I kept trying to work in a reference to "a man who knows the price of everything and the value of nothing". Yes, the value equation is the goal. Cost accounting is a skill in service of being able to understand and create value, but cost accounting is the antidote to technology for technology's sake, where science fiction intersects with reality. God help you if you put the bean counters in charge of making something valuable though.
Material Costs = Cost per unit x amount of waste per good unit
Could you clarify whether you meant:
1. Material Costs = Cost per unit + Cost of waste per good unit
or
2. "amount of waste per good unit" is the ratio "Total Material" / "Material in Good Units" (which is 1.0 with no waste and 2.0 if half the material is wasted)? This math works but assumes that the good unit is constructed entirely out of waste, which was the part I found confusing.
Looking at it with fresh eyes I think I messed that one up. The goal is to account for the cost of each good unit produced. So for an egg, you have the cost of the egg itself. If we buy a dozen eggs for $6 and only make 10 good ones but drop 2 on the ground, 2 eggs are now scrap. Each of the good ones are inventory cost ($6 / 12 or $2 per inventory egg) plus the cost of the scrap ($2 per inventory egg * 2 or $4 of total cost) which we allocate to the 10 good units (so $4 / 10 or $0.40 per egg). So the effective cost per good egg is $2.40 with a yield of 83.3% (10 out of 12 eggs were good units). Looking at your formulas, I believe that calculation most closely matches your first one, where they should be added instead of multiplied.
As you identified, there are many ways to get to these numbers by re-arranging the formulas. Some teams will just have scalars for waste, though that happens more in continuous manufacturing e.g. chemical productions, where liquids are mixed in vats and it's harder to count individual units. Some stuff just gets stuck on the walls of containers or evaporates. That's what I was thinking of when I wrote the scalar. For an example, let's say you make beer and you make 144 oz (a 12 pack of 12 oz cans). The total material costs for each (including the water, hops, barley, anything else) is $1. It involves 10% of waste, so every time you make a case, you lose 14.4 oz of what would otherwise be final product (maybe the staff keeps drinking it before bottling). The unit cost could be $1 per good unit times the waste scalar (so $1 x 1.1). If we make a case of 12, that’s 12 * $1 * 1.1 or $13.20.
The math from the previous formula works here too. We know the unit cost per item, so to find the waste take 14.4 oz divide by 144 oz, and you get $0.10 per oz to add to the cost per unit. That's what I got mixed up when I made it a multiplier, but also why you see both in production settings. Another way to look at it is that, at $1 per 12 oz, it is $0.0833 per oz. You spend $12 on the actual units and have 14.4 * $0.0833 of waste or $1.20 of waste per pack. The second formula you proposed works here, because it would be (144+14.4)/144 = 1.1 multiplied by $12 (the cost per unit) or $13.20.
Note I am doing this on an airplane instead of in a spreadsheet with a cup of coffee to avoid more dumb mistakes, but hopefully those different methods illustrate both the intent and how it should work in practice.
As a form of cost-benefit analysis. :)
I kept trying to work in a reference to "a man who knows the price of everything and the value of nothing". Yes, the value equation is the goal. Cost accounting is a skill in service of being able to understand and create value, but cost accounting is the antidote to technology for technology's sake, where science fiction intersects with reality. God help you if you put the bean counters in charge of making something valuable though.
I found the following equation a bit confusing:
Material Costs = Cost per unit x amount of waste per good unit
Could you clarify whether you meant:
1. Material Costs = Cost per unit + Cost of waste per good unit
or
2. "amount of waste per good unit" is the ratio "Total Material" / "Material in Good Units" (which is 1.0 with no waste and 2.0 if half the material is wasted)? This math works but assumes that the good unit is constructed entirely out of waste, which was the part I found confusing.
Looking at it with fresh eyes I think I messed that one up. The goal is to account for the cost of each good unit produced. So for an egg, you have the cost of the egg itself. If we buy a dozen eggs for $6 and only make 10 good ones but drop 2 on the ground, 2 eggs are now scrap. Each of the good ones are inventory cost ($6 / 12 or $2 per inventory egg) plus the cost of the scrap ($2 per inventory egg * 2 or $4 of total cost) which we allocate to the 10 good units (so $4 / 10 or $0.40 per egg). So the effective cost per good egg is $2.40 with a yield of 83.3% (10 out of 12 eggs were good units). Looking at your formulas, I believe that calculation most closely matches your first one, where they should be added instead of multiplied.
As you identified, there are many ways to get to these numbers by re-arranging the formulas. Some teams will just have scalars for waste, though that happens more in continuous manufacturing e.g. chemical productions, where liquids are mixed in vats and it's harder to count individual units. Some stuff just gets stuck on the walls of containers or evaporates. That's what I was thinking of when I wrote the scalar. For an example, let's say you make beer and you make 144 oz (a 12 pack of 12 oz cans). The total material costs for each (including the water, hops, barley, anything else) is $1. It involves 10% of waste, so every time you make a case, you lose 14.4 oz of what would otherwise be final product (maybe the staff keeps drinking it before bottling). The unit cost could be $1 per good unit times the waste scalar (so $1 x 1.1). If we make a case of 12, that’s 12 * $1 * 1.1 or $13.20.
The math from the previous formula works here too. We know the unit cost per item, so to find the waste take 14.4 oz divide by 144 oz, and you get $0.10 per oz to add to the cost per unit. That's what I got mixed up when I made it a multiplier, but also why you see both in production settings. Another way to look at it is that, at $1 per 12 oz, it is $0.0833 per oz. You spend $12 on the actual units and have 14.4 * $0.0833 of waste or $1.20 of waste per pack. The second formula you proposed works here, because it would be (144+14.4)/144 = 1.1 multiplied by $12 (the cost per unit) or $13.20.
Note I am doing this on an airplane instead of in a spreadsheet with a cup of coffee to avoid more dumb mistakes, but hopefully those different methods illustrate both the intent and how it should work in practice.