Profit & Loss

Square Root Costing: A Better Method

Square root costing is the only costing methodology based on an accurate understanding of complexity costs, say the co-founders of Wilson Perumal.
Stephen A. Wilson and Andrei PerumalApril 19, 2018
Square Root Costing: A Better Method

Most companies do not truly know where they make money.

This may be a shocking statement, but upon reflection it should ring true. If your company is like many others, you know your overall costs, but you do not know your costs at a more granular and actionable level.

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You know how much overall profit you make, but you do not have a clear picture of your profitability by product or by customer.

In today’s complex businesses, massive cross-subsidizations mask the true cost and profit of products, customers, market segments, and activities. As a result, it’s not surprising that many executives have confided in us that they don’t truly believe the standard cost and profit figures that their accounting or finance departments provide.

As a CFO, that’s an uncomfortable place to be. The issue, up until recently, was that even if CFOs saw the issues with standard costing, there was no practical alternative. The good news is, with the advent of square root costing, there now is.

Square Root Costing

Without a clearer and more granular view of real cost and profit than traditional costing methodologies can provide, companies are as the blind leading the blind. Consider the implications:

  • Undertaking product rationalization efforts without knowing how much profit each product actually generates
  • Setting prices without knowing the real costs of products and services
  • Advancing new products without understanding the likely full cost implications of those decisions, nor their impact on the profitability of other products
  • Making decisions around resource investments without really knowing the likely full costs and therefore returns of those decisions — including under-investing in the real drivers and creators of profit
  • Making acquisitions based on synergies that not only are not achieved but were never really there for the taking
  • Basing business plans on economies of scale that never materialize

Andrei Perumal

Activity-based costing (ABC) was to be the panacea for our costing ills. Developed in the 1970s and 1980s in the manufacturing sector, and defined in 1987 by Robert Kaplan and William Bruns in their book Accounting and Management: A Field Study Perspective, ABC initially sought to account for the indirect and overhead costs left out of traditional cost accounting, and later to correct for the growing cross-subsidizations involved in standard costing to more correctly allocate indirect costs to specific products.

However, ABC was not able to keep pace with the growing complexity of our world.

In application, ABC is a “bottom-up” methodology. It involves identifying all indirect activities and assigning the cost of each activity to all products (or customers) based on the actual consumption by each.

This worked well when the level of complexity — the variety of activities and products — was relatively still low. But as complexity grew, the level of effort required to apply ABC grew exponentially, and ABC initiatives became enormous, cumbersome, and unsustainable.

In lieu of ABC, some CFOs are turning to square root costing (SRC).

SRC is the most exciting development in the world of costing in many years. It is a practical methodology for correcting the cross-subsidizations that have plagued standard costing, and is far faster, much less cumbersome, and significantly less resource-intensive than ABC. SRC can accomplish this because it is the only costing methodology based on an accurate understanding of complexity costs.

Stephen A. Wilson

Many of our clients, using SRC, have quickly gained a much clearer view of their true product and customer profitability.

Figure 1 (below) shows complexity-adjusted operating margins by product segment for one of our clients, a major beverage company.

Product segment C includes the company’s major legacy brands. While it still comprised the majority of the company’s sales volume, overall sales in this market segment were flat. In addition, price points had been slowly declining, which had created pressure to find new and growing market segments.

Segment D represented a new and growing market opportunity, which consisted of specialty products, with much higher price points; hence, this was where the excitement, and investment, was.

The company’s standard cost figures (light bars) showed operating margins in segment D, at 26%, to be much higher than that of segment C, at just 14%. With segment D’s specialty products and much higher price point, it seemed to reason that it should be more profitable than the staid legacy segment C.

Figure 1.  Complexity-adjusted operating margin (dark bars) vs. standard operating margin (light bars) for a major beverage company

But these standard cost figures did not account for all the complexity and associated costs that were incurred in order to aggressively compete in and develop and deliver the specialty products making up segment D.

Adjusting for the real costs of this complexity showed not just that the legacy segment was subsidizing the specialty segment, but that the legacy segment was still the most profitable, at 19% operating margin (dark bars). The specialty segment’s much more accurate figure for operating margin was 9%.

The cost of all of the unrestrained product proliferation incurred in going after the specialty segment more than consumed the potential value afforded by the high price points.  The answer was not to shift away from segment D, but rather to pursue that segment in a more methodical, disciplined, and purposeful manner.

Three Types of Cost

How does SRC work? SRC is a top-down allocation methodology based on a fuller understanding of cost in today’s complex world.

In our book, Growth in the Age of Complexity, we explain how there are in fact three kinds of cost: variable costs, fixed costs, and complexity costs. It is important to understand the dynamics behind each of these, so first a little review.

Variable Costs. Traditional variable costs are simply proportional to some measure of volume (whether tons, gallons, dollars, hours). If you double the volume, from say two pounds of copper to four, you double the cost. The unit cost is independent of volume, meaning that it doesn’t change over the range of volumes.

Fixed Costs. Fixed costs are almost the opposite of variable costs. With fixed costs, it is the total cost, and not the unit cost, that is constant over volume. Another way to say this is that cost is independent of volume. For example, most design, engineering, product development, and registration costs for a product are independent of the volume sold.

These descriptions capture the essence of standard costing. When allocating costs, businesses typically treat costs as either fixed or variable, and since fixed is rather extreme, when in doubt CFOs usually allocate costs as variable costs.

We “peanut butter” spread those costs in such a way that we treat all products, customers, etc., as equal generators of those costs. That masks the real differences between products (and customers, etc.) in generating those costs, and creating cross-subsidizations in the process.

However, a significant and growing portion of costs — the large majority of non-value-added and complexity costs — fit neither the variable nor the fixed-cost category.

Those uncategorized costs tend to go up with volume, but not proportionally with it. Also, the cost-per-unit tends to drop with volume, but not as steeply as that of truly fixed costs. In our work and research we have discovered and categorized this third category of cost as:

Complexity Costs. These are the costs that are driven by variety, such as SG&A, working capital, and manufacturing overhead. Fifty years ago, this cost category was a relatively small proportion of overall costs. What has changed is that the world has become fantastically more complex — more products, more segments, more channels, more regulations, more sophisticated technology, more complicated processes and organizations, and more sophisticated and demanding customers.

Recognizing this third cost category, and stepping away from the narrow fixed-variable cost mindset, is a critical first step. The alternative is misallocation, typically in two key ways:

  1. For costs above the gross margin line (essentially cost of goods sold), companies tend to mistreat complexity costs as variable costs, peanut butter spreading these costs. The result is that they “under-cost” small-volume products, customers, activities, etc. By under-costing small-volume things, firms under-cost complexity, making complexity appear less costly, and therefore making organizations more tolerable of taking on more complexity.
  2. For costs below gross margin (essentially selling, general, and administrative expenses), businesses tend to mistreat complexity costs as fixed costs. That suggests that as they add more complexity and revenue, those fixed costs will not grow. But we know from experience that this so often fails to be the case.

In both cases, by mischaracterizing complexity costs as either variable costs or fixed costs, a business will underestimate the cost of complexity. By underestimating complexity’s cost, an organization leaves itself more tolerable and accepting of taking on more complexity; of overestimating potential fixed-cost leverage; of adding hidden costs; and of eroding the very economies of scale it may be expecting to realize.

The Breakthrough Insight

Along with the recognition that there are three types of cost, what unlocks this puzzle is knowing how complexity costs behave: all else being equal, complexity costs tend to follow a square-root of volume relationship, meaning that the cost is proportional to the square-root of the volume. Since unit cost is simply cost divided by volume, the cost per unit is proportional to the inverse square-root of the volume.

It’s important to note that we did not invent the square root of volume relationship, we discovered it.

Years ago we had built several “virtual plants” in support of our work for a pharmaceutical company. The virtual plants were mathematical models representing real physical plants to optimize things like production scheduling, plant loading, and capacity planning. In running the models, we began to notice patterns in the data.

We then experimented with the plant models, flexing different variables one at a time (such as product set up times, product demands, inventory holding costs) to see their impact. What we discovered was an ever-growing list of costs that were not proportional with volume (i.e., demand), or independent with volume, but varying exactly with the square root of volume.

For example, we found that in a make-to-stock production environment, with an array of products (each with different customer demand but otherwise the same, meaning the same setup time, run speed, yield) and an optimal production schedule, average cycle stock inventory levels by product were proportional to the square root of each product’s volume.

For example, if product A had four times the demand of product B, then product A had two times the average cycle stock inventory.

As we began to look further, we discovered other relationships: how the total time spent on setup per product also varied with the square root of volume and how safety stock varied with the square root of volume. We have since discovered this relationship in areas across a company, from COGS to SG&A.

By understanding these relationships, and leveraging them within a costing methodology, SRC can quickly and significantly improve the accuracy of costing figures.

In our experience, the square root of volume relationships in SRC correct for approximately 75% of cross-subsidizations taking place.

In practice, we often find other items to fix manually to address perhaps another 10% to 15% of the cross-subsidizations. Reaching this point, a business has sufficient clarity to inform business decisions, and going further just passes a point of diminishing returns.

A Final Note

Standard cost and profit figures typically only go down to the gross profit level. The rationale being that it is too difficult to assign SG&A and corporate overheads to specific products, or that such costs are too removed from a product and simply should not be tied to specific products.

We are emphatic in our belief that product profitability should be assessed all the way down to the operating profit level. Our experience helping transform companies has only solidified our resolve on this point.

Complexity is often the largest driver of overinflated SG&A and corporate overheads, and disconnecting these costs from the complexity in a business both gives them a pass and obscures islands of profit and a sea of costs.

Square root costing is the means to quickly get down to the operating profit level. By correctly treating complexity costs, SRC presents a clear picture of where an organization is really making money, and in so doing creates the right foundation for developing profit-generating growth strategies.

Andrei Perumal and Stephen A. Wilson are co-authors of Growth in the Age of Complexity: Steering Your Company to Innovation, Productivity, and Profits in the New Era of Competition and Waging War on Complexity Costs. They are co-founders and managing partners with consulting firm Wilson Perumal & Co.