Example: Cost & Cost Behavior

Profit: A Perennial Prime Concern.


Costs a key profit component:

Profit and cashflow tend to be the key concerns of most businesses, in good times and bad. Profit is a function of revenue and costs. Costs, in turn, can be viewed as a wide assortment of functions, depending upon how one "slants" the taxonomy. Among the many ways costs might be addressed are direct costs versus indirect costs or fixed costs versus variable costs.

For instance, the management of a widget factory asks us to determine the unit manufacturing costs for the month. Absent any other direction, we'll assume that what they want is, specifically, direct manufacturing costs. We do some checking and find that the aggregate figure was $10,000 for 500 units produced. The unit direct cost was, therefore, $10,000/500 = $20.


Breakeven Point:

Management, further, asks us to determine what sales level they must achieve to return to profitability. We find that non-direct costs approximate $75,000/month. Widget, Inc. must, therefore, sell $75,000/$20 = 3,750 units. That is, their monthly breakeven point (BEP), is 3,750 units. They, then, would also like to know what would happen to their BEP, if they were able to trim $15,000/month from their costs. Their new BEP would be 3,000 units, which, they respond, is still higher than what they deem to be a realistic sales goal in the current depressed market for widgets. So, they ask, by what would they have to reduce their non-direct costs to breakeven at a sales level of 2,250 units/month. We immediately respond, that they'd have to reduce their costs by $30,000/month, for a new figure of $45,000/month.


Costs as systems of differential equations:

Quick thought-experiment: In terms of monthly costs and productions, mentally plot the curve of fixed costs (FC) against unit production levels X-axis (output). What did you get? Good, yes, a flat line crossing the Y-axis ($) at whatever the period fixed cost happens to be because, dy/dx K = 0. Yes, there could, of course, be variances from budget, but we'll ignore them for a moment. To continue our Gedankenexperiment (Gedankenversuch, if you prefer), what would the graph of variable costs (VC) look like? Yup, a straight-line starting at the origin sloping upward towards the right. Hmm. Did you notice that we have two "slopes" mapping against variable production levels? Does the term, "rate of change," come to mind?


Costs and grad, div, and curl:

What would the graph of variable costs divided by output level (AVC) look like? Right, we've got another flat-line, because the unit variable costs (in our trivial model) are constant. In essence, we're looking at average variable cost. Continuing, what would the graph of period fixed costs DIVIDED by output (AFC) look like? At this point, it should be obvious from the shape of the AFC curve and the BEP results, why so many companies were and continue to be in serious trouble in the current economic climate.

So, if output levels could increase indefinitely, the average unit fixed costs would approach a limit of $0, i.e., asymtotic to the X-axis. This, of course, is what you intuitively knew; increase production to defray the period fixed costs across a wider unit pool. How do you size a electricity generator for a steady-state implementation? Right, run-the-hell-out-of the thing; same thing for a manufacturing facility.

Intuitively, we know that we cannot infinitely increase production with a finite productive capacity (FC); we have to become "bound" at some point. Note, now, that our cost curves have some common X-value (output) terminus. Hmm. Line segments with magnitude and direction ... "sounds" as though that might "rhyme" with vectors? What does the rate of change of AFC start to look like?

Sadly, once a firm has committed to high fixed costs (typically to reduce unit variable costs), it becomes a slave to production levels. As most firms tend to debt finance capital expenditures, the monthly debt payment (rent), their are left with few (and no, "good") choices.

Cost component analysis:

Now, we might want to know what the breakdown of direct manufacturing costs was between its components: material, labor, and overhead. You may know overhead as "burden," among a great many others (playing mix 'n match with synonyms is a job-security ploy used to great advantage by accounting-types).

We learn that the $10,000 is broken down as:
Material (M) $5,000
Labor (L) $3,000
Overhead (O) $2,000.

Alright, that's interesting enough, but not particularly informative. How many deluxe units did we produce for $10,000? (Let's assume, 100.) So, the average unit cost came to $100;

How much was the cost last month? How much was the cost for May of last year? What was the cost composition (MLO) for those periods? Yada, yada, yada. You get the picture.

Now, enter you with your analytical perspective. We have cost by product (deluxe), by cost component (MLO), by time (various bases), et cetera. Any twit can ask for and/or break this all down by percentages, cost mix, etc. What you ask (yourself) is, let's look at longer time horizons and try to see if costs are trending toward a limit? Is there consistency in the trend or is it "all over the place?" Is cost exhibiting acceleration, either positive or negative? Again, on and on.



Here's a question for you. The design engineering spec calls for a unit material cost of $43 and a unit labor cost of $27. What might be going on here? What if our plant is engineered and staffed with a production maximum of 75 units?

Cutting-to-the-chase and keeping it simple: The design capacity is typically termed in accounting/financial parlance, "the relevant range." So, what do we have when the production level approaches and passes that "range"? Correct, it's simply a discontinuity. (Our old chums, "holes," "cliffs," and "volcanoes," from baby calc, right?) Much can be made of the various functional relationships between cost and assorted bases.


Approach: Why do our modules and courses center on financial statement modeling? In whatever type organization you work or consult, you will be expected to communicate effectively with the non-quants. Their world is that of financial statements, sort of. (You'll learn tons about them.) Moreover, they don't cope well with numerics, so you must meet them on their terms. To do so, you must achieve utter mastery of graphical presentation and the underlying financial models ... and so you shall.

You may use whatever vehicle you wish, but the classes will be presented in Excel; for better or worse, Redmond rules. You will be provided with a range of Add-ins and other software as necessary, however, you must arrive with the Frontline Systems (especially, Solver) add-ins installed. BTW, your writer is a die-hard RTFM-type, but quite a bit of what is typically covered in the various courses is not in the manuals ... or any of the 1200 page doorstops.

For some courses, you may reinforce the coursework with specific textbooks. We try to use "previous" editions so that you can buy used copies.

Where desirable and practicable, you'll work with real-world problems and datasets.


This is THE foundation course for all of the others. Students of all backgrounds find it an incredibly intense learning experience, not surprisingly. You cover the key fundamentals from: macroeconomics, microeconomics, financial accounting, managerial accounting, managerial finance, and managerial marketing. Don't panic, we eliminate the repetition and skip the fluff which saves tons of time. However, to be sure, you will not be bored.

Analytically, you'll commence building non-trivial models within the first 15 minutes. You'll proceed to delve deeper as we cover formulation, perturbation, and optimization techniques. By the end of the week, you'll routinely produce multi-year projections incorporating the key MBA concepts, all couched within constrained optimization models, with which you will analyze key decision-making issues and outcomes as well as demonstrate and articulate key variable sensitivities.

More broadly, the course learning objective is for you to be able to understand business-speak, to assess a business situation, to identify the business problem, to analyze the problem so as to be able to reach a useful conclusion, and to present your findings in compelling fashion. You will be presented with in-class (brief) "situations"; you will, also, be given overnight mini-cases which are not so brief. You will be encouraged to work in teams, which is why we urge you to attend with friends/associates if possible.

Within the only three "quant" academic institutions, this course would typically be termed advanced business analytics. That said, the non-quant content approaches capstone EMBA courses. The course content ranges further afield than ISA-1, but the focus and the rigor are the same. Students find that their understanding of business deepens dramatically over the course of five days. Depending upon student abilities, elements from the following modules are anticipated:

Advanced Modeling: This centers upon real-world problem solving writ large. We use Access to provide an interstitial intermediary between an Excel front-end and SQL engines.

Statistical Modeling: This course is presented in SPSS 17, however, students typically use whatever they choose. The main focus is upon situational circumstance, experiment design, analytical technique, dataset approach, and findings presentation.

Investment Science: Just as the name implies. We draw from the academic industry standard, Investment Science by Luenberg.

Introduction to Financial Engineering: C++ recipes, Luenberg, and, when time permits, Hull's Options, too. This stops short of stochastic calculus and Ito's lemma, but no one's been bored yet.

Marketing Engineering: This is highly recommended for R&D engineering-types. Unlike the academe, we stress the importance of such "foreign" topics as target-costing and constrained optimization. This, in our opinion, is a real "sleeper" of an area with huge career potential for certain quant-types. Think: "Innovation meets profitability." That's no contradiction; check out what Honda Sochiro did and how he did it to England's entrenched motorcycle industry in less than 5-years. Lillien & Rangaswamy.