5 Methodologies to Forecast Revenues for the DCF Method; Estimate Future Revenues from Historical Data Six Ways from Sunday
When the current CAGR is higher than the g (i.e., CAGR(t) > g), the model creates a negative drift k( g — CAGR(t) ) toward g. Conversely, when the current CAGR is lower than the g (i.e., CAGR(t) < g), the model creates a positive drift k( g — CAGR(t) ) toward g.
Generally, valuators analyze historical financial information since it often serves as the foundation from which estimates of future projected revenues are made.
The historical period under analysis usually encompasses an operating cycle of the entity’s industry, often a five-year period. Beyond five years, data can become “stale.”
There are five commonly used methodologies by which to estimate future revenues from historical data:
- The current revenues method
- The simple average method
- The weighted average method
- The trend line-static method
- The pull to perpetuity growth rate method
1. Current Revenues Method
The current year’s revenues is sometimes the best proxy for the following year and future years in many closely held companies. Management insights will be helpful in deciding whether current revenues are likely to be replicated in the ensuing years.
If management indicates that next year will be very similar to last year, then current revenues may be used as the basis to value the company. It is also possible that next year’s revenues will be different from the past but still grow into perpetuity at an average constant rate.
Any such projection must be supported with sound underlying assumptions. Regardless of the method employed, dialogue with, or information from management can provide critical insight into future projections.
The current revenues method can be illustrated by the following example:
2. Simple Average Method
The simple average method uses the arithmetic mean of the historical data during the analysis period. The simple average method can be illustrated by the following example:
A simple average is used most often in developing the estimate of expected future revenues for the next 5 years, when historical normalized information does not discern an identifiable trend. If the historical analysis period encompasses a full industry operating cycle, the use of a simple average also may provide a realistic estimate of expected future performance.
However, it may not accurately reflect changes in company growth or other trends that are expected to continue. In this example, the simple averaging method may not work well in estimating future revenues.
The last three years’ results may be more indicative of the company’s value when the company has been growing consistently and 2020 was perhaps an anomaly (COVID year). A cursory glance would tell you that the next year’s revenues probably would be expected to be somewhat higher than NIS 4,300 millions providing that the historical data are representative of the business’s direction and mirror management’s expectations.
3. Weighted Average Method
When the historical financial information yields a discernible trend, a weighted average method may yield a better indication of the future revenues, since weighting provides greater flexibility in interpreting trends. In fact, under certain circumstances, specific years may be eliminated altogether, that is, have zero weight.
The computation of the weighted average requires the summation of a set of results that are the products of assigned weights times annual historical revenues. It can be illustrated by the following example:
In this example, the valuator has identified a trend that requires greater weight be applied to the most recent operating periods. In deciding upon a weighting scheme, the valuator should attempt to model future expected revenues accurately.
Any weights can apply to any of the years. For example:
In this specific example, the weighted average method still may not reflect anticipated revenues correctly. As with the simple average method, the resulting value in this example tends to be conservative and may understate value when future performance is expected to exceed the prior year.
Care must be exercised in using weighted averages including the weights and the years.
4. Trend Line-Static Method
The trend line-static method is a statistical application of the least squares formula. The method generally is considered most useful when the company’s past revenues have been relatively consistent (either positive or negative) and are expected to continue at similar levels in the future.
At least five years of data is suggested.
Where:
y = predicted value of y variable for selected x variable
a = y intercept (estimated value of y when x=0)
b = slope of line (average change in y for each amount of change in x)
x = independent variable
Where:
X = value of independent variable
Y = value of dependent variable
N = number of items in sample
is the mean of independent variable
is the mean of dependent variable
The computation can be illustrated as follows:
The next step requires solving the equations for variables a and b. Because variable b is integrated into the formula for variable a, the value of b must first be determined.
Solving further for variable a,
Finally, solving the original least square formula,
As can be seen, the trend line static method places the greatest weight on the most recent periods, even more so than the weighted average method. Depending on the facts, this may produce a more accurate picture of future revenues, particularly when growth is expected to continue.
There are various statistical measures that can also be used to test the reliability of the results derived from this method.
5. Pull to Perpetuity Growth Rate Method (Detailed Cash Flow Projections)
The assumption that the revenues behave like a stock price is a natural starting point but is less than ideal. One important difference between revenues and stock prices is that revenues appear to be pulled back to some indefinitely sustainable perpetuity growth rate (e.g., the expected long-run growth rate of the population).
This phenomenon is known as mean reversion. When the revenues 5-year compound annual growth rate (i.e., the annualized geometric average rate of revenue growth between the current year’s revenues and the revenues five years ago, assuming growth takes place at an exponentially compounded rate), 5Y-CAGR, is higher than the perpetuity growth rate, g, mean reversion tends to casue the 5Y-CAGR to have a negative drift.
When 5Y-CAGR is lower than the perpetuity growth rate, g, mean reversion tends to cause it to have a positive drift. Mean reversion is illustrated in the figure bellow.
In summary, the CAGR is pulled to a level of g at rate of k. In polanitzer’s model, the real-world process for revenue CAGR is:
where:
CAGR(t) = the CAGR at time t
CAGR(t-1) = the CAGR at time t-1
k = the rate of reversion to the g
g = the perpetuity growth rate
It is important to note that the first CGAR is the 5Y-CAGR which can be found by the following formula
The polanitzer’s model has a number of interesting features. First, it displays mean reversion to a long-run rate of g. The parameter k governs the speed of mean reversion. When the current CAGR is higher than the g (i.e., CAGR(t) > g), the model creates a negative drift k( g — CAGR(t) ) toward g. Conversely, when the current CAGR is lower than the g (i.e., CAGR(t) < g), the model creates a positive drift k( g — CAGR(t) ) toward g.
In order to obtain the rate of reversion, k, compute the reciprocal of the projection period (a period of five years excludes the representative year). In order to obtain the perpetuity growth rate, g, estimate the expected long-run growth rate of the population).
The expected long-run growth rate of the population is estimate at a level of 1.5%.
The pull to perpetuity growth rate method uses projections of revenues or other for a specified number of future years (generally five years) referred to as the “explicit,” “discreet,” or “forecast” period. This method is used to determine future revenues when using the DCF method.
This method has been widely accepted due to the flexibility it allows when estimating year-by-year benefit revenues over the explicit period. Theoretically, the length of the explicit period is determined by identifying the year when all the following years will change at a constant rate. Practically, however, performance and financial position after five years often are difficult to estimate for many closely held companies. Lesser periods are sometimes used as well.
With exceptions, five years is the standard length of the explicit period. One such exception is for start-up and early-stage companies whose profitability often is not projected until several additional years out. The period following the explicit period is called the “continuing value” or “terminal” period.
Projections often are determined by reference to historical financial information that has been normalized. Used as a foundation for future expectations, normalized financial statements may include both balance sheet and income statement adjustments.
Once the valuator has normalized the historical data, when applicable, it may be necessary to review all elements of revenue and expenses to ensure that future operating projections reflect as closely as possible the trends identified in the analysis of historical financial information. These trends can be discussed with management and related to future expectations and economic and industry research undertaken by the valuator in conjunction with the engagement.
In some circumstances, the past is not indicative of the future. Valuators must exercise care in analyzing projected performance in these situations. Adequate support must exist for the assumptions that the projections are based upon.
About the Author
Roi Polanitzer, CFV, QFV, FEM, F.IL.A.V.F.A., FRM, CRM, PDS, is a well-known authority in Israel the field of business valuation and has written hundreds of papers that articulate many of the concepts used in modern business valuation around the world. Mr. Polanitzer is the Owner and Chief Appraiser of Intrinsic Value — Independent Business Appraisers, a business valuation firm headquartered in Rishon LeZion, Israel. He is also the Owner and Chief Data Scientist of Prediction Consultants, a consulting firm that specializes in advanced analysis and model development.
Over more than 17 years, he has performed valuation engagements for mergers and acquisitions, purchase price allocation (PPA) valuations, goodwill impairment test valuations, embedded option and real option valuations, employee stock option (ESOP) valuations, common stock valuations (409A), splitting equity components and complicated equity/liability instrument valuations (PWERM / CCM / OPM), contingent liability, guarantees and loan valuations, independent expert opinions for litigation purposes, damage quantifications, balancing resources between spouses due to divorce proceedings and many other kinds of business valuations. Mr. Polanitzer has testified in courts and tribunals across the country and from time to time participates in mediation proceedings between spouses.
Mr. Polanitzer holds an undergraduate degree in economics and a graduate degree in business administration, majoring in finance, both from the Ben-Gurion University of the Negev. He is a Full Actuary (Fellow), a Corporate Finance Valuator (CFV), a Quantitative Finance Valuator (QFV) and a Financial and Economic Modeler (FEM) from the Israel Association of Valuators and Financial Actuaries (IAVFA). Mr. Polanitzer is the Founder of the IAVFA and currently serves as its chairman.
Mr. Polanitzer’s professional recognitions include being designated a Financial Risk Manager (FRM) by the Global Association of Risk Professionals (GARP), a Certified Risk Manager (CRM) by the Israel Association of Risk Managers (IARM), as well as being designated a Python Data Analyst (PDA), a Machine Learning Specialist (MLS), an Accredited in Deep Learning (ADL) and a Professional Data Scientist (PDS) by the Professional Data Scientists’ Israel Association (PDSIA). Mr. Polanitzer is the Founder of the PDSIA and currently serves as its CEO.
He is the editor of IAVFA’s weekly newsletter since its inception (primarily for the professional appraisal community in Israel).
Mr. Polanitzer develops and teaches business valuation professional trainings and courses for the Israel Association of Valuators and Financial Actuaries, and frequently speaks on business valuation at professional meetings and conferences in Israel. He also developed IAVFA’s certification programs in the field of valuation and he is responsible for writing the IAVFA’s statement of financial valuation standards.