Harvard Business School Confidential

by Emily Chan

  Another client, an oil refinery in Malaysia, wanted to improve the efficiency of its maintenance process. To understand the workload of the maintenance department, I followed a maintenance technician around for a week and documented all the work he did, how he did it, and how long it took. Then using this as a sample week, I redesigned the process and then calculated the time savings of the new process compared to the week sampled.

  THE UNGETTABLES

  Very often, critical data do not exist in readily available form and can’t be found in a useful amount of time. The ability to deduce these critical numbers is paramount to strategy. These are the techniques taught at HBS that I’ve found indispensable to any strategist:

  Logical deduction using limited data

  Compound annual growth rate

  Ballpark interview technique

  Scenarios

  Minimum threshold

  LOGICAL DEDUCTION USING LIMITED DATA

  In most HBS case studies, students get some data either within the text or in table format. But since the cases are based on real-life situations, they reflect the reality that the data available are most often not sufficient to analyze the issues in the case. The key technique needed is to know what you want and then use the numbers given to reach a reasonable estimate. As a simple example, say you need the market size of television sets in city X. In the case study, you are told that the population is 100 million in city X, and that the average life of a television is three years. Assuming no other quantitative data is available from the case write-up, here’s one way to estimate the market size:

  1. Since city X is in a developed country, assume the average household size is similar to the average U.S. household, around 2.5. This means 100 million people will make 40 million households.

  2. Since most families even at the lowest income levels have at least one television, assume each household has 1.5 televisions. Note the total of 40 million × 1.5 or 60 million televisions out there.

  3. Assuming their lifespan is three years; about a third ofthe televisions will need to be replaced every year. This means a market of approximately 40 million × 1.5 televisions × 1/3, or 20 million.

  4. Remember that the resulting number, 20 million, is just a ballpark figure and not hard data. Its sensitivity and validity need to be checked using techniques to be discussed in the next sections.

  This deductive, logical estimation technique to quantify key parameters based on existing data is a critical tool applicable to many HBS cases and in real-life strategic planning. In fact, this technique is so critical that many consulting firms like to include it as an interview question.

  When I was responsible for Greater China recruiting for BCG, for example, my favorite interview question to MBA graduates was “How many Toyotas do you think there are in Hong Kong?” The interviewees had no access to a computer or even paper and pencil. What I was looking for was the deductive, logical estimation technique, not the exact number. I did not even know the answer myself. I expected something like this: “There are seven million people in Hong Kong. Let’s say four people a household. This makes about 1.8 million families. Toyotas are for middle-income families. Let's say about 1/5 of the families are middle income. That makes about 400,000 middle-end cars. Of this market, there are other brands like Honda, Mazda, and Suzuki. None of them seems to have a bigger share than the others. So maybe the number of Toyotas is about 100,000.” It does not matter if any of these assumptions are right. The key is the ability to think logically and the comfort with numbers and estimates. Once the logic and comfort are there, researching assumptions and testing their validity is not difficult.

  It is useful to reference the two very simple frameworks sketched in Figure 11.1 to help you think of different systematic approaches when undertaking logical deduction:

  Top down–Bottom up. Top down means starting from macro numbers and narrowing down until you get to the parameter you are trying to estimate. Bottom up means starting from more granular numbers and expanding until you get to the parameter.

  Supply-and-Demand. This is self-explanatory.

  The Toyota example is top down, as it starts from macro data population and households and then narrows down. A bottom up approach to the Toyota example will be to start from the number of dealerships, then estimate sales per dealership per month, multiply by 12 months to get an annual figure. Assuming the life of a Toyota is about five years, then multiply by five.

  The estimate of Toyotas using demographics is demand-side deduction. Estimate of number of Toyotas based on number of dealerships is supply-side deduction.

  Compound Annual Growth Rate

  Compound Annual Growth Rate (or CAGR; pronounced KAY-ger) is very useful in logical deduction. CAGR is a critical quantitative concept because it has a very wide range of applications. It was not explicitly taught at HBS—the faculty assumed everyone knew it already!

  The concept of CAGR is similar to the idea of compound interest. It is the average annual growth rate when compounding is taken into account. For example, if a market grows from $1,000 to $5,000 in five years, the CAGR is 38 percent a year because $1,000 × 1.38 × 1.38 × 1.38 × 1.38 × 1.38 = $5,000. (The growth rate is not 500 percent over five years divided by five years.)

  The formula is similar to compound interest. The following explains how the formula of CAGR is derived:

  where FV is the future or ending value, PV is the present or starting value, and n is the number of years between PV and FV. This formula is best explained by examples:

  Example one: If the widget market was worth $300 million in 2000 and in 2007 it is $400 million, then n = 2007 – 2000 = 7. CAGR is (400/300)(1/7) – 1 = 4%

  Example two: If the historical average CAGR for the market in the last three years is 15 percent per year, the forecast market size in five years if it continues to grow at the same rate would be

  Future market size = Current market size x (1 + 15 percent)5

  Example three: Sales of company X doubled in the last four years. Doubled means (FV/PV) = 2. Hence

  CAGR = 2(1/4) – 1 = roughly 20 percent

  CAGR is extremely useful in the estimation of key parameters. For example:

  Historical CAGR can be used as the basis for estimating the future, as illustrated in example two. Often historical CAGR is adjusted up or down based on qualitative data. For example, if the market in example two is expected to slow down in growth in the next few years, then historical CAGR of 15 percent can be seen as the maximum growth rate and 10 percent or 12 percent could be used in the formula rather than 15 percent (picking the number involves an assessment of sensitivity, multiple estimates, and triangulation that will help ensure that the 10 percent or 12 percent used is valid even though it is a rough estimate. These techniques will be discussed later in the chapter.) In addition to market size, CAGR can be applied to competitors’ size and growth, price growth, and other growth estimates.

  Often, your data from interviews or trade journals will not give a growth rate. An interviewee may say “doubled in five years” or the trade journal may read “expected to treble in the next 10 years.” CAGR will allow you to work out a growth rate that can be used either to estimate the future market or business size or for comparison with other industries.

  Once you have CAGR, it is easy to assess this growth rate by comparing to benchmarks like GDP growth, inflation, or stock index growth to judge if the growth rate is attractive.

  To look smart, many MBA graduates use a shortcut calculation of CAGR. I call it the Rule of 75%. It goes like this:

  CAGR roughly equals 0.75 divided by the number of years the factor in question takes to double.

  Using this rule on example three, CAGR roughly equals

  0.75/4 = 0.19 (or roughly 20 percent)

  Appendix C shows the accuracy of this rule. This rule is useful to quickly work out CAGR in your head (or if you are trying to show off your skills in a discussion).

  Ballpark Interview Technique
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  When you try to do your research through interviewing, you will notice that many interviewees are reluctant to give quantified data. This greatly affects the value of the interviews. Without quantification, you really do not know what people mean when they give qualitative data like “fast”or “slow”,“big” or “small.”Usually it is not because they do not want to quantify but because they do not have the data and feel they don’t wish to be held responsible for giving the wrong number. What they do not understand is even a rough estimate is very useful as a start for quantification for strategy planning. “Ballpark technique,” as I call it, often works to help to get at least a rough estimate from interviewees. It involves giving the interviewee a few options to choose from. These options are sufficiently different from each other that they make the choice relatively easy. Once a “ballpark” option is chosen, further narrowing down can be done until the interviewee cannot provide further information. To demonstrate the technique, here is a possible conversation between an interviewer and an interviewee:

  INTERVIEWER TRYING TO GET DATA: How fast do you think the refrigerator market has been growing in the last few years?

  INTERVIEWEE: I don’t know. I don’t have any data.

  INTERVIEWER: Well, do you think it is closer to 0.5 percent, five percent, 15 percent, or over 25 percent?

  INTERVIEWEE: It has been slow but not completely no growth, probably closer to five percent than 15 percent.

  INTERVIEWER: Do you think it is more like three to six percent or more like six to nine percent.

  INTERVIEWEE: Don’t know but probably lower than higher.

  INTERVIEWER: So it is roughly three to six percent from your estimate?

  INTERVIEWEE: Maybe.

  Like the results of logical deduction, these ballpark figures need to be checked and rechecked. But at least this approach gives you a starting point for the necessary estimates.

  Scenarios

  If a key parameter is very difficult (or impossible) to estimate but yet very important to your strategy plan, a tool you can use is scenarios—asking “what if?” The idea is to define a few scenarios for your target parameter and then compare and evaluate the implications of the outcomes from various scenarios. Using the television example, say the market growth rate is very difficult to estimate. You have looked at all research reports and interviewed many people but you are not getting any reasonable ballpark estimates. So you decide to define three scenarios and then investigate the implications of each:

  Scenarios on Market CAGR from Now Until 2015

  Pessimistic: zero growth

  Average performance: five percent per year

  Optimistic: 10 percent per year

  A few points illustrated by this example:

  There are only three scenarios. It is important to limit the number of scenarios, as trying to set up too many will create confusion and distraction.

  This example is about estimating one parameter. It is advisable to apply scenarios to not more than a handful of parameters. Applying scenarios to too many parameters will also create confusion and distraction.

  Scenarios should be defined based on careful consideration of all information available. They should be realistic.

  It is useful to choose scenarios that will demonstrate the range of outcomes like the one shown here. Other choices include maximum, average, minimum; aggressive, base case, passive; or base case, accelerated, explosive. Base case can be the middle-of-the-road scenario (the “basic” scenario) or the most likely scenario depending on the analysis.

  Minimum Threshold

  If scenario analysis still makes it too difficult to estimate a parameter due to the huge range of possibilities, defining the minimum threshold could be a possible tool. Say you find that x percent per year market growth is the minimum needed to make an investment attractive. Then the question is whether you believe this market growth is possible.

  CONSISTENCY AND TRIANGULATION

  Naturally, the accuracy and validity of data estimated by deduction and data from sources such as interviews must be checked. Even data obtained from seemingly reliable sources should be checked. A few years ago, I used some population data straight from a China provincial government statistics book. The table I set up looked something like the one shown in Table 12.1 (though the reported data have been disguised, they follow the same pattern as the original).

  I was rushing to do my analysis so I did not spend time to think about the data. I just copied the data. In the middle of my presentation, my client pointed out that the population of the cities and non-city areas within the province added up to more than the total for the province! Needless to say, the mistake affected the credibility of the whole presentation.

  Table 12.1 Population Estimates

  Place Population 2003 (Millions)

  City 1 in this province 10.2

  City 2 in this province 4.4

  City 3 in this province 3.3

  Non-city areas within this province 30.4

  Total for this province 45.4

  Therefore, it cannot be overemphasized: check your data whenever possible. Two of the most direct ways for ensuring data accuracy are checking it for consistency and triangulating the item in question.

  Consistency

  If a certain parameter is important to the strategy, then multiple sources of data or deduction tools should be used. The results should be compared against each other. Since data from interviews and data deduced by tools are often rough ballpark figures, you can’t expect the figures to be identical, even if they are all consistent and valid. It’s only necessary for them to be “within each other’s range.” For example, if CAGR resulted in an estimate of market size of $2 billion and the top-down tool resulted in $1.8 billion, then these rough estimates can possibly be considered consistent. However, if you got $2 billion in the former and $1 billion in the latter, then you should revisit your estimates. There is no fixed definition of what “within range” is. It depends on the accuracy you need for your analysis. In most cases, a 10 to 15 percent difference could be acceptable for rough estimates. A difference of 30 percent or more is not so acceptable. When two or more estimates are “within range” but not exactly the same, a usual practice is either to take the average or use a range with a minimum and a maximum.

  Triangulation

  Data for different parameters must triangulate: They must make sense when they are put together. In the population data example shown in Table 12.1, the data for individual cities and the total for the province do not triangulate—they do not make sense when put together. Another example: suppose you are estimating market shares of major competitors. In that case, the sum of the percentage shares of major competitors should not exceed 100. If you have sales estimates for various competitors, the total should not exceed the estimated total market. If you have historical 2006 market sales and estimates for 2007 sales, 2007 sales should be reasonably larger than 2006 if it is a growing market. And so on.

  Table 12.2 Reported Percentage within Each Key Market

  Besides being very effective for testing validity when you attempt different ways to estimate a key parameter, triangulation is also extremely useful when you have to assess other people’s estimates quickly. It is surprising that even professional consultants often publish reports or give presentations that contain data that do not triangulate. Table 12.2 shows an example I recently saw in a professional presentation by a real estate consultant from Canada.

  Do you see the problem in the table? The Australia market adds up to 110 percent! Sometimes this kind of discrepancy is a typographical error, but sometimes it is a real estimation problem. Once you have the concept of triangulation ingrained in you, you will be able to pick these mistakes out quickly. You may be able to help a company avoid a wrong decision based on a mistake in a critical parameter. Even if the error is not in a critical parameter, you can look smart and alert in front of your superiors or clients (this is one of the key skills that often make MB
As look smarter than they are). But you must be careful not to point out the mistake in a way that will embarrass the creator of the estimate. This is related to social networking—it is always better to make friends rather than enemies.

  The more important the data, the more checking needs to be done. One of the key measures of importance is sensitivity. Sensitivity here means how much the data affect the decision you are trying to make. For example, if you are looking at a business with high fixed costs, then revenue projections are very important since once fixed cost is covered, every dollar of revenue largely goes to the net profit with very little lost due to variable cost.

  LAW OF ACCURACY

  Estimates often require further calculation: you need to add, multiply, subtract, or divide them to get the results you’re after. For example, if you estimate a market to be around $25 million and market share of a certain company is about one third, using the calculator gets you something like this:

  $25,000,000 × 1/3 = $8, 333, 333.33

  Some people are tempted to report this kind of number as the estimated company sales. But publishing it as it stands would violate a very important mathematical rule: the “Law of Accuracy” (see below).

  The “Law of Accuracy”

  When combining estimates with different numbers of significant figures, the accuracy of the result can be no greater than the least accurate of the estimates. This means when estimates are added, subtracted, multiplied, or divided, the result should not have more significant figures than the original estimates.

  The number of significant figures is the number of digits that have some degree of accuracy, plus the last digit. Most MBAs are not mathematicians and tend not get too technical or exact in the definition of significant figures (details such as when zero is counted as a significant figure and when it is not; which digits have some degree of accuracy and which do not; and what it really means to say “plus the last digit,” and so on).