I am seeing a few places where you may have gone wrong.
First is you are still using SP. Once we are working with Silver or Cold Iron weapons we're using GP for our costs (they're much more expensive). I'm going to just use Cold Iron throughout to make things easier.
I am seeing from my reading that the cost of the Cold Iron weapon is 40GP +4GP per Bulk. A dagger is light bulk so we round to 1 Bulk. So I believe this would be just 44GP and we are looking at 22 GP of material to get started. Since it is a rare/precious material there may not be enough of it around to craft, so you'd need to make sure even if you had the gold that the location you were in had at least 22 sp of cold iron available to purchase. This 22 sp of Cold Iron makes up part of your initial 22 GP investment.
I would also note that to craft a low grade precious metal item like a dagger we would need to be experts in crafting. We would also need to be at least level 2 and have a Cold Iron Dagger formula. I believe RAW there won't be a generic/interchangeable "level 2 formula" available to purchase. You would have to specifically look for a "Cold Iron Dagger Formula" even though all level 2 Formulas should be at the same price if they are available.
If you were successful on your crafting check (DC secretly set by the DM but normally around 16) after the 4 days of down time you would be able to finish with the remaining 22 GP.
EDIT: Thank you Taja the Barbarian for the correction. I am correcting my original statement to make it easier for the OP who asked the question to get the correct info.
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...I am seeing from my reading that the cost of the Cold Iron weapon is 40GP +4GP per Bulk. A dagger is light bulk however so I believe this would be just 40GP and we are looking at 20 GP of material to get started. ...
While it is not mentioned in the Precious Material Weapon rules, the general Precious Materials rules indicates Light bulk should be rounded up to 1 Bulk:
Materials with the precious trait can be substituted for base materials. For example, a hammer’s head could be made of adamantine instead of iron. Items made of a precious material cost more than typical items; not only does precious material cost more, but the crafter must invest more time working with it. In addition, more powerful items require precious materials of greater purity. A number of precious materials are described below. The Price entry for each material gives the Price of a simple non-magical item made of that material, based on its Bulk (if the item is lighter than 1 Bulk, use the price for 1 Bulk), as well as Prices for different amounts of the material itself. Prices for armor, shields, and weapons made of precious material are in the Armor (page 555), Shields (page 586), and Weapons (page 599) sections of this chapter.
Not certain if this is supposed to apply to weapon costs or not...
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...I am seeing from my reading that the cost of the Cold Iron weapon is 40GP +4GP per Bulk. A dagger is light bulk however so I believe this would be just 40GP and we are looking at 20 GP of material to get started. ...While it is not mentioned in the Precious Material Weapon rules, the general Precious Materials rules indicates Light bulk should be rounded up to 1 Bulk:
Materials with the precious trait can be substituted for base materials. For example, a hammer’s head could be made of adamantine instead of iron. Items made of a precious material cost more than typical items; not only does precious material cost more, but the crafter must invest more time working with it. In addition, more powerful items require precious materials of greater purity. A number of precious materials are described below. The Price entry for each material gives the Price of a simple non-magical item made of that material, based on its Bulk (if the item is lighter than 1 Bulk, use the price for 1 Bulk), as well as Prices for different amounts of the material itself. Prices for armor, shields, and weapons made of precious material are in the Armor (page 555), Shields (page 586), and Weapons (page 599) sections of this chapter.Not certain if this is supposed to apply to weapon costs or not...
Good catch. I would wager that it is intended to apply to Weapons too and would probably interpret it that way in my games to stay consistent.