Critical Equations

Critical Equation #1
"Breaking the Mystery about Pricing"

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% ∆ V = - % ∆ P / (CM % + % ∆ P)


How many times have you heard people say, “If we cut price, we can sell a lot more product”, or “let’s heavily discount this deal to win it…. make our money on future sales.” Pricing is the moment of truth in product planning and business negotiations. Pricing decisions have an enormous impact on the bottom line and, as a result, a company’s ability to create shareholder value over the long run. Yet, nothing is harder to get right (market valuation and market price being equal). Depending on the product/service offering, pricing decisions often are made without full knowledge of their financial impact and often are left to too late in negotiations. Not understanding price-volume trade-offs only exacerbates the situation and results in the sub-optimization of profit.

The Most Important Equation in Business

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Critical Equation #2
"Understanding and Analyzing Variances"

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Variance = OM I - OM J


All business leaders need to be able to create and manage a budget. This can be a relatively simple process of making sure expenditures do not exceed agreed upon limits or, when one has responsibility for an operating profit and loss statement, quite complicated and require considerable expertise. Careers have been made or lost because of the ability or inability to understand, communicate and take effective action on how a business is doing relative to its plan. The difference between a budgeted amount and the actual amount over a specified period of time, in either absolute dollars or percentages, is commonly known as a variance. The heart and soul of managing a small department or a global enterprise is in understanding the drivers of your business in the form of variances. Knowledge of operational finance, the language of business, is essential to successful applications of variance analysis.

Understanding Critical Equation #2 can:
  • Enhance your company’s competitive advantage
  • Demonstrate effective risk management, and
  • Increase the probability of meeting your commitments.

Variances come in three fundamental types: Planning, Execution and Growth. Effective business leaders need a working proficiency of all three. The difference between good and great companies often is a function of how capable their leaders are at understanding each of these variances. Success will be measured in incremental shareholder value.

Variance Analysis

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Critical Equation #3
"Key Financial Metrics - The DuPont Model"

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NI/S x S/A = NI/A x A/E = NI/E


A prerequisite for business leaders at all levels of an organization is the ability to make comparisons of financial data. These comparisons are typically made to time (trend analysis), to competitors (competitive analysis), or to a plan (variance analysis). Being able to draw insight from comparative data is essential to making decisions under uncertain conditions such as limited information, time pressure, divergent opinions, and limited resources. Drawing insight from financial data requires understanding the drivers of return on equity found in our equation #3. Understanding how we can impact these drivers from an operational perspective is central to creating short- and long-term shareholder value. The primary accounting tool, applicable across all industries, is the DuPont Model. Most importantly, the DuPont Model requires business leaders to be responsible for both the income statement and balance sheet (we will recognize the criticality of cash flow in due course). The DuPont Model, of course, is not without criticism, and we do not argue for its being the sole driver of business decisions. Its application must be balanced with the potential negatives we will discuss along with an understanding that no model can capture in its entirety the economic reality of every business. While numerous authors argue that use of the DuPont Model has eroded, we have seen no evidence of this across our many clients. In fact, we will demonstrate that a modified version of the standard DuPont Model that incorporates financial leverage can help explain the significant deterioration of many businesses during the recent global recession, in particular financial services.


Critical Equation #4
"Cost of Capital"

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KO = KD(1-T)(D/{D+S}) + KE(S/{D+S})


The economic goal of management is to create shareholder value. Fundamentally, this means earning a return on investment that exceeds the cost of capital. The only operational definition of profitable growth that makes sense is for earned returns to exceed the opportunity costs of those who have entrusted you with their money, typically in the form of debt and/or equity. This is evidence of your ability to create sustainable competitive advantage over time. Every business leader is paid to create value for shareholders. It is his or her fiduciary responsibility. If you do not expect to earn returns that exceed the cost of capital, you best “call it a day” and return the money so your investors can find value elsewhere.


Critical Equation #5
"Power Laws"

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Y = AXb


Every business leader is familiar with the Pareto Principle, a.k.a. the 80/20 rule or Juran's role of the vital few, Ziph's law, related to distribution or frequency of words in any language, and even Benford's law of 1s, widely used in fraud detection, are related to Pareto's logic. All are functions within the statistical family of power laws, the topic of our Critical Equation #5 for Business Leaders. Power laws state that large occurrences are rare, and small occurrences are common.

The classic and oft-referenced example of the 80/20 rule is when 80% of profits come from 20% of products. The importance is not so much in 80/20, but rather that we rarely observe 50/50. Historically, managers who understand this apparent imbalance (often called the Gini index) are able to focus on what really matters and hence better allocate scarce resources.

Without an understanding and application of power laws, meeting commitments, which has been at the heart of our other Critical Equations for Business Leaders, can be problematic. How many times have you missed your financial commitments (sales, operating margin, net income, cash flow forecasts) because you did not consider a wide range of alternatives in the planning and budgeting process? Odds are, your forecasting tools did not allow for the outliers or long tails inherent in power laws.

Over the past few years, we have seen an unprecedented increase in debate and discussion in board rooms and halls of academia on the relevance of Black Swans (positive and negative), outliers, data mining, variance in variance (i.e., volatility in the risk itself), and resurgence in scenario planning from the 1970s. Ambiguous environments of the past decade have, in many instances, made assumptions, such as normality in distributions, close to useless in forecasting.

Your ability to meet commitments (on operating margin, net income, cash flow and return on investment as well as non-financial measures) in a volatile and ambiguous world may be improved by applying power laws to your forecasting and making them part of your every thought. There is power in understanding power laws. What are the long tails in your business?


Critical Equation #6
"Options"

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Ct = St N(d1) – Xe(-rT) N(d2)


There is not a business leader in the world who would not argue the importance of being flexible in making decisions, being alert to the arrival of new information, and being certain their teams always think through their available options. These business leaders also would recognize that having options is essential to managing risk in a globally complex and ambiguous environment. They would acknowledge that the product and service differentiations that produce superior shareholder returns can come directly from a culture that understands and uses options in making decisions. Yet, while many talk about and recognize the relevance of flexibility in decisions, we know of no particular company that has fully endorsed an options perspective and has embedded it within their culture.

Understanding how to value an option is quite complex. Given the ambiguous nature of business today, organizations must engrain the concept of options or flexibility into their cultures to remain competitive. Everyone in an organization must continually be thinking in terms of creating options. This may require a change in the organizational processes and tools used to identify investment opportunities, but understanding, applying and having a culture around flexibility will improve the potential for profitable growth.


Critical Equation #7
"Bayesian Probability"

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P(A|B) = [P(B|A)*P(A)]/P(B)


All business leaders face risk and uncertainty when making decisions and investments. Whether explicit or implicit, all decision makers encounter scenarios that require an assessment of the probability of success. The probability of winning a bid is one of the most common of these scenarios. Proper information is critical to success in making decisions. We all are aware that information comes from varied sources. Rarely do we have perfect and complete information. Typically, the higher the quality of information, assuming correct interpretation of course, the better decision making under uncertainty. Statistics and probability, when properly applied, can be excellent sources of information that can yield more competitive decisions. The purpose of our Critical Equation #7 is not to make you an applied statistician, but to help you gain insight into the drivers of improving the estimation of probability, hence improving your decision-making and critical-thinking skills. Thinking in terms of probability can be very hard.


Critical Equation #8
"Economic Profit and TRI’s EP-Var©"

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EP = NOPAT - KO (Total Capital)


In our Critical Equation #8 for Business Leaders, we introduce a measure of value creation for shareholders that has existed for centuries, at least in concept. This measure is often referred to as Economic Profit (EP). In the past few decades, numerous value-based management consultants have introduced a variety of offspring to Economic Profit, the most common being Economic Value Added TM (EVA TM).

In his 1890 Principles of Economics (Macmillan Press), the esteemed economist Alfred Marshall promoted the fact that to create value for owners a return on investment should exceed the cost of capital. Expressions that evolved included abnormal earnings, excess earnings, excess income, excess realizable profit, and super-profits. What is common to all, and has never wavered over centuries of commerce, is creating sustainable differentiation, which is at the heart of so much strategy today. As far back as the 1920s, General Motors employed an early version of EP. The most operational of all expressions, residual income, was a term coined by GE in the 1950s. It is well known that many companies have implemented EP in various fashions, some successfully and some not. Many have linked there EP systems to Activity-Based Costing (ABC).

The academic and practitioner worlds have both shown that, while certainly not perfect, EP is reasonably correlated with share price performance, typically a higher correlation than other well-known financial metrics such as ROE, EPS, sales, cash flow, and dividend growth.



Critical Equation #9
“If the Cash Does Not Flow, the Answer is No”

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Cash flow = ∆ Cash = Operating, Investing and Financing Activities


There is an old saying, “If the cash does not flow, the answer is no.” A cash shortage is among the primary drivers that will lead to bankruptcy. It can easily cause a business to fall behind on payments and reduce its ability to reinvest for growth. This can lead to additional borrowing and the potential for spiral down. Never be fooled by profits, because you can go broke while recording those gains.

The bottom line is very simple: everyone in your organization needs to be aware of cash flow and understand their own impact on it. Cash is everyone’s responsibility. If the global financial crisis and its associated liquidity and solvency backdrop has taught us anything, it is that there is truth to the old adage, “Cash is king.”


Critical Equation #10
The Time Value of Money

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(1+R)N et al.


The time value of money is fundamental to all aspects of business decision-making. Consider the following: “Would you rather have $100 today or $200 10 years from now?” As simple as this question might seem, there are complex factors that can influence your choice. Our purpose is to explore and simplify the concept of time value of money, providing the insight and tools you need to answer this type of question and, ultimately, create shareholder value.

One aspect of time value of money that is critical to long-term growth is compounding. Einstein has been quoted as saying "The most powerful force in the universe is compound interest." Others have referred to compounding as the “8th wonder of the world.” While both quotes are anecdotal at best, they do emphasize the importance of understanding the time value of money.