Numbers. They have such a comforting certainty to them, don’t they?
Words can be interpreted. But, numbers, they have that beautiful mathematical ring of truth. I was thinking about this the other day, when I got a number from a friend. I was helping him review a model he had made, and I asked him what the median result was from the model. He told me 16.42%. I ask him, “Do you believe it’s 16.42%?” He responded, “Yes, 16.42%.” This was a very smart guy, with multiple advanced degrees in engineering from a great school. However, the data set from which he was calculating this percentage came from a group of people who are giving him estimates of the money they had spent on certain activities, as well as data from an accounting system. And yet, he was quite positive that the result was 16.42%. I.e., he thought that the result he calculated from the inputs had enough precision to generate FOUR significant figures.
Now, I’m sure that he would have realized, if he had sat down and thought about it for a second, that expecting this kind of precision when the inputs had virtually no precision of all, at least not the precision of four significant figures, was ludicrous. However, that’s the great thing about computers, especially when using spreadsheets like Microsoft Excel. They will give you as much precision as you want. In fact, to what does Excel default… two significant digits behind the decimal point.
What I find really funny about this is that most engineers have learned the hard way, over time, that there is this thing called “tolerance stack-up.” In other words, no matter what you specify on a CAD model or drawing, a machine only has so much physical capability to hold that dimension. Therefore, engineers become very proficient at specifying tolerances. In recent years, they have even become much better at understanding the stack up of these tolerances on the final dimensions of a part. In fact, there are very sophisticated software packages dedicated to helping engineers do this.
In more general usage, Monte Carlo modeling became all the rage 10 to 20 years ago. Monte Carlo was an attempt to recognize the inherent noise in numbers that we measure, and how that uncertainty affects the models that we make, especially financial models. However, the funny thing is that when it comes to calculating product costs, people ignore the precision question, and just assume they have the precision they wish they had.
Take a look at the figure below . Let’s go through a simple product costing in concept. For the part we are looking at, we first need to know the physical quantities that are used in making it. For example, we need to know the mass of the part, but that’s a tricky thing, because we have scrap and varying amounts of mass could be used up in certain processes. So, we might be +/-1-3% in our estimate of how much was used. Similarly, we need to know how much time is actually spent on each machine. However, this varies batch to batch, and measurements aren’t always so accurate. There may be many processes that make up the part, including extra inspections and re-work. Let’s say our measurement of the time it takes has a range of 5 to 15%.
Until this point in the analysis, at least we’ve been dealing with physical quantities, not financial quantities. But, if we move to financial qualities, the problem gets much worse. Even material rates are not such a certain thing. They move around over time with various surcharges for this and that from the different material providers. And, the number depends on what material is sent t0 what lines, etc. Labor rates and overhead rates are far more black magic. Accountants with green eye shades spend endless hours calculating these rates from monstrous ERP systems, using Byzantine Activity Based Costing allocation schemes. We hope that the allocated rates are accurate to the real truth on the floor, but I don’t think we can really expect them to be more than +/- 10-20% from what’s really going on.
Never fear though! At the end of the calculation, we have calculated that this particular part cost is $93.45. Why $93.45? Well, that’s what our spreadsheet model or our product cost management software told us. And, of course, a cost NEEDS to be within 10% of what we think the real cost is.
If the product cost management user actually calculated the tolerance stack-up of the uncertainties of the inputs that went into that cost, they would probably find that the costs are more than +/-10% from the true cost. If they seriously considered the possible precision, would they say the part cost $93.40-93.50? I doubt it. Would they say it costs $92.00-93.00? Nope . They probably would say that the part could cost between $88-$97. But, a range like that is not very comforting . It’s much more fun to hit that little “$” format button on Excel or cut & paste the number from the product cost management software .
It’s $93.45. That’s what it is. Because ignorance is truly bliss in the world of Product Cost Management.