Butler Pinkerton Calculator—Total Risk Allocator Frequently Asked Questions (FAQs)
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Q: How have Butler and Pinkerton quantified the seemingly unquantifiable when it comes to a company specific risk premium?
A: For more background on the theory, please see our articles on this topic (view articles here). However, the formula, in its most basic form is:
- Company-specific risk premium (CSRP) = (Total Beta – Beta)*Equity risk premium – Size premium.
Note: This formula springs from CAPM theory. If another theory or underlying model is used, such as the Fama French Three Factor Model, then a different formula would result. Equity risk premium is also knows as market risk premium.
Q: How do you derive that formula?
Total Cost of Equity (TCOE) = Risk free rate + Total Beta*Equity risk premium. This equation was developed by Professor Aswatch Damodaran at NYU. We also know that:
TCOE = Risk-free rate + Beta*Equity risk premium + Size premium + CSRP
Solving for the only unknown in the equations leads us to: CSRP = (Total Beta – Beta)*Equity risk premium – Size premium
The BPC, which is dependent upon the CAPM, can also be traced back to the Sharpe ratio, which is a direct measure of reward-to-risk.
Hypothetically, an investor can choose to invest in the market (S&P 500) or hold just one stock and be completely undiversified. For this investor to be ambivalent between the choice of investments, the following formula must hold where “s” stands for stock, “m” for market, SDs = standard deviation of the stock, SDm = the standard deviation of the market, and R represents the appropriate rate of return for a risk-free investment, Rf, or for the stock or the market:
(Rm – Rf)/SDm = (TCOEs – Rf)/SDs
which results in:
TCOEs = Rf + (SDs/SDm)(Rm – Rf)
which should look more familiar as:
TCOEs = Rf + (Total Beta)(Equity risk premium)
If one now knows TCOEs as well as Rs (from a well-diversified portfolio perspective), then the difference, TCOE – Rs, is a known quantity. Let’s call it Delta.
Therefore, Delta = Rf + (SDs/SDm)(Rm – Rf) – (Rf + Beta*(Rm – Rf))
Delta = (SDs/SDm)(Rm – Rf) – Beta*(Rm – Rf)
Delta = (Total Beta)(Rm – Rf) – Beta*(Rm – Rf)
Delta = (Total Beta - Beta)(Rm – Rf)
This equation should look very familiar as the BPC (excluding the additional allocation of the size premium). Delta represents the CSRP or the additional return required to compensate the completely undiversified investor for the incremental risk of holding only one stock in his or her portfolio.
The formula is not controversial. In fact, it has been used in its most basic form before for another application. Please see “Company Stock in Pension Plans: How Costly Is It?” written by Lisa Meulbroek, Ph.D. (Claremont McKenna College) and summarized in the Fall 2008 Edition (Volume 27, No.3) of Business Valuation Review by John J. Stockdale, ASA, CPA/ABV in the article titled, “A Test of DLOM Computational Models."
As stated in the summary article, this model was developed to investigate the cost of holding a single stock in a retirement plan as opposed to a more diversified portfolio. Accordingly, the underlying theory is that the DLOM is the result of being forced to carry extra risk in a single stock over and above that in a portfolio during the period in which the security cannot be sold.
The formula for the model is as follows: DLOM = 1 – (1/(1+R)^N) where “R” is the incremental rate of return from holding a single stock instead of a portfolio.
“R” is also defined as (SDs/SDm – beta) x equity risk premium where SDs represents the standard deviation of the return of the stock and SDm represents the standard deviation of the return of the market.
“N” is the period of time the investor is forced to hold the stock before being able to diversify.
“R” should look very familiar. In fact, we have called this the modified BPC in other writings (Please see Combined Company-Specific Risk/Size Premium Sample Template under Subscriber Services). SDs/SDm is Total Beta. Therefore, “R” = (Total Beta – beta) x equity risk premium. The BPC further breaks down total risk between CSR and size with the following formula:
CSRP = (Total Beta – Beta)*Equity risk premium – Size premium.
Interestingly, the summary article mentions some limitations to the Meulbroek Model which, obviously, can be applied to the BPC. Let’s see how the BPC handles these indirect criticisms:
- The computation of beta for an individual company using historical price and return data has certain difficulties. One problem is that beta may not be stable over time so that beta should not be determined at one particular time but should be studied over a period of time.
Subscribers to the Calculator can rather quickly calculate a range of betas from one year to five years if they desire. Moreover, we recommend that subscribers calculate betas for all five trading days of the week over the appropriate look-back period to better estimate the stock’s “true” beta. If you subscribe to commercial sources (print) of beta and do not use different assumptions you have no idea the sensitivity of your beta determination.
- In addition, beta computations based solely on fluctuations of return may not be statistically significant. That is, a regression analysis may indicate that there is a poor correlation between the company rate of return and the rate of return of the market. This situation commonly arises when computing beta.
We have programmed into the Calculator an indication of the quality of the regression using the t-stat. We recommend that if the resulting statistical confidence is less than 80%, then it is too subjective to allocate the risk. In these instances, we merely key in on Total Beta and the TCOE.
- This model is based on the assumption that beta is a meaningful statistic.
The TCOE side of the Calculator is based on Total Beta being a meaningful statistic. Prior to Mr. Kasper’s incorrect and misguided criticisms, no one had ever questioned the viability of Total Beta. The BPC or CSRP side of the Calculator is based on the assumption that beta is a meaningful statistic. However, we believe we have given subscribers useful tools and recommendations to make this determination on a company by company basis (t-stat hurdle, the ability to analyze all five trading days of the week and the ability to look over different look-back periods).
Interestingly, all size premium studies (Morningstar/Ibbotson and Duff & Phelps) and industry risk premiums as calculated by Morningstar/Ibbotson also rely on the implicit assumption that their betas are meaningful statistics. The Calculator allows one to look behind the curtain so-to-speak to make a determination on this issue as opposed to these other data sources that we as a community have collectively adopted as non-problematic (with respect to their beta calculations). The CAPM, despite its faults, is not going away and remains today the most popular cost of capital model.
Q: What is Total Beta?
- Total Beta equals either one of the following:
- Beta/R or (Note: We remove the correlation coefficient from beta)
- The standard deviation of the stock/standard deviation of the market. (See definitions below)
- Note: Dividing Beta by R transforms systematic (market) risk into total risk, meaning that Total Beta captures 100% of a stock’s risk (if it traded in an efficient market). Beta, on the other hand, may only pick a very small percentage of a stock’s total risk.
- Total risk includes the risk-free rate, Beta*Equity risk premium, the size premium and any CSRP.
- It measures risk from a stand-alone perspective, rather than from a well-diversified portfolio perspective, which is the reference point for Beta. A stand-alone perspective is the reference point we value privately-held firms from most of the time. For a deviation of this assumption, please see FAQ 46i.
- Standard deviation is the appropriate measure of risk for a stand-alone asset, meaning if the stock is the only asset in your portfolio.
- Total Beta measures the guideline comparable’s standard deviation relative to the market’s standard deviation. It is a relative volatility measure. Ironically, many appraisers have thought that Beta was a relative volatility measure when, in fact, Total Beta captured this relationship.
- Total Beta will almost always be greater than 1.0 since the volatility of any one stock (with rare exceptions) has been greater than the volatility of a broad based index.
Q: How do you derive the Total Beta calculation?
- Beta = Covariance (s,m)/Variance (m); where “s” stands for stock and “m” stands for market
- Beta = (Cov(s,m)/(SDs)(SDm))*SDs/SDm
- R = Cov(s,m)/(SDs)(SDm)
- Beta = R*SDs/SDm.
- Thus, Total Beta = Beta/R = SDs/SDm.
Q: Has the technique been peer-reviewed?
A: The calculation is dependent upon the CAPM, which, obviously, has been subject to significant academic debate. The calculation is also dependent upon a relatively new metric called Total Beta. Professor Aswath Damodaran developed the Total Beta calculation in the late 1990s (or at least the equation: TCOE = risk-free rate + Total beta*ERP). We have subsequently learned that total beta was introduced in 1981. Please see “The Beta Quotient: A New Measure of Portfolio Risk” by Robert C. Camp and Arthur A. Eubank, Jr. published in the Journal of Portfolio Management. (Note: Total Beta was referred to as the Beta Quotient in the article). Damodaran published a textbook in 2002 titled Investment Valuation, 2nd edition, which references the Total Beta technique in Chapter 24. Numerous other finance professors refer to Total Beta and other publications reference Total Beta.
We have published numerous articles in business valuation journals related to this technique, including one e-book in collaboration with Morningstar. (View many of the articles here and testimonials by PhDs and other highly qualified appraisers here.)
We have a standing invitation to the business valuation community to critique the calculation. Since 2007, we have spoken at numerous regional and/or national business valuation conferences (ASA, AICPA, NACVA, IBA) and/or national webinars as well as one international conference (CICBV). To date, we have not received any materially relevant criticism related to the calculation of Total Beta and have not heard any feedback which would render the BPC inferior to the purely subjective factor models. In fact, at each conference/webinar after initial skepticism and in-depth question and answer sessions, we left with the impression that most participants thought the technique was sound and superior to the traditional factor models.
The main criticism today is the technique is subjective. Our simple response is relative to what – the purely subjective factor models? Remember, this technique uses empirical, market-driven evidence. Our industry has been severely criticized for our use of the traditional factor models. “To judges,the company specific risk premium often seems like the device experts employ to bring their final results into line with their clients’ objectives, when other valuation inputs fail to do the trick.” Delaware Open MRI Radiology Associates v. Howard B. Kessler, et al. We believe the BPC effectively eliminates this criticism.
To properly use the BPC, be able to defend and support your assumptions/inputs into the calculations – no different than any other technique. The BPC depends on the CAPM. If you accept the CAPM, and by extension the build-up method, then the math is irrefutable.
While a limited number of appraisers have their concerns related to the technique (specifically related to the subjectivity of beta), other noteworthy appraisers, as well as PhDs, have expressed public praise and adoption of the technique (Please see testimonials link). For those appraisers who have concerns about the subjectivity of beta, they should also have these same concerns when applying any size premium or industry risk premium as these data points also rely upon beta and the CAPM. Moreover, total beta is generally less volatile than beta – over the same look-back period and/or over time.
For more information on the peer-review question, please see the "Winter 2008 BVReview Rebuttal" and the “Academic Commentary on Winter 2008BVReview Article” under the articles link, as we covered this issue in great detail there. In summary, total beta and the BPC have been peer-reviewed. Appraisers can use the Calculator with confidence.
Q: Has the technique been accepted by the Courts?
A: The BPC and Peter Butler (Valtrend) passed a Daubert challenge in mid-December 2010 in Alamar Ranch, LLC v. County of Boise, a decision by the United States District Court (Idaho)(Civil Case No. 1:09-cv-00004 BLW). In response to the challenge, Peter submitted sworn testimony listing the numerous instances of very favorable and independent peer comments regarding the BPC (see the testimonial page). As Peter also mentioned, he and Keith Pinkerton have spoken on the BPC on more than twenty-five different occasions and have written numerous articles in all of the U.S. professional business valuation journals as well as in one international journal. Hence, the technique has been subject to peer review; it’s been tested and gained acceptance among the professional BV community as well as the courts. In the Alamar Ranch case, Peter also described the positive developments in Mr. Skorheim’s case (see below). Trial testimony also highlighted the numerous positive endorsements of the BPC – some from Ph.D.s and finance professors - that recognize the model’s central technique stems from modern portfolio theory and is theoretically sound.
- Bankruptcy court says BPC is ‘Daubert-proof’ (BVWire Issue #111-2):
In Village at Camp Bowie I, No. 10-45097 (Bankr. N.D. Tex.)(August 4, 2011), the debtor planned to build a southwest Texas urban development in 2006—but by 2010, it defaulted on over $32 million in notes and filed for bankruptcy. A real estate equity group purchased the notes at an auction (and at a discount) and then objected to the debtor’s proposed reorganization plan in favor of its own ownership. To assess the debtor’s plan, the U.S. Bankruptcy court heard from several appraisal experts, including Paul French (Lain Faulkner & Co.), who estimated the required interest rate to return the present value of the equity investors’ claims.
Starting with the five-year T-bill rate of 1.71% as his risk-free rate, French adjusted it to account for specific risk factors associated with the debtor, the property, and the loan agreements, and then adjusted it further for each tranche (senior, junior, and equity) to reach “final” rates, as applied to two different appraisals of the property, of 6.25% and 7.75%. Without detailing the data from which French derived his numbers, “suffice it to say that his research was extensive and well-planned,” the court noted, adding that “his opinions are defensible under the most rigorous Daubert analysis.”
To reach his opinions, French used the Butler Pinkerton Calculator—Total Risk Calculator (BPC). In addition to the court’s approving his methodology, his “BPC calculations, along with all of my work, were entered into evidence without objections,” French tells the ’Wire. After making its own adjustments for some of French’s assumptions, the court ultimately concluded that it would accept a “cramdown” rate between 6.27% and 6.59%.
- James Skorheim, JD, CPA/ABV/CFF, CFE, CVA, CrFA used the Butler Pinkerton Calculator to calculate the appropriate discount rate for loss of goodwill value in the following case: LB4 Fish, LLC v. Developers Diversified Realty Corporation, et al. While the case was favorably settled in his client’s favor in California’s Second Appellate Division, the Court did not specifically discuss the Butler Pinkerton Calculator. However, Mr. Skorheim’s lost profit analysis and valuation were sustained after substantial consideration by the Court.
We also have heard other appraisers/subscribers comment it was one of the reasons that lead to a favorable settlement for their clients. Butler and Pinkerton have used and are currently using the technique on a number of litigated matters. We look forward to showing the technique in more court-room settings. Remember, the alternative is to use completely subjective factor models which have no empirical support.
Q: Traditional methods that "quantify" CSRPs, if well documented and supported, have been accepted by the Courts. Why should we use this technique now?
A: When the Courts accepted these “calculations”, no empirical evidence existed. With the introduction of this technique, this data now exists. Wouldn’t it be well advised to use empirical data, if it exists? We believe that if you do not use empirical data that exists, then your explanation as to why you chose to ignore it better be compelling. We do not believe that an appraiser’s experience and judgment alone are good enough any more. We, however, recognize that this technique might not be appropriate for all valuations.
Q: How do your I pass along the cost of this program to my clients?
A: Some of our subscribers impose a separate resource/technology charge for every valuation assignment. They know approximately how many appraisals they do per year and divide that number into the annual costs of the service, thereby passing along the resource (or technology) charges.
Q: The capital asset pricing model (CAPM) has many unrealistic assumptions. How does this impact this technique?
A: Those same assumptions are used in the calculation of Total Beta. However, Total Beta describes 100% of the guideline comparables’ total risk, whereas Beta (CAPM) may only explain 1%, or less, of a stock’s total risk.
Remember, the CAPM is a Nobel-Prize winning theory. Despite its faults, it is the most popular cost of capital model in practical use today. Other models, such as the Fama French 3-factor, also have their limitations and, for whatever reason, are not as popular as the CAPM. Therefore, the Calculator will continue to use the CAPM as its underlying theory.
While the technique violates CAPM (You can see that merely by the replacement of beta with total beta in the TCOE equation), it does not violate the financial theory behind the CAPM. The TCOE equation prices total risk (standard deviation). Often times, total risk is priced for privately-held companies. Why else have we added a CSRP in the first place? On the other hand, we know that total risk (standard deviation) is not priced for publicly-traded stocks since they are held in portfolios.
Also, remember that every privately-held company violates CAPM. CAPM indicates that we should all hold the market portfolio. Some people (such as private business owners) choose not to hold the market portfolio and endure more risk in pursuit of a potentially higher return.
Q: Can you use this technique with the build-up approach?
A: Even though we believe the CAPM and the build-up approach are essentially the same thing, we believe this technique is better suited with the CAPM. In the build-up approach, one assumes the Beta is 1.0 and then generally makes an adjustment for the industry premium. Whereas in the CAPM approach, one calculates Betas for guideline companies, which includes the industry premium when multiplied by the equity risk premium – a more specific calculation, in our opinion. Thus, even prior to this technique we were partial to the CAPM. After the introduction of this technique, we continue to recommend that you use the CAPM, instead of the build-up approach.
First, to calculate Total Beta and the CSRPs, you need to calculate Beta, so why not use it? You can calculate Beta up to your exact date of value, whereas Ibbotson’s industry risk premium may be a bit stale. Note: in a matter of seconds, this Calculator will calculate all of these metrics.
Second, if you use the build-up approach with this technique, you are comparing apples to oranges. For example, if you calculate CSRPs from guideline companies, then select an industry risk premium – an industry average of systematic risk, instead of the guideline companies’ actual Beta, you have no idea if the systematic risk of the industry average closely matches the industry risk of your specific guideline companies – which you used to calculate their CSRPs.
Having noted the criticisms with the build-up method above, should you still choose to use the build-up approach over the CAPM with this technique, as always be prepared to defend each of the components of the cost of equity. We believe strongly that this technique in combination with the build-up approach, is still superior to merely relying upon purely subjective factor models.
Moreover, one always has the option of just comparing the TCOE among guideline benchmarks in relation to their subject company. If one focuses on this level of risk, keep in mind that one must analyze all relative risk factors, not just company-specific risk factors. Calculation of CSRPs is an added value of the Calculator.
Q: Beta and, therefore Total Beta, depend on various assumptions, such as the selection of the market proxy, the frequency of measurement (daily, weekly, monthly, etc.) and the duration of the measurement period (3 years or 5 years, for example). One must also select the appropriate equity risk premium. Does this subjectivity adversely impact this technique?
A: We do not believe it does. All of these assumptions are required to calculate Beta, and we still use the CAPM. Therefore, one should not exclude this technique either. Remember, this technique captures 100% of a stock’s total risk, whereas Beta may only capture a very small component of total risk. Moreover, our alternatives are to rely on purely-subjective factor models with no empirical support.
If you are consistent within every engagement, then this will help mitigate some of these subjective issues. Let’s not forget that risks change and the pricing of risks change every day. This technique is no more subjective than the risk it attempts to measure. We believe this is one big benefit of the Calculator: The ability to see the trends in the pricing of risk.
Q: Is this a purely robotic technique?
A: Absolutely not. The appraiser is still required to use judgment and compare/contrast the indications of TCOEs and/or CSRPs from publicly-traded stock to his or her subject company.
We recommend reviewing a guideline publicly-traded stock’s SEC filings to analyze CSR factors to compare and contrast with your subject company. If one only calculates TCOE, then all risk factors must be considered and compared to appropriately quantify total risk for your subject company.
Q: Is this technique appropriate to consider for all valuation engagements?
A: Yes, we think it is. However, if a public company is purchasing a private company, one could make the argument that the public company may not care about the private company’s CSR – at least according to traditional financial theory. If a company is going public, one could also make the argument that CSR should not be priced. However, there is recent research to indicate that CSR cannot be fully diversified away even for publicly-traded stock.
We have used the technique, but then excluded its findings from further consideration. For example, this technique might not be appropriate for early-stage companies, if the publicly-traded benchmarks are significantly more established and mature. If this happened to be the case, we believe one would still gain some benefit by running the calculations – by understanding the potential “floor” for their subject company’s TCOE and/or CSRP.
Q: Do you recommend using a minimum number of guidelines to help select a CSRP for a privately-held company?
A: It seems that the best answer is the more, the better. However, as pointed out above, even one “comparable” can give you very valuable information.
Q: In your practice, have you "thrown-out" all of the old techniques such as the Black/Green model or other factor models?
A: No, absolutely not. These older techniques are very good in getting appraisers to consider the factors that comprise TCOE and/or CSR. However, we believe it is more appropriate to use them with this technique. We now have empirical data to better support our TCOE and/or CSRP conclusions.
Q: What data do I need to enter or select to allow the Calculator to quantify TCOE and/or CSRP for each guideline comparable?
- Risk-free rate
- Equity risk premium
- Ticker symbol
- Size premium
- Length of the look-back period
- Market proxy
A: We generally use a long term rate, such as the 20-year treasury rate to be consistent with a long-term valuation perspective. However, whatever rate you choose, be able to support it. You can find interest rates at the Federal Reserve Statistical Release website or by using the BVR Risk-Free Rate Lookup tool.
A: This is up to you – whether from Ibbotson’s Stock, Bonds, Bills, & Inflation Yearbook (ex-post), from a supply-side perspective (ex-post), from a forward-looking perspective (ex-ante) or from a combination.
Q: What are the minimum and maximum values I can enter for the risk-free rate and the equity risk premium?
- Risk-free rate: The minimum is 2% and maximum is 9%.
- Equity risk premium: The minimum is 3% and the maximum is 10%.
Q: Is the calculation of a CSRP and TCOE dependent on the Equity risk premium?
A: Yes, they are positively correlated. The higher the expected equity risk premium, the higher the TCOE and the CSRP. This is based on the assumption that company specific risk is priced the same as the market prices risk (See Sharpe ratio in FAQ 2d).
If market participants expect the stock market to return higher rates of return, it stands to reason that individual stocks’ required rate of return and expected volatilitywill also increase. Risk and return are linearly related.
Q: How do I select my guideline comparable companies?
A: One should use the same thought process as one uses in the guideline publicly-traded company method. First, focus on the relevant industry. Then, try to narrow it down based on all the typical metrics of observation. Keep in mind; however, this is the income approach to valuation – not the market approach. As such, we can foresee using more companies in this method than in the market approach. After all, company-specific risk is just that – company-specific. Any data is better than no data, and more data is better than less data. You can add up to 12 comparable companies at any one time.
We have added a Canadian index (S&P/TSX Composite) and access to Canadian publicly-traded companies as well as a German index (CDAX). If you are valuing a privately-held Canadian company, then we recommend that you run the Calculator with the Canadian index and Canadian guidelines. The same goes for German companies. Similarly, if you are valuing a U.S. privately-held company, then we recommend only using U.S. data. Otherwise, you will be mixing rates of return from different markets and different currencies.
If using Canadian tickers enter .TSE after the ticker; if using a German ticker, then enter .DE after the ticker.
Q: Where do I go to look up my guideline comparable companies’ ticker symbols?
A: While not an exhaustive list, the following are a few of the sources we have used:
- If you visit Yahoo! Finance, you can select the “Symbol Lookup” option towards the top of the screen. Simply enter the company’s name and click “Look Up.” Please note that the calculator contains a link to Yahoo! Finance in order to look up tickers.
- The respective company’s Form 10-K.
- The Wall Street Journal.
Q: How do I determine the Size premium for each comparable company?
A: There are four options: 1) One could use Morningstar/Ibbotson's size premiums; or 2) The Duff & Phelps Risk Premium Report data, as appropriate. One would need to know the market capitalization of the comparable company before referencing either of one of these databases (which can be found at Yahoo! Finance). 3) While subjective, one could calculate the guidelines’ size premium themselves. Remember, the size premium is just the actual return minus the expected return. The reason this is subjective is that each analyst probably will have a different estimate of the expected return over the look-back period. Even though this approach is subjective, it is intuitively appealing from the standpoint that the data would all be guideline specific. When we introduce data from either Morningstar/Ibbotson or Duff & Phelps, the data is no longer guideline specific (Please see FAQ #43 below for more details). 4) This last option eliminates any criticism related to a) introducing non-specific guideline information into the formula and b) the subjectivity of calculating size premiums for each guideline yourself. Under this approach, merely plug in 0% for the size premium. The result would be a combined CSRP:SP guideline specific output. (Please see FAQ below for more details).
Q: How do I determine the Size premium for each comparable company?
A: There are four options: 1) One could use Morningstar/Ibbotson's size premiums; or 2) The Duff & Phelps Risk Premium Report data, as appropriate. One would need to know the market capitalization of the comparable company before referencing either of one of these databases (which can be found at Yahoo! Finance). 3) While subjective, one could calculate the guidelines’ size premium themselves. Remember, the size premium is just the actual return minus the expected return. The reason this is subjective is that each analyst probably will have a different estimate of the expected return over the look-back period. Even though this approach is subjective, it is intuitively appealing from the standpoint that the data would all be guideline specific. When we introduce data from either Morningstar/Ibbotson or Duff & Phelps, the data is no longer guideline specific (Please see FAQ #43 below for more details). 4) This last option eliminates any criticism related to a) introducing non-specific guideline information into the formula and b) the subjectivity of calculating size premiums for each guideline yourself. Under this approach, merely plug in 0% for the size premium. The result would be a combined CSRP:SP guideline specific output. (Please see FAQ #45 below for more details).
Q: How long should the look-back period be?
A: In general, we use 5 years to be somewhat consistent with many commercial sources that calculate Beta. The Calculator has a maximum of 261 data points, or observations. If the frequency is weekly, this correlates into 5 years worth of data. However, if the analyst is aware of changes in the guidelines between year 5 and year 3, for example, which potentially make the longer look-back period problematic for comparison purposes, then the appraiser should select only three years of data. In summary, the choice of the length of the look-back period is up to the appraiser. We believe this is another benefit of the Calculator. Previously, if you relied upon a commercialized source for your Beta calculations, you were beholden to those assumptions whether they were appropriate for your valuation or not. We believe this Calculator empowers analysts to make decisions. Just be able to defend and support your assumptions/decisions, which is no different than any other technique.
However, often times, guideline companies will not have historical trading data covering this number of years, and you will have to make do with what is available. The Calculator will handle gaps in the data (for more information, see question 30).
We are aware of a leading investment textbook which recommends at least 3 years worth of weekly stock price returns to calculate Beta.
Q: What proxy for the market should I use?
A:We often use the S&P 500 (this is the Calculator’s default) since this is a very common measure of the U.S. stock market’s performance. In theory, any proxy can be used. However, practically-speaking, one should use a broad market index. Other options that this Calculator allows are the the Dow Jones Wilshire 5000, the NYSE Composite, the Toronto Stock Exchange (S&P 500/TSX) for Canadian valuations, and the CDAX for German valuations.
If you are valuing a foreign company other than a Canadian or German company, you will want to use an appropriate foreign stock market index. Currently, this is not an automatic look-up option, however, you can select the cut/paste method and paste this data in, if required.
Q: What is the source of the guideline comparables’ historical stock price information?
A: Alpha Vantage. Specifically, the Calculator obtains data from the adjusted closing stock prices as reported by Alpha Vantage. The adjusted closing prices are adjusted for stock splits. Alternatively, the user has the ability of manually copying and pasting closing stock prices from Yahoo! Finance, Google Finance, or any other source.
Q: What is the frequency of stock price data that you obtain?
A: We use trading data in weekly steps, once again, to be somewhat consistent with some other commercial sources (Value Line, for example) that calculate Beta. While a monthly look-back is popular, there are generally 30 days in a month. Given the variability in beta, we think a weekly frequency measure is most appropriate and a better time-saver. One can compare the variability by only looking at the five trading days in the week, as opposed to 30 days in any given month.
You, however, can cut and paste data if you desire. Remember, the lesser the frequency, the longer your historical period should be to ensure a robust sample, all else being equal. One makes the selection of automatic lookup, or manual copy and paste from another source, in Step 2 of the calculation.
Q: What pricing data does the Calculator obtain from Alpha Vantage?
A: The Calculator pulls weekly, adjusted closing stock price data. Adjusted means adjusted for stock splits. The Calculator reports the closing price on the “effective date” first, and then the closing price seven days prior, and so forth for the number of weeks in the “look-back period.” If there was no trading for the stock on the day when the Calculator is searching (e.g. Christmas day), the Calculator will pull the closing price for the prior day.
Example: If a user selected an “effective date” of 7/18/07, the Calculator would report the adjusted closing stock price for 7/18/07 (a Wednesday) and would provide the historical adjusted closing prices on a weekly basis for length of the “look-back period.” When the Calculator gets to 7/4/07 (a Wednesday, but a holiday, so no trading), it will pull the adjusted closing price for 7/3/07 (a Tuesday). After that, the Calculator will return to pulling the adjusted closing stock prices each Wednesday for the length of the “look-back period.”
Q: What if there is a gap in the historical trading prices for one (or more) of my guideline comparable companies (e.g. the stock didn’t trade for several weeks)?
A: If there is a gap in the historical trading prices for one (or more) of your comparable companies, the Calculator will fill in these weeks with the last historical closing price (essentially reporting no change in price, an assumption of zero return for these periods).
If gaps exist in trading, the user will be notified via a pop-up window. The pop-up window will ask the user if he or she wants to continue with the calculation.
Q: The Calculator automatically obtains adjusted closing stock price data, meaning adjusted for splits, but not adjusted for dividends. Is this a concern?
A: If the stock had no dividends, the CSRP and TCOE calculations would be the same, all else being equal.
If the stock distributes dividends, then “adjusted for dividends closing prices” will lead to different conclusions than “non-adjusted for dividends closing prices”. From our experience, since generally dividends only occur once per quarter, the differences in the calculations are immaterial. Moreover, the differences do not occur in any one direction. For example, non-adjusted for dividend data may lead to a larger TCOE and/or CSRP than adjusted for dividend data for one stock, but lead to the opposite conclusions for another stock.
You can compare the calculations by pulling the non-adjusted dividend closing prices from Alpha Vantage and then manually cutting/pasting the adjusted dividend closing prices from Yahoo! Finance.
BVR is providing adjusted closing values as a service to the user. BVR gets this data from a service provider, Alpha Vantage, that makes no warranties as to its accuracy. Users may want to verify with another source the accuracy of the adjusted closing values displayed in the Calculator results. Keep in mind, this data is adjusted for splits and not adjusted for dividends. As an alternative, the user may want to provide the data themselves in Step 1.
If you use the Calculator to calculate TCOEs and/or CSRPs for REITs, we recommend you use the cut/paste function from Yahoo! Finance to pull adjusted for dividends closing prices since REITs’ rates of return are so dependent upon dividends.
A: No, we recommend looking at all days of the week (Monday – Friday). When you pull stock price data for an effective date such as a Tuesday, for example, as opposed to a Monday, it is much more than one more day of trading. It actually represents 261 days worth of different data for a five-year look-back. For instance, if your effective date is a Monday, the Calculator will pull 261 Mondays (for five years) of closing prices and similarly for Tuesdays. There may be (material) differences in the outputs.
Before this Calculator, analysts may not have considered just how sensitive the calculation of beta might be to various inputs. When you subscribe to printed commercial beta sources, you are at the publishers’ mercy for the accuracy and lack of sensitivity of the data. Here, you can control and understand the reasons behind each input and see the sensitivity, or lack thereof, in your own calculations
Thus, we recommend that you look at all days of the week (Monday – Friday, making sure not to pull pricing after your date of value) and then calculate an average (or median) of the benchmark CSRPs (for those which are statistically significant) and TCOEs, for example.
Generally, what you will find is that total betas are much more stable than betas (over time and during the same look-back period). This has to do with the higher variability in the correlation coefficient of many betas. This is one reason why some appraisers like to key in on Total Beta and TCOE.
Q: I notice that, after inputting my ticker, the stock prices are populated but the company name is not populated. Why is this?A: The company name is not automatically populated using the Alpha Vantage service. If you would like to include the company name in your export, you can populate the company name by typing into the corresponding field.
Q: What happens if Alpha Vantage experiences a glitch on its web-site and we are not able to upload guideline historical stock price and/or index data?
A: While this may never occur, we have programmed the Calculator to be able to use a copy and paste function to allow the user to still populate the input page. Other (although certainly not a complete list) potential sources of historical stock price information are Yahoo! Finance and Google Finance.
Under this, hopefully, unlikely event, the user would be responsible for appropriately populating the input page.
Q: If I select the cut and paste method, how do I retrieve the historical stock prices for my guideline comparable companies and input them into the Calculator?
A: If one were to visit Yahoo! Finance, for example, they could search for their guideline comparable company by entering the ticker symbol into the appropriate box on the website. The user can then select the option to search for historical prices. The user would need to enter the “look-up period” (date range) for the historical prices (with the end date being the “effective date”). The user would also want to ensure that they select “weekly” returns. When the results for the historical prices appear, the user will want to select the “Download to Spreadsheet” option at the bottom of the page. Once the spreadsheet of historical prices has been opened, the user will want to select the “copy” function for historical prices and then will want to use the “paste” function to paste them into the Calculator. This would be repeated for each guideline comparable company.
The Calculator’s weekly pricing will (most of the time) be different than Yahoo’s pricing. Therefore, appraisers must be careful when using the Calculator to compare results between the two pricing sources. For example, the Calculator will report (and use) weekly closing prices for every Thursday for a given benchmark if the effective date is a Thursday (not accounting for any holidays). However, Yahoo will pull the latest Thursday’s close and then report the Friday’s close the week before and for every Friday before that for the length of the look-back period. Essentially, Yahoo reports the closing prices on Friday for any search performed with a weekly frequency – regardless of the effective date. If your goal is to match Yahoo and the Calculator’s pricing service, enter an effective date of Friday into the Calculator. Remember, if the stock pays a dividend, the pricing will be slightly different between the two sources.
Q: Do these guideline comparables have to exactly match the guideline comparables in my market approach to valuation?
A: No, this technique is separate and distinct from the market approach. We believe that CSR is just that – company-specific. Thus, we perceive the possibility of having more “comparables” to help quantify a CSRP than you use in the guideline publicly-traded method under the market approach.
Q: What do you do if you do not consider any guideline companies as comparables?
A: In the past this has not stopped you from “quantifying” TCOE and/or the CSRP. It should not stop you now. Thus, we believe this technique is appropriate to consider in all valuations that use the income approach to valuation. It is up to the analyst to appropriately weight the indications of value.
Alternatives to quantify company-specific risk (CSR) lack any empirical data. The BPC supplies empirical data. So, the choice is use the BPC with maybe “not-so great” guidelines or use the various factor models alone, for example, which do not have any empirical data.
Any time we appraisers use the income approach, as you well know, we generally get our discount rate inputs (beta, equity risk premium, size premium, and industry premium) from publicly-traded stock data. We do not throw out the income approach because there are no good guideline companies. Thus in our opinion, we should not throw out the BPC if there are no “good” guideline companies. We calculate TCOE and/or the CSRP from the same publicly-traded data.
We have used the microbrewery industry as an example in our articles, so we will use it again to make our point. Let’s say hypothetically, we have a small private brewer and we believe it has less CSR than the smallest indication of CSR of the guideline companies equal to 6%. We cannot think of a good reason not to use Anheuser Busch (AB) when it traded as a “comparable” to give us a better indication of company-specific risk for our private brewer. We are confident that our small private brewer will not have a company-specific risk premium (CSRP) less than AB at 3.5%, for example. Thus, AB has given us guidance on a CSRP for our small, private brewer. We feel confident that our subject company’s CSRP is now between 3.5% and 6.0%, for example – even though we would never consider using it in the market approach. So, we believe that since this is the income approach to value, and that company-specific risk is just that – company-specific - that you can widen your search for guidelines.
Having said all of that, we do want “good” guidelines with the BPC. Good, however, is relative and varies from engagement to engagement. For example in a recent engagement, we valued a subject company which had significant customer concentration risk (Two customers represented almost 90% of the firm’s revenues). We specifically searched for “guidelines” in the particular industry as well as for guidelines outside the industry, keying in on public companies which reported significant sales concentration risks.
Q: Some appraisers believe that the public stock market and the market for privately-held companies are different “animals” and do not feel comfortable using public stock to value private companies. What is your response to this?
A: We have a hard time accepting this viewpoint. The same economic and industry forces act upon companies whether they are public or private. Business owners, as well as prospective business owners, have a choice to invest in private companies or to invest in the stock market. Therefore, the law of substitution (as well as revenue Ruling 59-60!) requires us to look at rates of return available from alternative investments. This technique does just that.
It is always up to the analyst in any particular engagement to weight the relative indications of value accordingly.
Q: What do the outputs of the Calculator mean? (Please see other references for more detailed definitions)
- Standard deviation: The positive square root of the variance. This is the standard statistical measure of the spread of the sample. The sample that we recommend is the weekly stock price returns of your guideline comparables. Standard deviation is the accepted measure of risk for stand-alone assets – generally, the perspective to value privately-held companies.
- Levered beta: A measure of systematic risk. It measures the sensitivity of a security’s return to movements in the underlying market (S&P 500, for example). According to traditional financial theory for a well-diversified portfolio, which is under constant debate, this is the only measure of risk we care about. Thus, if a stock’s Beta is 1.05, we would expect the stock to be up 1.05% when the market is up 1%, and down 1.05% when the market is down 1%.
- Correlation coefficient (R): A standardized statistical measure of the correlation between two variables. It measures the degree of linear association between two variables, in this case – the guideline comparables’ stock price returns with the returns of the market. This measure always falls between -1.0 (perfect negative linear association) and 1.0 (perfect positive linear association). If R is 0, then no relationship exists. A low correlation coefficient may mask significant volatility of the guideline. Thus a very low beta may have a commensurate very high total beta.
- Total cost of equity (TCOE): TCOE is the comparables’ required rate of return if the security was a stand-alone asset – not part of a well-diversified portfolio. The more the TCOE is allocated to size (i.e. using a larger size premium), the lower the CSRP and vice/versa.
TCOE = Risk-free rate + Total Beta*Equity risk premium or
TCOE = Risk-free rate + Beta*Equity risk premium + Size premium + CSRP.
- Company-specific risk premium (CSRP): Also known as the unsystematic risk premium or the idiosyncratic risk premium. According to traditional financial theory, this is the risk that, as the name implies is company-specific and, therefore, completely diversifiable in a well-diversified portfolio. Note: CSR may, in fact, be priced (Some portion of CSR may be priced given the inability of investors to properly diversify. However, the benefits of diversification will always be present and will always eliminate some, but possibly not all, CSR) in the public markets.
- Coefficient of determination (R-squared or R2): The square of the correlation coefficient (R). This measures the ability of the variation about the mean in the market index (independent variable) to describe the variation about the mean in the guideline company (dependent variable). This measures the “goodness of fit” of the best fit linear regression line. In this case, the best fit linear regression line is the following:
Weekly return of comparable = constant + Beta*Weekly return of market index
The Beta is the slope of the best fit linear regression line. The R-square always falls between 0.0 (no explanatory power) and 1.0 (complete explanatory power).
- T-Stat: Beta/standard error. If the T-stat is greater than a certain value, it indicates the confidence we have that Beta is something other than 0. See Confidence Level below.
- Confidence level: If for example, the level of statistical significance is 1%, we are 99% confident that the slope (Beta) is something other than 0.
- Degrees of freedom: The number of observations (weekly returns) minus the number of coefficients estimated. Since in this case, we estimate the constant and Beta, the degrees of freedom will always be two less than the number of observations.
Q: Why do you calculate CSRPs? Couldn’t you just calculate the publicly-traded stock’s TCOE and stop there?
A: Yes, you could. In certain cases, maybe that would be best. (See answer below). However, you also may want to look at the combined size:CSRP for the following reason. We like to understand why the guideline TCOEs are what they are, so we allocate the total risk among systematic risk and the rest (size:CSRP) when not too subjective to do so.
Q: Do you recommend ignoring, or excluding, a guideline’s results if its T-stat indicates a confidence level below a certain level?
A: Admittedly, this is another subjective part of the calculation. We typically exclude a reference point if the T-stat confidence level is below 80%. (You can pick a different hurdle rate, if you desire). However, remember since Total Beta captures 100% of the stock’s total risk, one could key in on the TCOE as a reference point – rather than depend on CSRP calculations based on questionable determinations of Beta. A low T-stat may be an indictment of the CAPM, not necessarily this technique, which captures 100% of a stock’s total risk from a standalone perspective.
One other item to keep in mind, maybe a low beta (and, therefore, low t-stat) are capturing exactly what they should be capturing - a stock with low systematic risk.
Q: Does one need to be concerned if a guideline comparable could be considered a thinly-traded stock?
A: Yes. There might be some lack of liquidity issues in the calculation of a benchmark TCOE and CSRP. Thus, you should be aware of this when assigning a lack of marketability to a minority interest in a privately-held firm.
As an aside, but on a somewhat related matter, appraisers need to be cognizant of the fact that some of the pre-IPO transactions used for guidance to determine lack of marketability discounts may have been entered into by an under-diversified investor. Therefore, the difference between the pre-IPO price and the IPO price may incorporate more than just marketability, such as the difference in required rates of return between under-diversified and diversified investors (read: CSR may have mattered in the pre-IPO transaction and not mattered in the IPO transaction as investment bankers do not price CSR since the company is going public). This unquantifiable impact is probably more substantial as the period between transactions (Pre-IPO and IPO) increases since the under-diversified investor’s “assurance” of an IPO would be less as the window between transactions increases. This issue may also be relevant for restricted stock studies, albeit to a lesser extent, if the purchaser of the restricted stock was under-diversified and priced CSR in some fashion.
- The Calculator’s output shows each benchmark’s reported volume for the analyst to make a determination on this issue.
- The reported volume for any given week is the average daily volume for the last five trading days, including volume for the effective date.
- If a guideline is inefficiently/thinly traded (i.e., gaps in trading), then analysts may wish to look at the following options
- Compute a “Corrected Total Beta”. (Note: The Calculator will not perform this function). Corrected Total Beta = Sum Beta/R as opposed to Beta/R. The correlation coefficient, R, (See FAQ 38c) would (most likely) be different for both the total beta and the corrected total beta. Please refer to SBBI, 2008 Valuation Yearbook for the definition and calculation of Sum Beta. In summary, sum betas allegedly capture the lagged response of a company’s reactions to movements in the overall stock market. With rare exceptions, this modification effectively increases the beta measurement and the calculation of the stock’s systematic risk. Some items to consider if one wants to pursue this calculation:
- Other than when gaps exist in trading, it could be viewed as quite subjective to determine when it might be appropriate to use this Corrected Total Beta calculation. Just because a stock is thinly traded does not necessarily mean that it traded in an inefficient market where one would question the merits of OLS beta. For example, Sum Betas for Decile 3 stocks (market capitalization between $5.0 billion and $9.2 billion) increase the measure of systematic risk from an OLS beta of1.08 to a Sum Beta of 1.13 (Source: SBBI, 2008 Valuation Yearbook – Tables 7-10 and 7-11). We will leave it up to the individual analysts to determine if this correction is necessary or not, but please consider the following when making the determination:
- Compute a “Corrected Total Beta”. (Note: The Calculator will not perform this function). Corrected Total Beta = Sum Beta/R as opposed to Beta/R. The correlation coefficient, R, (See FAQ 38c) would (most likely) be different for both the total beta and the corrected total beta. Please refer to SBBI, 2008 Valuation Yearbook for the definition and calculation of Sum Beta. In summary, sum betas allegedly capture the lagged response of a company’s reactions to movements in the overall stock market. With rare exceptions, this modification effectively increases the beta measurement and the calculation of the stock’s systematic risk. Some items to consider if one wants to pursue this calculation:
Quoting Morningstar’s Beta Book, 2006 ed.:
“Because of non-synchronous price reactions, the traditional betas estimated by ordinary least squares are biased down for all but the largest companies.” (Emphasis added)
The non-synchronous price reactions referenced above are company-specific price reactions. We know that Total Beta already captures all of these price reactions. Since Total Beta captures these along with every other known risk, the fact that some small guideline companies have potentially low measurements of systematic risk should not be a concern for the business appraiser.
Total Beta’s measurement of CSR picks up the OLS Market Beta’s “slack” in the measurement of total risk – again, our reference point when we value privately-held companies. Thus, there is no need to “correct” systematic risk if our reference point is total risk and the benchmark is an efficiently traded stock. Please note that the above quote does notsay:
“Because of market inefficiency, the traditional betas estimated by ordinary least squares are biased down for all but the largest companies.”
The market for many smaller stocks is efficient. Their total risk just happens to be dominated by CSR, rather than systematic risk. If the market for a particular stock is efficient, regardless of its “low” measure of systematic risk, its corresponding Total Beta never needs corrective action (at least from the authors’ perspectives). This, obviously, is another benefit to the Total Beta measurement.
Why bother with this Sum Beta adjustment if the stock trades in an efficient market? While the OLS Market Beta may be low (although who really knows for sure?), by apportioning more of the total risk to systematic risk through the sum beta calculation, the natural result is a smaller and artificially low CSRP – since the total risk of the company should not change for an efficient stock. Thus, we believe that Sum Beta is an unnecessary and subjective step for efficient stocks after the introduction of Total Beta.
This “correction” results in an inequality as far as how Total Beta is calculated from the other side of the identity: standard deviation of the stock/standard deviation of the market. While it is fairly easy to manipulate the Beta and R (by calculating Sum Beta), one cannot change the historical volatility of the guidelines, representing a mismatch between Sum Beta/R and standard deviation of the stock/standard deviation of the market.
Even with the CAPM’s many unrealistic assumptions, the investment community strongly relies upon OLS betas, rather than sum betas.
If gaps exist in trading (possibly an inefficient market), ignore the guideline from consideration.
If gaps exist in trading over a five-year look-back period, for example, then shorten the look-back period to see if the gaps can be eliminated over this shortened period. If no gaps exist and the analyst determines the guideline traded efficiently, the authors believe there is no need to calculate a sum beta for CSRP determination.
Q: Have you ever calculated a CSRP less than 0%?
A: No, with the following disclaimers (see b and c below). All publicly-traded stocks we have analyzed exhibit a positive CSRP – whether it is priced or not. Thus, never apply a negative (meaning less than 0%) CSRP to any private company.
For short time periods, we have calculated negative CSRPs on some occasions. Our thought is that anything is possible over relatively short measurement periods.
After working with the Calculator and running hundreds of searches, we have calculated (or have had the calculations pointed out to us) indications of negative CSRPs for a five-year look-back period, for example. These occasions occur when, for example, the guideline company drops in market value from a Decile 9 stock to a Decile 10 stock and we originally chose to rely upon the significantly larger size premium in Decile 10 for our calculation. However, if one chooses to use the size premium correlated to Decile 9, or an average of the two, we end up calculating positive CSRPs. A CSRP is dependent upon our choice of the size premium since CSRP is the residual in the formula: CSRP = (Total beta – beta)*Equity risk premium – Size premium. The size premium has always presented interesting issues – whether in this technique or other techniques to calculate a cost of equity. (Please see question below).
We have been given hypothetical (unrealistic?) examples of companies during our presentations where the audience participant believes a negative company-specific risk premium is appropriate. The following is one such example: A company that has had a government contract for the last 100 years and is expected to have the same government contract for the next 100 years. Why can it not have a negative CSRP? Well, there must be some possibility that the company could lose the contract (presumably a very large customer) in the next 100 years. The company may deserve a very low CSRP, possibly even less than Exxon Mobil or General Electric, but it does not deserve a negative premium. We have yet to calculate a publicly-traded stock’s CSRP at less than 0% (with the disclaimers noted above). We call it risk for a reason.
Q: The calculation of Beta and Total Beta are stock-specific for guideline comparables, yet you use an average for the size premium (Decile 1 - 10 from Ibbotson’s Stock, Bonds, Bills & Inflation Yearbook or Portfolios 1 – 25 from Duff & Phelps Risk Premium Report). Is this an inconsistency?
A: In a perfect world, calculating a size premium for each specific guideline company would be ideal. However, we do not believe this is practical, given the inherent subjectivity in calculating this piece of the overall risk (Actual return minus expected return from CAPM theory). The expected return may be quite subjective depending on the inputs to the CAPM, particularly what beta to use to calculate expected return over your look-back period. In fact, this is one of the criticisms of the CAPM - it might not be that helpful in estimating future returns. Moreover, if everyone uses the same data, such as the accepted size premium databases (Morningstar/Ibbotson’s or Duff & Phelps), as opposed to calculating their own subjective size premiums, one result should be a certain amount of “stability” to the determination of guideline CSRPs and ultimately private company CSRPs.
Given the valuation community’s acceptance of Morningstar/Ibbotson’s size premium (and in the future, potentially Duff & Phelps’ research), we have also chosen to accept these average calculations as representative for our guideline companies. We believe we are being consistent when we use data from the same source for both our guideline companies as well as our subject private company. We believe inconsistencies might develop if one uses the standard size premium databases (Morningstar/Ibbotson, Duff & Phelps) for private companies and then calculates subjective size premiums for the guidelines. In other words, if you calculate size premiums yourself for your guidelines then you should consider these size premiums in some fashion for your private company to be consistent. The Calculator presents other options on how to handle size, however. Please see FAQ below.
Q: Do you recommend using decile 10b from Ibbotson?
A: The user should be aware of certain controversies regarding the use of decile 10b; in general, we do not use 10b by itself.
Q: I do not believe the size premium exists. Why does the program rely on this concept?
A: Even though the size effect is cyclical, over the long-term it has manifested itself. Therefore, we have programmed the Calculator to account for its existence. If you do not believe in, or want to use a size premium in your calculations (see 45 b. below), you can: 1) Completely focus on the guideline’s TCOE; or 2) Calculate the guidelines’ combined CSRP and size premium. Under this approach, the equation becomes:
TCOE = Risk-free rate + Total Beta*Equity risk premium = Risk-free rate + Beta*Equity risk premium + combined CSRP:SP. To effectively accomplish this, merely plug in 0% for the size premium when prompted by the Calculator, resulting in the following equation:
Combined CSRP:SP = (Total Beta – Beta)*Equity risk premium.
Note: the combined CSRP:SP will be higher (for all but Decile 1 stocks) than we otherwise would have calculated if we had accounted for the size premium using either Morningstar/Ibbotson or Duff & Phelps’ data. However, the TCOE remains the same – the allocation of the total risk premium just changes. Remember, this Calculator is also a risk-allocator.
- Plugging in 0% for the size premium is also effectively concluding that it is somewhat subjective, if not impossible, to separate CSR from size. For example, we have often used the micro-brewery industry in our writings and presentations. After we reviewed the pertinent 10-Ks, we developed 18 different “CSR” factors to compare our subject company to the guidelines. Of the 18, it is relatively easy to consider 8 factors (product line diversification, number of company-owned breweries, number of contract-leased breweries, number of distributors used, geographic location of sales, number of suppliers, management depth, and access to capital) as having elements of size imbedded in the factor. Thus, this potentially could be another reason to use 0% when prompted for the size premium as it is somewhat subjective to attempt to separate out size and company-specific risk factors, even though they are two different components of risk.
Remember, if you decide to separate out size and CSR, you always have the TCOEs as reasonableness checks. You also have the TCOEs as reasonableness checks if you decide to allocate total risk into systematic risk (beta) and all of the rest (such as when we plug in 0% for the size premium, resulting in a combined CSR:SP output from the Calculator. In this case, the output of the Calculator for all guidelines (Total Beta, Beta, combined CSR:SP) would all be guideline-specific).
Moreover, if CSRP is priced in some fashion (which is still a controversial statement, but may be possible), then it appears that the standard industry sources for size premiums may include at least some CSR (Please see recent academic research indicating that it is not possible to completely diversify away CSR). Thus, the size premiums in Duff & Phelps and/or Morningstar/Ibbotson may also be capturing CSR, leading to artificially low CSRPs for the guidelines, all else being equal, and not considering the stock-specific calculation of size premiums. This potentially is another reason to plug in 0% for the size premium and then carefully look to both size and CSR factors when qualitatively comparing your subject company to the guidelines as accepted data sources (Morningstar/Ibbotson and Duff & Phelps) may not be able to separate the two components of risk as alluded to in the academic research cited below conducted by Burton G. Malkiel and Yexiao Xu in their research titled “Risk and Return Revisited” and Idiosynchratic Risk and Security Returns”.
These two researchers claim that the residual risk or idiosyncratic volatility (read: CSR) of individual stocks is strongly related to the size of the company. They hypothesize that the size effect found by Fama and French may be reflecting idiosyncratic volatility.
Q: What are the "holes" in this technique?
A: Relative to traditional methods to “quantify” CSRPs, we have found no holes. Yes, subjectivity still remains, as described in more detail throughout the answers to the questions on this page. However, if you are consistent in each valuation and use the same assumptions for every guideline company, you will arrive at a defensible range of CSRPs and/or TCOEs, which you will be able to use to better defend and support your determination of a CSRP and/or TCOE for your private company.
Beta, for many stocks (but not all), is inherently unstable. We believe it is appropriate to account for this “fact” by examining the t-stat and related statistical confidence calculations. Reiterating, if the t-stat correlates to a confidence level less than 80%, we do not bother allocating the total risk. However, unless the stock traded in an inefficient market, we still rely upon the guidelines’ TCOE. We have never claimed that the BPC is any better (or worse) than other methods in projecting the future. However, the calculated historical beta for each guideline (assuming efficiency) is what it was, so-to-speak.
One can test the historical stability of beta if desired (In fact, we recommend calculating TCOEs, Total Betas, Betas and combined size:CSRPs using all five days of the week. Please see FAQ #32). One can also use different look-back periods to gain an appreciation for the stability, or lack thereof, of the guidelines’ betas. We actually believe this to be one of the great benefits of the Calculator. If you rely upon printed-sources for betas, you have no idea their sensitivity to different assumptions.
Assuming betas are normally distributed, one can also review the expected range of betas falling under 95% of the distribution, for example. However, keep in mind that both the mean and median of a normal distribution are equal. In the authors’ estimation, analysts should have a very good reason to use a guidelines’ beta (and total beta) other than the calculated beta and total beta, such as the beta and/or total beta correlating to the 95th percentile, for example. While there is a range for any probability curve, the mean/median (using all five trading days) is the best estimate of the appropriate representation of beta and/or total beta.
CSRP and/or TCOE are impacted by many “types” of risk, including both operational risk (supplier concentration risk, etc.) as well as financial (leverage) risk. Analysts must compare the guidelines and their subject company on the impact of leverage on their relative CSRPs and/or TCOEs. The authors view this no differently than comparing the guidelines on any operational risk factor. The Calculator determines the guidelines’ total CSRP, which is dependent upon both operational and financial risks. The Calculator cannot separate the CSRP due to leverage versus operational risk – similar to its inability to separate customer concentration risk from supplier concentration risk, for example.
However, while the Calculator will not automatically perform the following calculation, analysts can measure the impact of leverage on their guidelines. We are all familiar with various formulas to un-lever Beta (Hamada, Miles-Ezzell, Harris-Pringle). We can apply these same formulas to un-lever Total Beta. Remember, the Calculator calculates a levered Total Beta as well as a levered CSRP. We merely have to replace levered Beta in the formulas with levered Total Beta to calculate an un-levered Total Beta. Appraisers can then select the appropriate un-levered Total Beta for their subject company and then re-lever with an appropriate capital structure if they want to key in on TCOE directly.
Also, using the Hamada formula as an example, one can determine a guidelines' un-levered CSRP.
CSRP un-levered =
((Total Beta levered – Beta levered)/(1+(Debt/equity)*(1-tax rate)))*ERP - SP
Thus, one can compare the guidelines’ CSRP levered with CSRP un-levered to appreciate the impact of leverage if one wanted to build-up the discount rate.
Yes, subjectivity still exists, which is a good thing. If CSR was purely objective, we might all have much less valuation work to perform. However, regardless of the subjectivity and/or criticisms mentioned above, should you choose to solely rely upon purely subjective factor models, you are implicitly saying that no empirical evidence is better than some modestly subjective empirical evidence.
We believe that analysts distinguish themselves from the competition by properly quantifying CSR and total risk, not necessarily systematic risk. CSR is what makes the subject company’s TCOE truly unique. We recommend that you use the BPC. Regardless of the subjectivity, it is much better than using an educated guess alone, which is what appraisers do by relying upon purely subjective factor models.
Many of the criticisms described above relate to CAPM (and must also apply to the build-up approach since the build-up approach is essentially the CAPM). We do not believe it is appropriate to place these burdens or hurdles upon the BPC as arguments for its exclusion. In other words, if you use the CAPM or build-up method, the BPC is a natural extension of that data. The math is incontrovertible if you accept the CAPM (and the build-up method). The BPC merely fills in a blank – a blank that appraisers have always filled-in somehow. The BPC provides empirical evidence of what that blank should be, contrary to the ability of purely subjective factor models.
We hear that some appraisers might dismiss this technique because they believe it requires appraisers to use multi-billion dollar companies as proxies for private company valuations. First, there are many “small” publicly-traded companies that appraisers can use. You just have to look for them. Second, many appraisers already use these same multi-billion dollar companies to value their subject companies when they apply an equity risk premium (ERP) or an industry risk premium (IRP). Importantly, the Calculator can provide the TCOE (including the CSRP), not just the IRP, for all of the stocks in a particular SIC code. Many appraisers are finding this application particularly useful when attempting to impeach their opponent’s cost of capital derived from completely subjective guesses.
We also hear that some appraisers might dismiss the technique because they fear that they might also have to perform the guideline publicly-traded method (market approach) with the same guidelines used with the Calculator. First, this notion is not correct. How many appraisers have felt compelled to use the market approach when they use an IRP in the income approach? Our guess is not a single one. Second, CSR is just that – company-specific. The guideline multiples do not fully capture the CSRP anyway and, therefore, must be adjusted (Please see question 50f below). As previously stated, we can foresee many more guidelines in the income approach. We, in fact, have used the Calculator and completely ignored the market approach in certain engagements. We also have used the same guidelines for the market approach in other engagements. It just depends. As inferred, it might very well be a good idea to use the same guidelines under each approach (income and market), depending on the engagement and the budget. You have to ask yourself if you do high quality work or not? It does not make any sense to be afraid of using a far superior technique in the income approach (the most theoretically correct way to value a company) because, heaven forbid, you might want to consider (and possibly use) the same guidelines in the market approach.
There was alleged criticism in a presentation at the 2009 ASA Advanced BV Conference in Boston that total beta and the BPC provide maximum TCOE, combined size:CSR premium and/or CSRP benchmarks, meaning that the metrics stem from a completely undiversified portfolio perspective. Yes, this is true; although, no one had to point it out. Ironically for the critics, however, this observation is an implicit endorsement of the BPC.
What the “critics” have failed to realize is that the maximum values are still data points that we have never had before. Thus, you do not have to completely guess at these metrics for your undiversified pool of buyers or, for that matter, your partially diversified pool of buyers (see below). Moreover, completely undiversified may be a reasonable perspective to assume for the pool of buyers. It depends upon the assignment.
How have the “critics” handled the level of (un)diversification for the pool of buyers before the BPC? When appraisers placed a completely subjective 5% CSRP on a company, what analyses were performed to hypothetically lower a 7% maximum CSRP to only 5% because the pool of buyers was partially diversified? Or, hypothetically, did we as an industry just assume maximum CSRP and/or TCOE? Total beta and the BPC allow appraisers at least to consider such issues.
After the conference in Boston, we have done more than just qualitatively consider the ramifications of diversification. We have developed an Excel spreadsheet to assist appraisers in making informed, quantitative decisions related to the question of diversification. Please click here to access the spreadsheet now. (This is a new spreadsheet as of April 29, 2010, which should replace the use of the prior spreadsheet).
We believe the instructions and assumptions are relatively straight-forward. Please refer to the Comments Section of the spreadsheet. While somewhat subjective, the ultimate goal of this spreadsheet is to price risk depending on any level of diversification you may find is appropriate for the average investor in the buyer pool.
Q: Is it possible for a private company to exhibit a TCOE and/or a CSRP either above or below the range calculated for your guideline companies?
A: Yes. Thus, the determination of a TCOE and/or a CSRP for your private company may be a little more subjective than otherwise would be the case.
Q: After I calculate a range of TCOEs and/or CSRPs from the publicly-traded comparables, how do I use this information to select an appropriate TCOE and/or CSRP for my privately-held company?
A: We recommend obtaining the relevant public filings (10-K, 10-Q, etc.) to compare/contrast identifiable Total risk and/or CSR factors. We have used a ranking system to help rate each company, including our subject company, within each total risk or CSR factor as well as to rate each factor by relative importance. For more information, please see our articles and sample templates.
Q: Is there potential for a mismatch if one only looks to the most recent Forms 10-K, yet uses 5 years worth of historical pricing data to calculate TCOEs and/or CSRPs?
A: Yes there might be, if for example, a total risk or CSR factor was prevalent 5 years ago, and has subsequently been eliminated in more recent filings. You may wish to review more than one Form 10-K per guideline company to ensure all total risk and/or CSR factors have been accounted for over the measurement period.
Q: Other than determining TCOE and CSRPs, are there any other uses for this Calculator?
A: Financial reporting:
Yes. We discovered that the Total Beta calculations are excellent to calculate a private company’s implicit volatility for SFAS 123R reporting purposes.
Remember, that a firm’s TCOE = Risk-free rate + Total Beta*Equity risk premium and that Total Beta = SDs/SDm. So, TCOE = Risk-free rate + SDs/SDm*Equity risk premium. After you use the Calculator to determine your private company’s TCOE, you can solve for the only unknown in the above equation, SDs.
Your private company’s implied volatility, SDs, is an important input to calculate the value of employee stock options required for SFAS 123R. The SDs will now correlate perfectly with your private company’s TCOE.
Thus, you no longer have to completely rely upon guideline public companies’ historical volatilities, implied volatilities or reported volatilities when estimating volatility for your private company. Rather, you can look to your specific private company for this information. Please see our article on this subject for more detailed information.
Calculation of marketability discounts:
Of course, this implied volatility can also be used to help determine a lack of marketability discount for a minority interest in a privately-held company. There are a variety of quantitative models (one being put option theory) which depend on volatility as an input. (Please see FAQ #2e for one such method).
Adjustments to guideline publicly-traded multiples for the market approach:
If for example, the P/E of a particular stock (a guideline) was 20 and its CSRP was equal to 5% as determined by the Calculator, an appraiser could rely upon research performed by Professors Covrig and McConaughy from California State University, Northridge and use the following formula to adjust the multiple to a private company multiple:
|P/E private =|
|Thus, the P/E private =||1||= 10|
Of course, this is just a benchmark. To estimate your subject company’s P/E multiple, differences in growth, size, systematic risk and CSR must also be analyzed.
One benefit of the Calculator that has been understated thus far is its ability to calculate market beta. This benefit alone is valuable given the Calculator’s relative flexibility (as shown below in the table comparing the BPC Calculator to a selection of other commercial sources for market beta). As one can see, the Calculator ranks second only behind Bloomberg Professional Service (not the free website), which Wall Street firms subscribe to. While Bloomberg Professional Service offers a plethora of financial data and news, it also is exponentially more expensive than the BPC Calculator.
The BPC Calculator allows appraisers to see behind the beta calculations and to better understand the inherent stability, or instability of market beta as the case may be, for each guideline company. If appraisers rely upon a printed source of market beta rather than an online source such as either Bloomberg Professional Service or the BPC Calculator, then they will have no idea the sensitivity of the calculations to various changing inputs.
Commercial Beta Sources:
Over 20 domestic series
None; or (0.67*OLS Beta)+(0.33*1.0)
Adjusted toward peer group
3 domestic series;