Week 4

Chapter 6 Financial Projections for the Firm

Learning Objectives

· To understand the basic typology of projections

· To learn to deal with information (or lack of information)

· To understand revenue and cost relationships

· To understand seasonality

Case: Desert Divers

Larry Gibbons and his friend Alex Huhn were having dinner and discussing their favorite hobby, scuba diving. Both were local businessmen in Tucson, Arizona. Their discussion centered on the need for a dive shop in Tucson. The Sea of Cortez was only a 6-hour drive from Tucson, and there was a steady supply of enthusiasts who were either already active in the Tucson dive community or interested in receiving the training to become divers. The men were not happy that the dive shop that had historically served the community was closing down, not because of lack of demand for diver training, equipment sales, and dive trips to the Sea of Cortez but because of mismanagement. The existing firm had gone bankrupt and discontinued its business. Both knew that historically there had always been a good market for a dive shop in the desert. Out of this discussion, the concept of Desert Divers was born.

Within a short time the name was secured, the lease on the old dive shop location became available, inventory was identified, instructors were found, and it became time to put in the money. The two friends had the money, but they did not want to put it into the company until they knew what to expect with respect to its financial performance. How much would the cash flow be? What would the profitability look like? How much initial inventory should there be? They didn't have the answers to these and many other questions. They wanted to be responsible and invest enough money to cover the worst case that they might expect during their startup phase. To find the answers they needed, they decided to make a projection for the first 2 years of the new Desert Divers Company.

Making financial projections is as much art as science. It is an activity that has both ideal and practical aspects. The “idealized” aspects of the process include two main factors:

1. The identification and a conceptualization of what the underlying inputs to the projection should be

2. How the underlying assumptions regarding these inputs should be assembled together to produce projected outcomes that will react to varying inputs in the same way as the firm would react to those same inputs in practice

Basically, the firm's financial projection should “work” the way the firm “works.” In financial projections, the practical problems aren't ones of conceptualization and model building but rather problems of a best practice and implementation nature. Key problems are

1. Determining the proper time horizon for the projection

2. Overcoming the paucity of historical information

3. Creating shorthand explanations of what may otherwise be complicated relationships

This chapter addresses these questions and others. Remember, always do financial projections with a projection of units sold and their price. This cannot be emphasized enough. The most common mistake made in making or conceptualizing projections is to initially project sales in currency (dollars) instead of units sold and their selling price. This is true for both manufacturing and service companies. Every firm sells a unit of something, whether a unit of manufactured product, a unit of time to use something (like an office or a piece of equipment), or a unit of time in which a service is provided (like an hour with an attorney or an accountant). Often firms sell a hierarchy of products—for example, an hour of a senior partner's time, an hour of an associate's time, an hour of paralegal's time, and an hour of a typist's time. However, it must be emphasized that projections that are done in dollar units instead of product unit are next to worthless. Only with product units does the analyst have the flexibility to vary both units sold and price per unit to produce projections that are flexible and robust.

Chart 6.1 Schematic of  Chapter 6

Finally, as with many business problems, the actual execution is difficult, time-consuming, and problematic. Financial projection as a subject matter has been given color and texture by a very large body of research, a wide range of analytical techniques, and many diversities of opinion. All of these factors make implementation difficult. While it is impossible for one chapter to fully explain all or even a majority of the rich variety of technique and practice embraced by this subject matter,  Chart 6.1  presents a schematic representation of the material covered in this chapter. This information is a good starting point for understanding the overall subject.

Making projections is a process that involves several basic steps:

1. Obtaining data (where and how it is obtained is discussed later)

2. Using a model to represent the data so that it can be understood and manipulated

3. Applying an analytical method to the manipulated data to make a projection beyond the data range

Types (i.e., Forms) of Projections

In the discussion of different types of projections, confusion can occur. One may suppose that the “type of projection” may be defined by the technique being used to make it (for example, linear regression), or one may presume that the type of projection may refer to the thing being projected (for example, sales projection). When discussing types, we are referring to neither technique nor subject but to form. The form of the output defines the projection just as clearly as does the technique and the subject matter. To understand projections, it is best to start with form. While many techniques can be brought to bear on many diverse subject matters, there are only four forms of output: flat projections, untrended projections, trended projections, or patterned projections.

Our discussion must start with the introduction of data that explain the construction of various forms of projection.  Table 6.1  is a table of historical unit sales data for years 20xx through 20zz. As can be seen in the table, annual unit sales have been increasing over the 3-year period. The rise from 20xx to 20yy was small, a .28% increase, and then from 20yy to 20zz, sales increased by a larger amount, 10%.  Chart 6.2  shows these unit sales data graphically.

Flat projections are projections where no new information is used and no new assumptions are made. In essence, the projection for the coming year is exactly what happened for the past year. This type of projection can take two forms: Monthly unit sales will be exactly the same as they were in the past, or total sales can be used to calculate a monthly average and then forecast the next year's monthly sales based on the average monthly sales from last year. Either way, the projection of total sales will equal what it was last year. The only difference between the two methods employed is using an average monthly amount or last year's actual monthly amount as the projected amounts. Flat projections are limited in nature, but they do have two redeeming features:

Note: Totals may vary slightly due to rounding.

Chart 6.2 Unit Sales by Month

1. This type of projection is easy to make.

2. This type of projection can be used to test the impact of single variables (for example, unit sales or unit price or cost of direct material) on the bottom line given the assumption that the firm is performing exactly as it did in the immediate historical past.

In  Table 6.2  and  Chart 6.3 , we see a flat projection that uses the average monthly amount of unit sales in 20zz (16,783 units) to forecast next year's total unit sales of 201,393 (totals may vary slightly due to rounding). This 201,393 of annual unit sales is the same as in both the historical period and the projection period.

An untrended projection works in a way that is similar to a flat projection; however, it does not assume that total unit sales are the same in the projected period as they are in the prior period. When making this type of projection, sales are assumed to increase (or decrease) by some amount, for example, 10% (see  Table 6.3  and  Chart 6.4 ). In the untrended projection shown in  Table 6.3  and  Chart 6.4 , unit sales are 10% higher than in the historical year 20zz.

The easiest way to make an untrended projection is to apply an annual growth rate to either the average monthly unit sales of the prior period or to the monthly unit sales amounts. Either way, the total unit sales for the projection period will end up being higher than the unit sales in the prior period. This type of projection is called untrended to distinguish it from a flat projection. A flat projection assumes no growth, indeed no change from the prior period. An untrended projection may have a flat look, but it does assume a change from the prior period, if only an annual increase or decrease.

Note: A flat projection is the one that is the average periodic amount that will sum to the total of the prior year.

Chart 6.3 Actual Sales Versus Flat Projection Sales

Chart 6.4 Actual Sales versus and Untrended Projection with 10% Increase

Untrended projections are useful starting points.

1. They are easier to use and make than trended projections.

2. They can be turned into trended projections without much effort.

In projections, more information is captured than a simple repeat of the prior year or a fixed upward revision in prior year sales. Most of the time, one wants to closely reproduce whatever patterns are inherent in the business, and linear trends provide more information than either a flat or an untrended projection. Analysts have identified three basic types of trend patterns:

1. Linear

2. Nonlinear

3. Seasonally adjusted

In the remainder of this section, we will deal with linear trended projections and then seasonal adjustments and patterns dealing with nonlinear and seasonally adjusted trends. Linear trends are most useful. These types of projections produce a sense of direction in unit sales as well as an expression of the gross impact of year-to-year or period-to-period changes. There are basically two ways to produce a linear projection:

1. Applying an appropriate periodic growth rate equally through a 12-month period, thus producing a trended projection resulting in a desired annual unit sales projection (after which the trend may continue should the analyst desire)

2. Using a linear regression methodology to produce a trended projection of unit sales for the desired period

Table 6.4  and  Chart 6.5  indicate what turning an untrended projection that has increased by 10% over the prior year (20zz) into a trend looks like. If each of the monthly unit sales amounts in the projection are added together, their total will be equal to the projected sales in total unit sales in  Table 6.3  (the untrended example). There is a small difference due to rounding.

To make a trended projection using an annual growth rate, one needs only make a choice regarding the starting point and the annual growth rate. To further develop an example, let's assume that we wish to start our projection at 201,393 units per year (this is the level of unit sales indicated in  Table 6.2  for year 20zz; totals may vary slightly due to rounding). Using a desired annual increase of 10% would mean in the projection period, 221,532 units would be sold. This is the annual unit sales that were indicated in  Table 6.3 . However, unit sales in  Table 6.3  are untrended. To work out a trended forecast, the following steps are used to calculate a monthly projection of units sold for the next 12 months:

Notes: Calculate monthly growth rate (slope of projection) as follows: For 10% annual growth, the monthly amount is .10/12 or 0.008333.

Calculate monthly projected unit sales as follows:

· For the first period, use the average monthly amount, in this case 18,461. Then multiply this amount by 1 plus the periodic growth rate (.008333), in this case (1 + .008333).

· For each of the other periods, multiply the prior month's unit sales times 1 plus the periodic growth rate. For February, we would multiply January's unit sales by (1 + .00833), and so on.

· Center the trend. This means that the trended projection should cross the untrended projection in late June.

· We can ensure this by adjusting the initial average monthly amount downward to 17,485 from 18,461. The amount is arrived at via trial and error.

· Excel's Goal Seek function can be used to determine January's initial value (before adding monthly growth) that is necessary to make the annual unit sales total 221,532.

· We have done this in this case to arrive at January's initial value of 17,484.

Chart 6.5 Actual Sales versus Trended Projection Sales with 10% Increase

1. Determine the periodic trend rate. Mathematically, it is the annual trend rate divided by the desired number of projection periods in the year; in our example, it is (10% / 12) = .08333.

2. Except for the first monthly projection, each projected monthly value is going to be a function of the prior period. Mathematically, the values for projection period 2 through period N will be determined as follows: Unit projection for each period n = Unit projection period n − 1 * (1 + .08333).

3. For the first projection period, a little more work needs to be done. We know the projection needs to total 221,532 annual units. We know that the average monthly units for annual unit sales of 221,532 are 18,461 units. However, if we compute the first period's projection by using the 18,461 number, we will end up with too many annual units (231,973 versus the expected 221,532). To end up at the correct point, we need to reduce the 18,461 unit number to a lower number that then results in the annual sum of the trended projection being very close to 221,532 units. Through trial and error, we can identify 17,630 units as the starting point for period 1. That starting point will produce an annual total of 221,531, which is very close to the desired 221,532.

The disadvantage of trended projections is that they do not anticipate new information. The trends continue unless new information is incorporated into the historical data being used to calculate them.

Another type of linear trended projection is a linear regression. This type of projection has two basic characteristics:

1. The projection is a purely mathematical construct. There is no input in the growth rate, the boundaries, or the limits of the projection.

2. The projection is entirely dependent on the amount of historical data used in the process. Relatively more or less data will have a large impact on the regression projection.

Linear regressions are built around the idea that a straight line can be drawn through a plot of historical unit sales (or other data) and that that line can be drawn in such manner so as to describe the data very well. The line can then be used, via extension, to project the data in a meaningful way into a future projection period. The formula for such a line is ^Y = a + bX, where ^Y = the value for the output value on the Y axis given a constant of a (the line's intercept on the Y axis) given a line slope of b at point X on the X axis. The placement of the line within historical data is somewhat involved and beyond the scope of this chapter. Basically, the line passes through the data set in such a way that the sum of the perpendicular distance from each data point on the top of the line to the line equals the sum of the perpendicular distances of each data point on the bottom of the line to the line.

Chart 6.6 Actual Sales versus Regression Projection Sales

In  Table 6.5  and in  Chart 6.6 , the regression projection for unit sales for the next 12 months (periods 13 through 24), given the data of the past 12 months (periods 1 through 12), is provided. Projections done using the linear regression technique are worthwhile if the projection period is kept short, such as no more than 2 or perhaps 3 years.

Notes: Totals may vary slightly due to rounding. The regression formula is ^Y = K + bX, where

· The period to project (X) = the value of the period on a sequentially numbered time line,

· Constant (K) = 12,500,

· Coefficient (b) = 678.38.

Types of models and methodologies that produce outputs that exhibit various patterns include various types of curvilinear analysis and higherorder polynomial math functions, and while we do mention these techniques, we will not spend much time trying to master them. We do deal with these types of techniques in the section “Seasonality and Patterns.”

Models and Methodologies

To date in this discussion, the models or methods have not been addressed that can be used to

1. Process data

2. Duplicate within the planning model the firm's day-to-day activities

3. Make projections or test hypotheses

4. Assess the performance or effectiveness of management or existing firm processes

By reviewing the types of projections, we were in fact reviewing generic types or forms of projection. The common types of projections encountered in business fall into the categories that were previously discussed. Following is a discussion of the types of models and methodologies that can be used to handle data and make projections.

Models are analytical means used to summarize or describe data. Methodologies are analytical means used to make projections from the raw data or models of data available (Armstrong, 2001). It is possible and often the case that a particular model may also be a methodology; for example, a linear regression may be used to describe historical data and to project the linear trend of that historical data into the future.  Table 6.6  lists a number of models and methodologies that are commonly used.

Four classes of mathematical techniques can be used as models or methodologies (and sometimes both):

1. Average based

2. Trend following

3. Statistical systems

4. Miscellaneous

With respect to the techniques classified as average-based systems, there are three primary types:

1. Arithmetic average, the simplest form of average calculation, is employed in the normal way by adding the various sample numbers together and dividing by the sample size. The formula is 

2. Moving average is another type of computation involving averages. When calculating this type of average, a predetermined number of sequential data points are used to compute their average. This average becomes the model output for the last day of the input sequence. The second step is to then drop off the first data point in the series, add the next data point, and recompute the average. This average becomes the model output for the next period. This process can continue as long as there are data. Inputs may be in series lengths that are chosen by the analyst (for example, 3 days, 9 days, 20 days, or any other relevant period). Moving averages serve to smooth data, eliminating extremes in either direction. The formula is  where N =number of observations.

3. Arithmetically weighted moving averages are similar to moving averages except the data are weighted in proportion to their proximity to the most recent date of the series. For example, if we are computing a 3-day arithmetic moving average, we would weigh the data from the third day more than the data from the second day, and we would weigh the data from the second day more than the data from the first day. It would look like the following:  where 6 = sum of the weights applied to the data points.

The strength of all the analytical techniques that involve averages is that they are easy to compute. They also yield results that are close to recent historical results so they are not usually prone to spectacular error. Their weakness is that they contain very little information about trends or patterns in the data.

Trend-following models are data models where the data are expressed as a linear but sloped line. There are two basic forms of these models: (1) the trended linear model and (2) a linear regression model. The trended linear model is used when a linear trend is desired to increase or decrease a variable in a straight-line manner. An example of a linear trended projection is presented in  Table 6.4  and in  Chart 6.5 . Those examples are relevant to this discussion. Linear trends are most often characterized as

where

· Vt = value at point t,

· Vt-1= value at point t − 1,

· g = growth rate from one period to the next.

One important issue regarding these types of trend computations is that the growth rate is usually based on some estimate provided. The motivation behind the estimate is usually either subjective in nature or loosely based on recent historical trends. In either case, the linear trended projection is not good at identifying patterns within the seasonal cycle of the firm, nor is it good at closely fitting the slope of the trend line to the historical data that are available.

Linear trends may also be calculated via linear regression. Linear regression was discussed earlier, with examples given in  Table 6.5  and  Chart 6.6 . As a data analysis technique, it is one of the most common. The big advantage of linear regression is that the resulting trend line is closely fitted to the historical data used. This represents a clear advantage if historical data are important to the projection. However, just as with the models we have discussed to this point, linear regression is not useful in capturing the impacts of business cycles or seasonal data. The linear equation is the equation for a straight line: ^Y = a + bX, where ^Y = the value for the output value on the Y axis given a constant of a (the line's intercept on the Y axis) given a line slope of b at point X on the X axis. The important feature of this technique is that the “line” is placed in the historical data in the most optimal spot in terms of generating explanatory power, as previously discussed.

Other trend-following models can be used when we want to summarize existing data and project future performance based on trends exhibited within the data. Multiple regression analysis assumes that the relationship of more than one independent variable X is related to the status of the dependent variable Y. If various independent variables X1 … Xn are examined, then the movement of Y is projected on the basis of its relationship to each of the Xs examined in turn. Multiple regression analysis adds value in making a projection in that the increased number of independent variables will likely allow for more finely tuned explanatory power; the regression output will still be inadequate in capturing seasonality and business cycle impacts because the relationships are still linear in nature. The results are completely captive to a historical relationship between variables.

If linear explanations of existing data and trends are not desired or if they will not be adequate in their explanatory power, then curvilinear regressions may be used. In this type of model, the projection is a function not only of the linear equation but of higher order contributing polynomial relationships. In this technique, trends may be described that are nonlinear, a clear advantage. The explanatory power of these models will likely be higher than with linear models. The disadvantage is that this technique is no longer as amenable to informal problem formulation and computation. With curvilinear regression, rigorous problem setup and computer processing time need to be used. Basically, users of this method must be knowledgeable and skilled in more math and more computer science than those who use other techniques. Curvilinear output does capture data in a unique way.  Chart 6.7  shows an example of a curvilinear regression.

The classic technique used to summarize the statistical distribution of outcomes is the Monte Carlo simulation. This method is often used to project the most likely outcome given the statistically determined movements of input variables. A model is built to describe the relationship among firm inputs of unit sales, prices, direct costs, general and administrative costs, and taxes. The designed methodology projects net income (or some other output such as EBITDA or cash flow) given a specified level of unit sales. The values of the variables in this analysis are described on the basis of their historical behavior (or expected behavior). This means that each variable (for example, the cost of raw material) will have a unique statistical profile. It will have an average, a standard deviation, and a distribution profile (normal, discrete uniform, etc.).

Chart 6.7 Curvilinear Regression Example

When operating a simulation program, the average, standard deviation, and distribution profile for each variable will be input into the model. The computer will then step through the model one variable at a time and select a value for each variable; that value is calculated based on the variable's entered statistical characteristics. Once all variables have been assigned values, the program will then calculate the value for the desired output (i.e., dependent variable). This calculated output will be a result of statistics, not scenario or history.

The final step in the program is to perform the calculation thousands of times and summarize the results statistically. The final projection of the desired output is an average of thousands of calculations based on statistical estimates of the behaviors of input variables. Monte Carlo simulation offers an interesting perspective on the expected value and range of behavior of an identified output variable. However, the methodology is not useful for observing how the day-to-day work of the firm proceeds.

There are a couple of other models of data treatment. These techniques are not easily placed in the previous classifications. The first is called econometric. This modeling technique is often used to view problems in a “top-down manner” in light of the many linear relationships between the desired projected variable and a number of other independent variables. In one sense, the econometric model is the same as multiple regression analysis. However, as a matter of scope, it is usually a much broader formulation of the environment. Banks and trust companies use an econometric approach to project next year's investment climate. In their models, input variables range from gross domestic product (GDP) growth to interest rates to energy prices to money growth and industrial productivity. Many hundreds of variables can be brought into the analysis as independent variables. Historical relationships dominate the process, and specific relationships between variables are hard to assess since those relationships make relatively small contributions to the overall outcome of the projection. This is a method involving large databases and many hours of computer time.

Finally, all data can be “seasonally” adjusted. Seasonal adjustment should not be thought of as a means of projecting magnitude or trend but a means of analyzing the inherent seasonal patterns of the firm and adjusting output data so that these seasonal patterns stay intact. Seasonal adjustment will be discussed later in this chapter.

Dealing with Data (or Lack of Data)

Bringing all of the various views regarding type of projection, model, and methodology together is difficult. Not just because there is a plethora of information and concepts to learn but because the concepts overlap and duplicate both form and function. For example, a model used to describe data such as a simple average can also be used to project results. In fact, most models can also be methodologies that can be used to make projections. A type of a projection, such as a trended projection, may also seem to be a method of projection, and indeed it is once the starting point and growth rate for the trend have been determined. Once the decision is made about the assumptions and how to describe projected results, then types of projections and methods of data summary become full-fledged projections. Put another way, once historical data have been identified and key assumptions have been made, then constituent parts of the process lead to a coherent useful projection.  Chart 6.8  summarizes the discussion in this section.

Chart 6.8 Dealing with Data

The time horizon of a projection and the nature of available data for the projection are key issues that need to be addressed. Generally, time horizons may lengthen given the operating history of the firm and/or the variability of revenues:

1. For startup firms, projections over long time horizons are rarely supported by either historical data or by methodologies that have good predictive power (because of the lack of data and an imprecise understanding of the firm's operating characteristics). There is simply too little history either on the data side or on the operational side to make reliable long-term projections. For the startup firm, 3 to 5 years is a usual time horizon over which to project results, with the last 2 years being very inaccurate.

2. Intermediate-sized firms with substantially more operating history allow projections that range from the 3- to 5-year time horizon to be made. The farther-out years are also not highly reliable but more so than for startup firms; data and methodology can be used to make projections to that time frame.

3. Firms with long operating histories may facilitate projections in the 3- to 7-year time horizon. Projections that range beyond 5 years are rarely accurate and serve negligible purpose.

4. The only exception to this 3- to 7-year limitation is for firms that are utilities or are similar to utilities; firms like this typically have lots of historical or operating data, and the variability of their month-to-month revenue is small. These unique characteristics make longer projections possible. For utilities, 30-year projections are routine.

What data and how much data to consider in a projection are case specific and really depend on the specific circumstances surrounding each projection. As much data should be used as are readily available and coherent. Historical data should be used to the extent that they do not contain discontinuities such as changes in the way the data are acquired or calculated or contain “black swan”–type disruptions. If these types of intervening factors exist in the data, then the flaws need to be recognized and steps taken to adjust for their impact. Depending on the analysis being done, expert opinion or judgment can be applied to the data to improve their relevance to the problem at hand.

The most obvious source of actual data is the firm itself; historical accounting information is the starting point for all projections when it is available. Supplemental data on industry sales come from industry sources, government sources, specialized research reports, and trade associations in the form of census and economic reports. Data on the economy can be found in these same government sources, as well as specialized sources such as the Federal Reserve System and regional economic or industry studies performed by universities, banks, and development agencies. Market sizes are often assessed by reviewing local sales tax records. Sales taxes are reported by category (for example, restaurant sales, clothing sales, and fuel sales). Despite this wide range of data sources, when historical data are limited in their availability, then a number of data sources that have proven to be helpful should be used in the firm's projections.

1. Fee-for-service consultation:

· AMR Research—supply chain:  www.amr-research.com

· Frost & Sullivan—new technologies and markets:  www.frost.com

· Gartner—IT research:  www.gartner.com

· IDC—broad-based capabilities:  www.idc.com

· DisplaySearch—communications:  www.displaysearch.com

· Jupiter Internet Marketing—Internet:  http://jupiterinternetmarketing.com

· Yankee Group—telecom:  www.yankeegroup.com

2. Private company research:

· Dun & Bradstreet:  www.dnb.com

· Hoover's:  www.hoovers.com

· VentureSource (part of Dow Jones’ VentureOne suite of information services):  www.venturesource.com

· VentureExpert (part of Thomson's Venture Economics):  http://banker.thomsonib.com/ta/help/webhelp/Thomson_VentureXpert.htm

3. Industry sources:

· AlwaysOn Network—technology:  http://aonetwork.com

· Charlene Li's Blog—media and marketing:  www.charleneli.com/blog

· Corante—technology, media, and innovation:  http://corante.com

· SEMI—Semiconductor Industry Association—industry research:  www.semiconductors.org

· Datamonitor—public companies and industry analysis:  www.data-monitor.com

· Open Source Technology Group—software:  www.openmagazine.net

· BioWorld—biotechnology (a Thomson publication):  www.bioworld.com

· Annual Biotechnology Industry Report, Burrill & Company:  www.burrillmedia.com/collections/annual-biotechnology-industry-reports

· Genetic Engineering News (GEN):  www.genengnews.com

· Windhover Information—health care:  www.windhover.com

· Clean Edge—clean energy industry research:  http://cleanedge.com

· Nanodot—nanotechnology:  www.foresight.org/nanodot

· Small Times—nanotechnology:  http://electroiq.com/mems

4. Financial information:

· Ibbotson Associates, 2013, Stocks, Bonds, Bills, and Inflation: Valuation Edition 2013 Yearbook, Morningstar Inc., Chicago, IL, various pages.

· L. Troy, 2014, Almanac of Business and Industrial Financial Ratios, 2013 Edition, CCH, Chicago, IL, various pages.

· BioWorld—biotechnology (a Thomson publication)

· Securities & Exchange Commission—EDGAR:  www.sec.gov/edgar.shtml

· Government (federal, state, and local)

· Bank regional econometric forecasts

· Local and state tax authorities

· University research

· U.S. Census:  www.census.gov

The availability of historical data is a main driver in the selection of approaches to make the projection. The model and methodology used depend on the data available. If historical data are available, then statistical models and methodologies offer the most logical solutions to making projections. If historical data are not available, then judgment-based models and methodologies will be used.

Statistical methodologies are methodologies that are highly dependent on data to generate results. Included in this class of methodology are the following:

1. Extrapolation, the extension of an existing set of data into the future. Useful methodologies would include flat projection, trended, and regression. The projection considers only the available historical data.

2. Analogous firm analysis, useful for firms where there are limited data or operational history data from an analogous firm, is used to formulate a projection for the subject firm. Franchises are the clearest example where this type of projection is used. The franchisee is just starting up, and a projection for the new franchise is problematic, but many examples of similar businesses, such as existing franchises, can be used as a template for the startup's projection.

3. Multiple regression and multivariate analysis are techniques that focus entirely on existing data to generate results. The objectives are to search for relations between one or more dependent variables on a number of independent variables. Usually more limited in scope than an econometric methodology, these are more closely designed to describe the day-to-day workings of the firm.

4. Econometric methodology is geared toward looking for relationships between a large number of independent variables of an economic nature and one or more dependent variables. These relationships on their own may or may not seem to be relevant to the firm, its day-to-day business, and the projection of the desired variable.

At every step of the way, judgment plays a role in making projections; when historical data are not available, some form of management or expert judgment plays the central role in the construction of the projection when estimates of data are needed. In startup firms, no historical data are available, so the following three sources of data and methodology can be used:

1. Expert opinion is just what it sounds like. An industry expert exercises his or her skill and judgment to make a projection of the key information needed to make a projection of the desired variables. Often the expert is a member of the firm's management, an engaged expert consultant, or a market research firm specializing in market research.

2. Conjoint analysis occurs when a market study is undertaken to identify things like consumer preferences, price sensitivity, market growth rates, and potential size. This type of analysis usually involves focus groups, surveys, and/or beta tests. The results can be assembled into an initial projection of how the product will do over the short to intermediate time frame. This type of analysis is very expensive.

3. When bootstrapping, management makes a forecast based on its judgment of the reasonable expectations of results. Often projections using the bootstrap method focus on the capacity of the firm and a ramp-up from a low initial percentage of capacity to full capacity over time. A variation of this approach is for management to assume a degree of market penetration and then ramp up sales and product to meet that level of sales.

Revenue and Costs Relationships

One question that needs to be answered is, How do you project expenses? The short answer is that you don't project expenses. The cost of some elements of the firm's expenses can of course be projected, but the actual expenses incurred are a function of unit sales, production, and the fixed costs of the firm. If the firm sells 1,000 units of its product priced at $15.00 per unit, the firm's sales revenue is $15,000. The first step of making a revenue projection is projecting unit sales, and the second step is to project a per-unit selling price. The combination of these two projected variables allows for projected revenues to be calculated. It is in this area that the real effort of making projections should be focused—on projecting unit sales and selling price.

When dealing with expenses, costs are not projected in the same manner as revenue. If the cost of raw material is $3.00 per unit, then the raw material expense is a function of the number of units sold, not some other function. This means that the prices of the input elements to the production process should be projected, but the total expense for any given element of production will be a function of the firm's unit sales, except for the cost per unit of material or labor, and not a function of some extraneous relationship. The projection for the firm's expenses should respond to the day-to-day work flow of the firm.

There are two ways to relate the firm's expenses to its unit sales and revenues:

1. The pro-forma method is the simplest. In this system, the relationship between the expense category and the unit sales is held constant. If the relationship between last period's unit sales and the raw material expense was $3.00 on a per-unit basis, then the pro-forma projection will retain that relationship throughout the projection time horizon regardless of any economies of scale that may occur. The pro-forma projection model is easy to implement but does not provide the best day-to-day description of the firm.

2. The input-output method of making projections captures the actual relationships that exist between production levels and component expenses. This type of projection attempts to capture the relationship between raw material and units sold within various production ranges. For example, per unit costs might be $3.00 per unit for the production range of 1 to 999, but the cost might decline to $2.75 per unit when the production range increases to 1,000 to 2,499. The input-output projection model is more complex and gives better results in duplicating the actual workings of the firm on a day-to-day basis. It is somewhat more elaborate and difficult to design and implement.

Both of these projection methodologies need to be used to project cash flow, not just net income or EBITDA. In the valuation section of this book, we discuss how to estimate free cash flow by adjusting net income. Usually, projections of cash flow and cumulative cash flows give the most valuable information for startup firms.

Seasonal Adjustment and Patterns

We have seen that various models and methodologies can exhibit various patterns. Typically, all of the trend-following methodologies produce unique patterns, as do curvilinear regression and econometric projections. These patterns may contribute some information regarding future firm results, but they are artifacts of the computation embedded in the model and method rather than the day-to-day patterns found in the firm. Seasonality is really the gold standard that will relate projections to the day-to-day patterns found in the firm's activities.

Seasonality is a predictable cyclic behavior in the demand for products. Seasonality is distinguished from fluctuations in demand due to noise or casual activities such as price-driven or promotionally driven demand in that it varies independently of these factors (Moore, 2010). Seasonal demand variation is often tied to weather, holidays, or specific events. Seasonality is a phenomenon embedded in almost all business or industrial activity. Some businesses tend to exhibit more seasonality than others. For example, according to the National Retail Federation (2014), the retail industry generates 20% to 40% of its annual sales during the Christmas holiday season. Computing seasonality is important, particularly by using seasonally adjusted numbers when dealing with cash flow forecasts. Being able to combine adjustments for seasonality with other output methodologies is a valuable, useful skill. The process of imposing seasonal patterns on projected outputs is discussed below.

There are two ways to estimate seasonality: (1) Use government data for industry seasonality, or (2) estimate seasonality using historical data. The problem with using government data is that they generate results that are not unique to the case in hand and can vary substantially from the results of the firm. Government numbers come from industry data and do not distinguish between large or small firms or startup firms in their declining years. The problem with determining seasonality using historical data of the firm is that data are needed to do it. Many firms in the early stages of the business have not been around long enough to capture data that will exhibit seasonality. It usually takes at least 2 to 3 years of data to be able to decipher seasonal patterns.

The following example uses the sales data in  Table 6.1  to show how to incorporate seasonality into the firm's projections.  Table 6.7  indicates the process based on these data using each of the following steps:

1. Determine the seasonality for each month given the historical data. Using the historical sales data for 20xx, 20yy, and 20zz, we summed the sales for each month and divided it by the total sales for the 3-year period. For example, total January sales for the 3 years were 39,868 and total sales for the 3 years were 566,897. Therefore, January contributes 39,868/566,897 = 7.03% of yearly sales. As you can see from  Chart 6.9 , the firm hits a soft patch in sales in month 4 and sees a spike in sales in month 11.

Chart 6.9 Average Monthly Sales as a Percentage

2. Convert the regression forecast into an untrended forecast. We previously showed a regression forecast in  Table 6.5  and  Chart 6.6 . To change the regression forecast to an untrended forecast, we simply divide the annual regression-projected sales by 12. In our example, the total of the regression forecast is 301,514, which we divide by 12 to get an average of 25,126 per month.

3. Calculate the difference due to regression. By subtracting the untrended forecast from the regression forecast, the amount that is due to the trend can be determined. For January, this would be 21,302 − 25,126 = −3,824.

4. Seasonally adjust the untrended forecast. This is done by multiplying the total forecasted sales by the monthly seasonality computed in Step 1. For January, this would be 301,514 × 7.03% = 21,509.

5. Calculate the difference due to seasonality. Subtracting the untrended forecast from the seasonally adjusted forecast determines the amount that is due to seasonality. For January, this would be 21,509 − 25,126 = −3,921.

6. Adjust by untrended forecast by the amount due to the trend and the amount due to seasonality to obtain the seasonally adjusted and trended forecast.

Chart 6.10  presents the seasonally adjusted trended forecast.

Chart 6.10 Regression Projection, Untrended Projection, and Seasonally Adjusted Projection

As you can see from the chart, the pattern now looks like the seasonality pattern we saw in  Chart 6.9 , but the values are magnified due to the trend component.

Summary

As indicated at the beginning of this chapter, making projections is as much an art as a science. When making a projection, the ultimate objective is to minimize the cumulative error between the projected values and actual values over the relevant time horizon. Choices need to be made on the many forms of projection, models, methodologies, and the internal structures describing relationships between unit sales and expenses. These choices offer many routes to a final predictive solution. Key things to remember are the following:

1. Some forms of projection are easier to use and simpler to explain than others. Complexity may not be essential to getting good results. Use the simplest projection that does the job.

2. Data are key to a good projection. Data need to be continuous and calculated in a uniform manner to be helpful. This applies to both historical data and data derived through judgment-oriented processes.

3. Models and methodologies may also range widely in their complexity and difficulty of use. Choose models and methodologies that are adequate.

4. Make projections work the way the firm works. The pro-forma approach to relating expenses to unit sales is quicker, but it does not produce flexible or robust projections. The input-output approach is far superior, but it is harder to execute. It does produce flexible and robust projections.

5. Always project units of sales and prices at which the units will sell. Revenue is a logical computation that flows from these variables. Revenue just in dollars does not give clear, accurate results. Revenue is a function of the two most important variables that a business projection should contain—unit sales and sales price per unit.