FactSet/BVR Control Premium Study Frequently Asked Questions (FAQs)
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Note: All share price and other currency values are reported in USD.
| Terms | Definition |
2 Month Equity Premium | Equity premium computed by comparing the price ultimately paid to the common stock price 2 months prior to the announcement date. = (Purchase Price Per Share / 2 Month Price) - 1 |
1 Month Equity Premium | Equity premium computed by comparing the price ultimately paid to the common stock price 1 month prior to the announcement date. = (Purchase Price Per Share / 1 Month Price) - 1 |
1 Week Equity Premium | Equity premium computed by comparing the price ultimately paid to the common stock price 1 week prior to the announcement date. = (Purchase Price Per Share / 1 Week Price) - 1 |
1 Day Equity Premium | Equity premium computed by comparing the price ultimately paid to the common stock price 1 day prior to the announcement date. = (Purchase Price Per Share / 1 Day Price) - 1 |
FactSet Equity Control Premium | Equity premium computed by comparing the price ultimately paid to the unaffected stock price. = (Purchase Price Per Share - FactSet Unaffected Price) / FactSet Unaffected Price |
Implied Equity Minority Discount | An implied discount on equity computed from the FactSet Equity Control Premium. = FactSet Equity Control Premium / (1 + FactSet Equity Control Premium) |
FactSet Invested Capital Control Premium | Invested capital premium computed by comparing the company’s invested capital value using the per-share takeover price to the company’s invested capital value prior to the announcement of the acquisition. = (Target Invested Capital - ((Shares Outstanding * Unaffected Price) + Total Interest Bearing Debt and Preferred Stock)) / ((Shares Outstanding * Unaffected Price) + Total Interest Bearing Debt and Preferred Stock) |
Implied Invested Capital Minority Discount | An implied discount on invested capital computed from the FactSet Invested Capital Control Premium. = FactSet Invested Capital Control Premium / (1 + FactSet Invested Capital Control Premium) |
FactSet Unaffected Price | Target company's common stock price per share unaffected by the acquisition announcement. This price is selected by FactSet after analyzing each transaction in detail. |
1 Day Price | Target company's common stock price per share 1 day prior to the acquisition announcement date. |
1 Week Price | Target company's common stock price per share 1 week prior to the acquisition announcement date. |
1 Month Price | Target company's common stock price per share 1 month prior to the acquisition announcement date. |
2 Month Price | Target company's common stock price per share 2 months prior to the acquisition announcement date. |
LTM Net Sales | Target company's sales based on the latest reported 12-month period (LTM) prior to the transaction's announcement date. Sales are reported in millions and rounded. |
LTM EBITDA | Target company's earnings before interest, taxes, depreciation and amortization (EBITDA) based on the latest reported 12-month period (LTM) prior to the transaction's announcement date. EBITDA is reported in millions and rounded. |
LTM EBIT | Target company's earnings before interest and taxes (EBIT) based on the latest reported 12-month period (LTM) prior to the transaction's announcement date. EBIT is reported in millions and rounded. |
LTM Net Income | Target company's net income (loss), excluding extraordinary items, based on the latest reported 12-month period (LTM) prior to the transaction's announcement date. Income is reported in millions and rounded. |
Cash and Equivalents | Target company’s cash and equivalents, based on the latest reported period prior to the transaction’s announcement date. Cash and Equivalents is reported in millions and rounded. |
Interest-Bearing Debt | Target company’s interest-bearing debt, based on the latest reported period prior to the transaction’s announcement date. This field includes the values for current and non-current operating lease liabilities. Interest-Bearing Debt is reported in millions and rounded. |
BV Preferred Stock | Target company’s book value of preferred stock, based on the latest reported period prior to the transaction’s announcement date. BV Preferred Stock is reported in millions and rounded. |
BV Target Common Equity | Target company's book value (BV), sometimes referred to as shareholder's equity or net tangible assets, is based on the latest reported period prior to the transaction's announcement date. Book Value is reported in millions and rounded. |
Target Invested Capital | Target company's implied total invested capital (TIC) based on the sum of implied market value of equity plus the face value of total interest bearing debt and the book value of preferred stock outstanding prior to the announcement date. TIC is reported in millions and rounded. |
Book Value per Share | The target company's BV Target Common Equity divided by the target company's Common Shares Outstanding. |
Common Shares Outstanding | Target company's number of common shares outstanding shown in millions and rounded. |
Operating Profit Margin | = LTM EBIT / LTM Net Sales |
Net Profit Margin | = LTM Net Income / LTM Net Sales |
Implied MVE | Target company’s market value of equity (MVE) based on the purchase price per share times total shares outstanding reported in the period prior to the transaction's announcement date. Market value of equity is reported in millions and rounded. |
Price/Sales | Purchase price-to-sales ratio for the target company based on the implied market value of equity divided by the latest reported 12-month net sales prior to the announcement date. = Implied MVE / LTM Net Sales |
Price/Income | Purchase price-to-net income ratio for the target company based on the implied market value of equity divided by the latest reported 12-month net income prior to the announcement date. = Implied MVE / LTM Net Income |
Price/Book Value | Purchase price-to-book value ratio for the target company based on the implied market value of equity divided by book value of the target company. = Implied MVE / BV Target Common Equity |
Target Invested Capital/EBIT | Target TIC-to-EBIT ratio for the target company based on TIC divided by the latest reported 12-month earnings before interest and taxes prior to the announcement date. = TIC / LTM EBIT |
Target Invested Capital/EBITDA | Target TIC-to-EBITDA ratio for the target company based on TIC divided by the latest reported 12-month earnings before interest, taxes, depreciation and amortization prior to the announcement date. = TIC / LTM EBITDA |
Date Announced | Date that the acquisition was announced. |
Date Effective | Date that the acquisition became effective. |
Deal Value | The aggregate purchase price given to shareholders of the target company's common stock by the acquiring company. Shown in millions and rounded. |
% of Shares Acquired | Percent of the target company's common shares purchased by the acquirer in the acquisition. |
% of Shares Held at Date Announced | Percent of the target company's common shares held by the acquiring company on the date announced. |
% of Shares Held after Acquisition | Percent of the target company's common shares held by the acquiring company following the transaction. |
Purchase Price Per Share | The total consideration paid per share for the target company's shares. |
Common Shares Acquired | Number of target company's common shares acquired by the acquiring company in the acquisition, shown in millions and rounded. |
Consideration | Consideration denotes the method of payment provided to the target company. The single character codes are C = Cash, D = Debt, L = Liabilities, S = Stock, X = Other (warrants, contingent payments, etc.) |
Attitude | These are only applied to tender offers. The types of attitude are: Friendly, Neutral and Hostile. |
Form | The form of the acquisition can take one of the following types:
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Transaction Purpose | The two types of Transaction Purpose are Strategic and Financial. These are defined as follows:
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Q: How often is the FactSet/BVR Control Premium Study updated with new transactions?
A: The platform is updated weekly with new controlling-interest transactions that have occurred. When the weekly refresh occurs, any changes and additions FactSet may have made to the data set will be reflected in the FactSet/BVR Control Premium Study.
Q: What is the source of the information in the FactSet/BVR Control Premium Study?
A: The sources of the information used include SEC/government/regulatory filings and public announcements for mergers & acquisition transactions. Transactions included are only for when a public target is being acquired. An analyst will conduct further research into supporting press releases and SEC filings to find the unaffected price.
Q: Are there any limitations that come with a subscription to the FactSet/BVR Control Premium Study?
A: Both subscribers and day pass purchasers receive access to the full FactSet/BVR Control Premium Study platform, including unlimited searches, comparable company statistics, summarized results, transaction reports, and PDF exports. Subscribers, but not day pass buyers, receive access to all current and historical issues of the Control Premium Study Quarterly Report (a quarterly publication analyzing data from the FactSet/BVR Control Premium Study database).
Subscribers to the database are limited to 500 unique transactions that can be exported to Excel in a day and 1,000 unique transactions that can be exported to Excel in a month. Day pass purchasers are limited to 200 unique transactions that can be exported to Excel in a day.
Only unique exported transactions within a 24-hour period will be deducted from the daily limit, and only unique exported transactions during the month will be deducted from the monthly limit. In other words, once a particular transaction is exported to Excel, exporting that same transaction again during the 24-hour period will not count against the daily export total, and exporting that same transaction again any time during the month will not count against the monthly export total.
If you are a subscriber and would like to increase your daily and/or monthly export limits, there are several upgrade options. For more information, please contact us at: 503-479-8200 ext. 2 or sales@bvresources.com.
Q: Do the historical data in the FactSet/BVR Control Premium Study ever change?
A: Starting in 2019, BVR worked with FactSet to establish a data feed that creates the Control Premium Study from the FactSet Mergers database. This feed is run each week and the results refresh the data available in the FactSet/BVR Control Premium Study. This allows the database to reflect any corrections or revisions that have been made to historical data, and it updates the database with new transactions.
Q: Does the FactSet/BVR Control Premium Study include transactions of privately held companies?
A: No, the FactSet/BVR Control Premium Study only includes transactions where the target was a publicly-traded company.
Q: What are the inclusion criteria for the transactions that appear in the FactSet/BVR Control Premium Study?
A: The following criteria is the screening process for transactions to be included in the Study:
- Buyer’s control in target company must be from a minority stake (<50%) to a majority stake (>50%) – (“Deal Type” must be Acquisition/Merger or Majority Stake)
- Example: Company A acquires 100% of Company B shares
- Example: Company A already owns 49.9% of Company B shares and acquires an additional 5% in Company B
- Target company must be publicly traded
- Deal type is not a merger of equals, a bankruptcy, or a scheme of arrangement
- Deal must have price per share as well as target per share prices
- Target must have revenue greater than $0 (Note: Based on the online display rounding and only showing 2 decimal places, some companies will show $0.00 for LTM Sales even though their revenue figure is greater than zero).
- Target company’s financials may not be more than two years older than the deal’s announce date
- Deal must be complete
Q: I noticed that the FactSet/BVR Control Premium Study includes SIC codes that aren't part of the master OSHA list. Why is this and what are these codes?
A: In order to better classify the industries of certain acquirers and targets in the FactSet/BVR Control Premium Study, FactSet created additional SIC codes. These codes are not part of the master OSHA list, but are used in the database. These additional codes are:
- 2837 - Generic Drugs
- 3445 - Cables
- 6189 - Asset-Backed/Mortgage-Backed Securities
- 6197 - Finance Companies
- 6199 - Finance Services
- 6771 - Venture Capital/Private Equity
- 6781 - Special Purpose Vehicles
- 8747 - Project Management Services
- 9011 - Local Agencies
- 9141 - Sovereign Government
- 9151 - Province/State Government
- 9161 - Municipal Government
- 9171 - National Agencies
- 9181 - State Agencies
Q: Are bankruptcy deal types included the FactSet Control Premium?
A: No. Bankruptcy deal types are excluded from the database.
Q: What are the guidelines for calculating the FactSet Equity Control Premium?
A:
- Determination of the unaffected stock price
- Determination of the final price that the acquirer offers, per share, to purchase the target company's common stock, per terms of a tender offer
- Computation of the equity control premium using the following equation: = (Purchase Price Per Share - FactSet Unaffected Price) / FactSet Unaffected Price
Q: What are the guidelines for calculating the FactSet Invested Capital Control Premium?
A:
- Determination of the unaffected stock price
- Determination of the final price that the acquirer offers, per share, to purchase the target company's common stock, per terms of a tender offer
- Determination of the target company’s invested capital value (TIC)
- Computation of the control premium using the following equation: = (Target Invested Capital - ((Shares Outstanding * Unaffected Price) + Total Interest Bearing Debt and Preferred Stock)) / ((Shares Outstanding * Unaffected Price) + Total Interest Bearing Debt and Preferred Stock)
Q: How does FactSet determine an unaffected stock price?
A: FactSet looks at the trading volume and stock price fluctuations for the year prior to the date of announcement. If they discover there is a significant change in stock trading activity, they conduct research to determine the reason for such changes. If the reason is due to potential M&A activity (i.e. the target company has hired a financial advisor to seek a buy-out opportunity, or the target company is in talks with potential buyers), then the earliest date before such announcements will be selected as the unaffected date, since this date is representative of normal pricing activity. If no talks or rumors were disclosed prior to the announcement, one day prior to the announcement will be selected as the unaffected date. The FactSet Unaffected Price is the stock price on the unaffected date.
Q: Does the Purchase Price Per Share include any contingent value rights?
A: Yes, contingent value rights are included in the Purchase Price Per Share. However, this is uncommon and primarily only in transactions of pharmaceutical companies.
Q: How does FactSet determine which financial statements to use for the target acquired?
A: FactSet uses the latest financial statements that were available prior to the announcement date. For example, if the announced date was February 25, 2011 (bidder agreed to buy target and announcement was made), FactSet would use the latest financial statements of December 31, 2010. If this deal closed on April 20, 2011, FactSet would not use the financial statements of March 31, 2010 - the latest financial statements available prior to the announced date would be used, which would be the financial statements of December 31, 2010.
Q: Can you give an example of calculating the FactSet Equity Control Premium?
A: As an example, let's use the acquisition of Optical Coating Laboratory Inc.
- Unaffected price is $119.25 per share
- Purchase price per share is $179.12
- FactSet Equity Control Premium is 0.502 (or 50.2%)
- 0.502 = ($179.12 - $119.25) / $119.25
The acquirer paid a premium over the FactSet Unaffected Price per share of 1.502 times the FactSet Unaffected Price per share (or a control premium of 50.2% more than the FactSet Unaffected Price).
Q: Can you give an example of calculating the FactSet Invested Capital Control Premium?
A: As an example, let's use the acquisition of Optical Coating Laboratory Inc.
- Unaffected price is $119.25 per share
- Purchase price per share is $179.12
- Shares outstanding are 14.262 million
- Target Invested Capital is $2,609.537 million
- Implied Market Value of Equity is $2,554.609
- The difference between TIC and Implied MVE is face value of total interest bearing debt and the book value of preferred stock (here $54.93 million)
- FactSet Invested Capital Premium is 0.486 (or 48.6%)
- 0.486 = ($2,609.537 - ((14.262 x $119.25) + $54.93)) / ((14.262 x $119.25) + $54.93)
The acquirer paid a premium over the target’s invested capital of 1.486 times (or a control premium of 48.6%).
Q: Why has the FactSet Invested Capital Control Premium been added to the Study? Can you provide an example of the use of the invested capital premium contrasted with the use of the equity premium?
A: The FactSet Invested Capital Premium was added because some practitioners believe that the target company’s capital structure could affect the premium when the premium is computed solely using target company’s equity value. Below is a hypothetical example of computing and applying an invested capital and equity premium.
| Target company invested capital value (prior to announcement) | Target Company A | Target Company B | Target Company C | |
| Market value of aggregate equity prior to acquisition announcement | $110,000 | $80,000 | $60,000 | |
| Market value of debt prior to acquisition announcement | $40,000 | $70,000 | $90,000 | |
| Market value of invested capital prior to acquisition announcement | $150,000 | $150,000 | $150,000 | |
| Computing equity premium | ||||
| Take-over aggregate equity price | $140,000 | $110,000 | $90,000 | |
| Market value of aggregate equity prior to acquisition announcement | $110,000 | $80,000 | $60,000 | Avg |
| Equity premium | 27% | 38% | 50% | 38% |
| Computing invested capital premium | ||||
| Take-over aggregate equity price | $140,000 | $110,000 | $90,000 | |
| Market value of debt prior to acquisition announcement | $40,000 | $70,000 | $90,000 | |
| Take-over invested capital price | $180,000 | $180,000 | $180,000 | |
| Market value of invested capital prior to acquisition announcement | $150,000 | $150,000 | $150,000 | Avg |
| Invested Capital Premium | 20% | 20% | 20% | 20% |
| Scenario 1 (equity premium) | Subject Company |
| Market value of invested capital on a noncontrolling basis | $100,000,000 |
| Less: Market value of debt | $20,000,000 |
| Market value of equity on noncontrolling basis | $80,000,000 |
| Plus: Control premium of 38% | $30,400,000 |
| Market value of equity on controlling basis | $110,400,000 |
| Scenario 2 (invested capital premium) | |
| Market value of invested capital on a noncontrolling basis | $100,000,000 |
| Plus: Control premium of 20% | $20,000,000 |
| Market value of invested capital on a controlling basis | $120,000,000 |
| Less: Market value of debt | $20,000,000 |
| Market value of equity on controlling basis | $100,000,000 |
Q: Why do negative premiums exist in the FactSet/BVR Control Premium Study?
A: A number of factors can contribute to this. If the buyer is public and paying with its own stock, its stock price may have decreased between the announcement and the time the deal closes. An example of this is when Bank of America’s price dropped from $33.74 to $14.08. Another factor may be that the selling company could be struggling and on the verge of failure, as with Bear Stearns in 2008.
This paper available here provides research and insight into why negative premiums occur.
Q: What is "attitude" and how does FactSet determine the "attitude" for each transaction?
A: Attitude indicates the way the target's board of directors viewed the acquirer's proposal to enter into a transaction with the target - hostile, friendly, neutral. This data item is only populated if the transaction is a tender offer.
- Hostile: the target's board of directors viewed the acquirer's proposal unsatisfactory and recommended that shareholders reject the offer. Once a transaction is hostile, it will remain hostile even if it is subsequently recommended by the target's board.
- Friendly: the target's board of directors viewed the acquirer's proposal as satisfactory and recommended that their shareholders accept the offer.
- Neutral: the target's board has not yet made a determination of whether to reject or accept the unsolicited offer OR the offer is a legally required, mandatory tender offer for additional shares in which the target's board has no discretion.
Q: I noticed that the FactSet/BVR Control Premium Study calculates a minority discount; what is the formula that the database uses to calculate this discount?
A: The database uses the following calculation: Implied Discount = 1 - [1/(1 + control premium)]
An alternate equation that can also be used to determine the Implied Median Minority Discount (where CP is the Control Premium) is: Implied Minority Discount = CP / (1 + CP)
Q: Is there any theoretical research that affirms that the inverse of a control premium is an implied minority discount - or is this simply accepted in the business valuation profession?
A: The minority discount is widely perceived of as the inverse of the control premium, where as an acquirer would assumingly pay a higher price for control in a company and pay a lesser amount for a minority stake.
An alternative theory used by appraisers and other professionals, was that the control premiums that were observed in the public markets tended to be paid by strategic buyers, or buyers that had the ability to derive synergies from combinations or had other, specific, strategic intent.
There is another large category of acquirers of companies, the financial buyer. Financial buyers may not have the ability to derive synergies from an acquisition, but they can seek financial returns from their investments. The FactSet/BVR Control Premium Study can be searched by financial buyers only, should the analyst wish to.
Q: How does a practitioner know when to apply a control premium or a minority discount?
A: This document is an excerpt from the PowerPoint for BVR's March 2008 webinar, Getting the Most from the FactSet/BVR Control Premium Study, and is helpful in thinking about this question.
Q: Does the FactSet/BVR Control Premium Study exclude any outliers or valuation multiples deemed to be outliers?
A: Because the CPS is the result of an analysis of the data by FactSet research analysts who review each controlling acquisition for its relevancy for inclusion in the Study, the CPS does not include transactions deemed to be outliers.
The CPS also does not include the valuation multiples for transactions where the valuation multiples fall outside the following ranges (the transactions are included, though):
- Price/Sales: 0-10X;
- Price/Income: 0-40X;
- Price/Book Value: 0-10X;
- TIC/EBIT: 0-35X
- TIC/EBITDA: 0- 25X
These values were established as acceptable ranges when the Study was first put together in the early 1990s. The ranges were developed and verified through FactSet's relationships with investment banking firms (specifically HLHZ). While it is true that excluding multiples from the ranges could introduce bias, FactSet's experience has been that the vast majority of transactions fall within these ranges (for at least one category). Please note the valuation multiples are excluded but the transactions are not.
Q: How does FactSet/BVR Control Premium Study calculate LTM sales figures for banks?
A: LTM revenues for banks are calculated from interest income and non-interest income such as commissions, foreign exchange income, etc.
Q: Does the Purchase Price Per Share include any contingent value rights? A: Yes, contingent value rights are included in the Purchase Price Per Share. However, this is uncommon and primarily only in transactions of pharmaceutical companies.
Q: In the FactSet/BVR Control Premium Study, what is the amount of shares that the acquirer needs to purchase from the target for the transaction to be included in the study?
A: The study includes all deals in which the buyer has both a controlling stake in the target (50.1% or above) after the transaction and had a minority stake (or 0% stake) in the target prior to the purchase. So, if a company owned 40% and purchased 11%, the purchase of 11% would be included. But if a company had a 54% stake and bought 11%, the purchase of 11% would not be included. As of September 2020, approximately 70% of all the transactions in the FactSet/BVR Control Premium Study were the purchase of a 100% interest.
Q: How does FactSet determine the two transaction types (financial and strategic)?
A: By definition, they are as follows:
- Financial acquisition: Indicates the acquirer in the transaction is making the acquisition for investment purposes and is not making the acquisition for strategic business purposes. Financial buyers frequently include private equity firms, buyout funds, or any other finance related company whose principle line of business is not directly related to that of the target company. Financial buyers are generally concerned about their return on investment, the strength of the management team and the size of the market. They prefer to maintain current management and provide the tools and assistance for growth. They frequently make acquisitions with the intent of exiting at some point in the future when they can maximize their return.
- Strategic acquisition/merger: Indicates the acquirer in the transaction operates in the same business or industry as the target company in the transaction. Unlike financial buyers, strategic buyers are often looking to find synergies with the target company and generally want to acquire the target and hold on to it, whereas a financial buyer generally want to make an acquisition and exit their investment in the target company within a relatively short time frame. Strategic acquisitions can be horizontal (e.g., acquiring companies in same market sector to expand product/service offerings, etc.) or vertical (e.g., acquiring suppliers or other members of the distribution channel to improve efficiency and reduce costs, etc.).
Q: What is the main difference between the FactSet/BVR Control Premium Study database and the FactSet Review publication?
A: When calculating the premium offered, the FactSet Review uses the stock price on the acquisition five-days prior to the announcement date, while the FactSet/BVR Control Premium Study uses the unaffected price, which may be the stock price one day prior to the announcement or another day where the price was determined to be unaffected by rumors, negotiations, or announcement of the acquisition. Furthermore, the FactSet/BVR Control Premium Study includes only controlling purchases while the FactSet Review includes transactions when a 5% minimum stake is acquired.
The FactSet/BVR Control Premium Study provides the actual transactions, their multiples, control premium, and implied minority discount and builds from there to deliver the range, mean and median premium/discount, and other statistics selected by the user. The FactSet/BVR Control Premium Study database provides the ability to develop figures and statistics over a longer time period than the FactSet Review, and also only provides information on transactions of public companies, and only closed deals. The FactSet/BVR Control Premium Study database is updated quarterly, and your purchase includes access to all current and historical issues of the Control Premium Study Quarterly report in PDF format.
The FactSet Review provides individual transaction details in the Transaction Roster; Termination Fee Roster, Cancellation Roster, and List of Transactions by SIC Codes, (with details being customized for the specific needs of each roster). It should be noted that the individual transaction details in the FactSet Review are not as comprehensive as those in the FactSet/BVR Control Premium Study database. The FactSet Review also processes the individual transactions into aggregate results – used for overall M&A market analysis, industry analysis, geographical analysis. The FactSet Review provides information on transactions of both private and public companies, and for cancelled, closed and announced deals. Aggregate calculations only include announced and closed deals. The FactSet Review essentially does a lot of the heavy lifting for the user, by providing statistics, summaries, charts, and graphs. The FactSet Review publication is updated annually, but your purchase also includes the monthly emailed Flashwire Monthly Review in PDF format.
Information in the FactSet Review is only limited to transactions involving where one party (either the acquirer or the seller) is a domestic company, and will contain public targets, private targets, and divestitures. The FactSet/BVR Control Premium Study is an in-depth extension of the public portion of the FactSet Review.
For a more detailed comparison, please see our Control Premium Study database vs. FactSet Review publication Comparison Chart.
There are advantages for any firm to owning both publications because there is little overlap. The FactSet Review covers a much broader spectrum of M&A deals and provides useful and insightful summaries. The FactSet/BVR Control Premium Study provides greater detail on individual transactions and focuses on control premiums and implied minority discounts.
Q: Are all transactions in the FactSet/BVR Control Premium Study stock purchases, or are some asset purchases?
A: The vast majority of transactions in the CPS are stock purchases. Generally, asset purchases get weeded out in FactSet's screening process for a variety of reasons. The price paid is for assets only, there was no per share amount reported for shareholders, the sale went through bankruptcy courts, there were no financials available for only the assets purchased, etc.
Q: I see that you show the harmonic mean (labeled as “H Mean” in the Statistics tab and Summary tab) for the valuation multiples. What is the harmonic mean?”
A: On the Statistics tab and the Summary tab, the FactSet/BVR Control Premium Study presents medians, averages, coefficients of variation, harmonic means, and other statistics, depending on the data. When price is the numerator, many practitioners and academics believe the harmonic mean is a better measure of central tendency for valuation multiples than the mean (the arithmetic average
Shannon P. Pratt writes on page 140 of his 2nd edition of The Market Approach to Valuing Businesses:
Although the harmonic mean is not used frequently, probably because it is unfamiliar to most readers of valuation reports, it is conceptually a very attractive alternative measure to central tendency.In addition, Gilbert Matthews of Sutter Securities Inc. wrote an article in the June 2006 issue of Business Valuation Update that explains what the harmonic mean is and provides a detailed example. Mark G. Filler of Filler & Associates P.A. replied to Matthews in the August 2006 Business Valuation Update. In addition, Matthews was quoted in the July 2001 Business Valuation Update as follows:
The harmonic mean is preferable in any ratio in which price is the numerator. For yields, when the price is in the denominator, an arithmetic mean is correct. An example is the “earnings yield” (EPS/P) rather than PE used by the British. If price is the numerator, the result is an inverted ratio for which the harmonic mean is statistically a more appropriate measure of central value. The harmonic mean gives an equal weight to an equal investment in each company, while the arithmetic mean gives three times the weight to a multiple of 30x compared to a multiple of 10x. For most other uses in valuation, the arithmetic mean is appropriate. For a fuller discussion, see “Fairness Opinions” by Mark M. Lee and Gilbert E. Matthews and page 139 and 140 of the 2nd Edition of The Market Approach to Valuing Businesses by Shannon Pratt.
Q: I see that you show the weighted harmonic mean (labeled as “WH Mean” in the Statistics tab and Summary tab) for the valuation multiples. What is the weighted harmonic mean?”
A: The weighted harmonic mean is often used in finance to average multiples.
Quoting Wikipedia:
The weighted harmonic mean is the preferable method for averaging multiples, such as the price–earnings ratio (P/E), in which price is in the numerator. If these ratios are averaged using a weighted arithmetic mean (a common error), high data points are given greater weights than low data points. The weighted harmonic mean, on the other hand, gives equal weight to each data point. The simple weighted arithmetic mean when applied to non-price normalized ratios such as the P/E is biased upwards and cannot be numerically justified, since it is based on equalized earnings; just as vehicles speeds cannot be averaged for a roundtrip journey.Quoting Investopedia:
The harmonic mean helps to find multiplicative or divisor relationships between fractions without worrying about common denominators. Harmonic means are often used in averaging things like rates (e.g., the average travel speed given a duration of several trips).The weighted harmonic mean is used in finance to average multiples like the price-earnings ratio because it gives equal weight to each data point. Using a weighted arithmetic mean to average these ratios would give greater weight to high data points than low data points because price-earnings ratios aren't price-normalized while the earnings are equalized.
Some practitioners, including Toby Tatum, have stated that that weighted harmonic mean is the appropriate averaging formula when all of the numerators and denominators in an array of ratios are different.
Q: Can you provide an example of computing the average (mean), harmonic mean, and weighted harmonic mean?
A: Below is an example of computing the mean, harmonic mean, and weighted harmonic mean using a set of comparable companies:
Comps | Selling Price | Cash Flow | SP/CF Multiple | |||
A | $365,842 | $136,508 | 2.7 | |||
B | $258,951 | $159,876 | 1.6 | |||
C | $753,159 | $258,963 | 2.9 | |||
D | $589,122 | $101,698 | 5.8 | |||
Average (mean) = (2.7 + 1.6 + 2.9 + 5.8) ÷ 4 = 3.3 | ||||||
Excel function is =AVERAGE | ||||||
Harmonic mean = 4 ÷ ((1 ÷ 2.7) + (1 ÷ 1.6) + (1 ÷ 2.9) + (1 ÷ 5.8)) = 2.7 | ||||||
Excel function is =HARMEAN | ||||||
Weighted harmonic mean = ($365,842 + $258,951 + $753,159 + $589,122) ÷ (($365,842 ÷ 2.7) + ($258,951 ÷ 1.6) + ($753,159 ÷ 2.9) + ($589,122 ÷ 5.8) = 3.0 | ||||||
There is no Excel function | ||||||
Now, let’s take a look at another example and see how the averages change if our fourth company, Company D, becomes a greater outlier:
Comps | Selling Price | Cash Flow | SP/CF Multiple | |
A | $365,842 | $136,508 | 2.7 | |
B | $258,951 | $159,876 | 1.6 | |
C | $753,159 | $258,963 | 2.9 | |
D | $589,122 | $55,698 | 10.6 | |
Average (mean) = (2.7 + 1.6 + 2.9 + 10.6) ÷ 4 = 4.4 | ||||
Harmonic mean = 4 ÷ ((1 ÷ 2.7) + (1 ÷ 1.6) + (1 ÷ 2.9) + (1 ÷ 10.6)) = 2.8 | ||||
Weighted harmonic mean = ($365,842 + $258,951 + $753,159 + $589,122) ÷ (($365,842 ÷ 2.7) + ($258,951 ÷ 1.6) + ($753,159 ÷ 2.9) + ($589,122 ÷ 10.6) = 3.2 | ||||
Q: Can you provide another example of the arithmetic average (mean), harmonic mean, and weighted harmonic mean?
A: The below paraphrases examples provided by Toward Data Science and The Chemical Statistician.
Consider taking car trip where you drive for 240 miles at 2 different speeds:
- 60 miles/hour for 120 miles
- 40 miles/hour for another 120 miles
You may intuitively apply the arithmetic average for this trip and conclude the average speed is 50 miles/hour: (60 mph + 40 mph) ÷ 2 = 50.
But consider again: because you travelled faster in one direction, you covered those 120 miles quicker and spent less time overall traveling at that speed, so your average rate of travel across your entire trip’s duration is not the middle point between 60 mph and 40 mph, it should be closer to 40 mph because you spent longer traveling at that speed.
The average speed for your trip (the harmonic mean) is:
Average speed = 2 ÷ ((1 ÷ 60) + (1 ÷ 40)) = 48 miles/hour
Notice that the speed for your 2 trips has equal weight in the calculation of the harmonic mean – this is valid because of the equal distance travelled at the 2 speeds. If the distances you traveled were not equal, you would then use a weighted harmonic mean instead.
Now, consider you take a car trip where you drive 240 miles at 2 different speeds and for 2 different distances:
- 60 miles/hour for 100 miles
- 40 miles/hour for another 140 miles
Then the weighted harmonic mean of your speeds (i.e. the average speed of your whole trip) is:
Average speed = (100 + 140) ÷ ((100 ÷ 60) + (140 ÷ 40)) = 46.45 miles/hour
Q: Would you please explain the "coefficient of variation" and how we should utilize and interpret each calculation?
A: The coefficient of variation = standard deviation/mean (the mean is also known as the average).
The coefficient of variation is a measure of dispersion around the mean (average).
The theory is that the valuation multiples with the lowest coefficient of variation are those with the least dispersion around their respective means and may be the better indicators of value. The value derived using these valuation multiples may be weighted more heavily than those with larger coefficient of variations.
Q: Can I use public company data to value a private company?
A: Yes, sale details on publicly traded companies (valuation multiples for publicly traded companies can be found in the DealStats database and the FactSet/BVR Control Premium Study) can be used to value a private company. The indicated value utilizing the sale of an entire public company will result in a control value. It normally would not be appropriate to add a control premium. One or more discounts may be appropriate, depending on the valuation assignment. For more details, see The Market Approach to Valuing Businesses by Shannon Pratt (New York: John Wiley & Sons, 2001. p. 39).
Q: Why don't I see my SIC or NAICS code of interest in the search engine's list of SIC or NAICS codes?
A: The website's search engines use the underlying data to create the list of SIC and NAICS codes. If your SIC or NAICS code is not listed in the search engine, this means there are no transactions with that SIC or NAICS code in the database. You may want to search the other databases to see if they have any helpful data or expand your search criteria to include similar SIC or NAICS codes.
Q: Can I print more than one transaction at a time?
A: To print a group of transaction reports, utilize the icon that looks like an orange piece of paper in the upper-left section of the “Data” tab—it is labeled “Batch Transaction Report.” When printing more than a couple of detailed transaction reports, this will save you time by printing all of your selected transaction reports.
Q: I have questions about the “Save” feature. Can you explain that more to me?
A: The “Save” feature allows you to save your work for future use. The “Save” feature will save anything you have done within that session of the FactSet/BVR Control Premium Study, including any search criteria utilized on the “Quick Search” tab and “Search” tab, any fields you have selected or rearranged using the “Display” tab, any sort preferences you have made on the “Sort” tab, and any transactions you have deselected (unchecked) on the “Data” tab.
If you want to save just the view of certain fields and their order, enter the FactSet/BVR Control Premium Study, make your modifications on the “Display” tab, and select “Save.”
If you want to save just your search criteria, enter the FactSet/BVR Control Premium Study, specify your search criteria on the “Quick Search” tab and/or “Search” tab, and select “Save.”
Saving your search criteria, then revisiting it later, will return all new transactions that meet your search criteria. If you only want to see transactions that were available as of your initial search, navigate to the “Search” tab, select the “Live Date” field, choose the operator “Less or Equal,” then specify the date of your search.
All saved information is account-specific (an individual user only has access to his or her own saved displays and searches). If you would like to save a display, field layout, or other customization to be accessible firmwide, we can set your firm up with a portal. Please contact BVR at sales@bvresources.com or 1-503-479-8200, ext. 2.
There is no limit on the amount of saved items you can have, nor do they expire.
You can retrieve a saved search and change any criteria you like, then save the search again using the same name (which saves over the previous saved search), or you can give it a new name (which saves it as a new search). Think of it like an Excel file—you can open, make changes, and then save it, or you can save it with a new name, which saves it as a new file (and leaves your previous file intact).
Q: On the “Search” tab, does the “and” and “or” logic apply to all pieces of criteria specified?
A: Yes. All pieces of criteria on the “Search” tab will be applied using either “and” or “or” criteria, depending on what you select. Regardless of your selection for the specific criteria within the “Search” tab, the criteria between the “Quick Search” tab and the “Search” tab will be applied using “and” logic.
Q: Where can I view my accumulated filters (the various selection/filter criteria I have made)?
A: You can view your entire search/filter criteria on the “Summary” tab. The information on the “Summary” tab can be downloaded using the “Download” tab (click the “Analysis Tabs” options), or you can use the “Copy” feature at the top-right of the “Summary” tab to copy and paste all your information into a Word document or Excel file.
Q: Do you get different transactions if you search by SIC versus NAICS, or does the database “recognize” when you put in an SIC code the associated NAICS codes and includes them as well in your search?
A: Each transaction has both a SIC and corresponding NAICS associated with it. So, you should be able to search by either and receive the same transactions (e.g., if you’re looking for software companies, you could search by SIC 7372 or NAICS 511210 and receive the same transactions).
The one potential exception to this is where the relationship of SIC to NAICS is not one to one (where one SIC could correspond to two NAICS codes or more). In those situations, since the SIC is more general, you will receive more transactions when searching by the SIC code then by the NAICS code, since the NAICS is more specific.
Each transaction has up to three SIC codes and up to three NAICS codes assigned to the target company, depending on the products/services the target business offers. You can choose to search by primary SIC/NAICS only, or by primary, secondary, and tertiary SIC/NAICS.