Why is this yield factor equation the way it is?

July 14, 2009 10:15 AM

Why is this formula for food yield factor the way it is?

One of our clients is a meat wholesaler - bacon, sausage, pork, deli, etc. They want a food cost calculator on their site, and this is the formula they gave us:

Yield Factor = ((Starting Weight x Cost)/Final Weight)/Cost

Doesn't the cost cancel out of the equation? Why isn't it just Starting Weight / Final Weight?

posted by starvingartist to food & drink (11 answers total)

Is the cost the same cost? Maybe the Cost in the numerator is the cost they pay for the meat and the cost in the denominator is the cost they sell it for.
posted by If only I had a penguin... at 10:19 AM on July 14, 2009

They didn't specify two different costs, just "cost".
posted by starvingartist at 10:22 AM on July 14, 2009

Usually, this is due to the component parts of the calculation being separate named values, and someone just substituted it in to give to you, without thinking it through. This kind of thing is often very simplified, and usually there is an underlying worksheet, and those intermediate values are shown, so it's not as useless there.

If it makes you feel better, this page gives the same formula.
posted by smackfu at 10:50 AM on July 14, 2009

The costs don't cancel out; it can also be written: starting weight/(final weight/cost)
posted by TedW at 12:17 PM on July 14, 2009

TedW - What about the first cost factor? I wrote it out on paper and expanded it, and to me it looks like it comes out to this:

SW X C
---------
FW X C

So the C (cost) cancels out, and you're left with SW over FW.
posted by starvingartist at 12:20 PM on July 14, 2009

If you look at the examples on the page smackfu links, cost does cancel out of the equation. As far as I can tell, it's just that the author is bad at math and doesn't realize it. You get exactly (to several digits, at least, with errors presumably due to rounding) the same yield factor if you ignore the cost and just calculate SW/FW. (Which is simply the reciprocal of the fraction of the total weight that's useful.)

As far as I can tell, what they're trying to do (albeit in a needlessly complex way) is to be able to calculate the effective cost of food per unit usable weight. For example, if you are trying to compare boneless chicken breasts at $4.99/lb. vs. bone-in chicken breasts at $3.49/lb., you can find out which is the better deal^* by multiplying each by their yield factor (very close to 1 for the boneless, significantly more for the bone-in) to find the cost per pound of usable meat for each option. Or, if you're serving an 8 oz. filet to a customer and want to know how much that meat cost you, you have to base that on the amount of usable meat you bought, not the whole weight.

^*Assuming there is no labor cost for deboning the bone-in breast, which is clearly not the case, but I'm not surprised the sort of person who doesn't realize cost cancels out of that equation wouldn't think to consider the cost of labor either.

I also object to their simply assuming different types of usable meat have the same unit value, as they do in the chicken breast + cracklings example, but that's a whole other issue.
posted by DevilsAdvocate at 1:23 PM on July 14, 2009 [1 favorite]

When you expand it it should be [(sw x c)/c]/(fw/c). Then the c's only cancel out for the numerator. The same is true of the equation on the linked page.
posted by TedW at 1:47 PM on July 14, 2009

TedW -- check your work.

The equation as given is [(SW*C)/FW]/C . Numerator is (SW*C)/FW. Denominator is C. Multiply each by (1/C) and you get new numerator SW/FW, and new denominator of 1.
posted by losvedir at 2:53 PM on July 14, 2009

I think that the formula for yield factor is the way it is because it's been lifted from the first food-related site in a Google search for "yield factor".
posted by flabdablet at 4:49 PM on July 14, 2009

Hey, fun thing, I was just covering this in class (chef school, cost control class) a couple weeks ago.

Here's how it works.

Starting Weight x Cost gives you the initial cost of the item. E.g., 10kg beef x $2/kg = $20


/Final Weight) gives you the actual cost per unit. E.g. 8kg final weight = $2.50/kg actual cost


/Cost then gives you a percentage you can use for anything if your constants remain the same. Although I'd imagine they would want the inverse of that number. I have a whole textbook sitting here ...somewhere... so please feel free to ask if you have further questions.
posted by dirtynumbangelboy at 1:11 AM on July 15, 2009

Which does in fact mean that Starting Weight / Final Weight gives you that exact same percentage, and if that percentage is indeed what you actually want to calculate, then multiplying and subsequently dividing by Cost really is redundant.
posted by flabdablet at 4:04 AM on July 15, 2009