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The Butler Pinkerton Calculator: The Butler Pinkerton Calculator: The ChoiceThe Choice

October 20, 2009

Peter J. Butler, CFA, ASA

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Learning Objectives:• Problems with traditional factor models: Use at own

peril!• The Choice: Empirical Data v. No data

– The choice is yours: • Make it wisely• Impeach inferior cost of capital estimates

• Secondary Choices: Empowerment/Transparency• Other Applications for the Calculator

Determination of the proper capitalization rate presents one of the most difficult problems in valuation – RR 59-60

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Traditional Factor Models: Use at Own Peril!Negative risk factors +/- Numeric Listing

Operating history, volatility of rev & earn. +++ 3.5 X

Lack of management depth ++ 1.0 X

Lack of access to capital resources + 0.5 X

Over reliance on key persons ++ 1.0 X

Lack of size and geographic diversification + 0.5 X

Lack of customer diversification 0.0

Lack of marketing resources + 0.5 X

Lack of purchasing power 0.0

Lack of product/market. dev. resources + 0.5 X

Over reliance on vendors/suppliers 0.0

Limitations on distribution system 0.0

Limitations on fin. reporting/controls + 0.5 X

Positive risk factors

Long term contracts, unique product 0.0

Patents, copyrights, franchise rights - (1.0) X

Net increase to Cost of Equity 7.0 7.0 7.0

Where is the

empirical data?

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The Problem: What Do the Courts Want? • Gesoff v. IIC Industries

– “This court has also explained that we have been understandably . . . suspicious of expert valuations offered at trial that incorporate subjective measures of company-specific risk premia, as subjective measures may easily be employed as a means to smuggle improper risk assumptions into the discount rate so as to affect dramatically the expert’s ultimate opinion on value.”

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The Courts Want Empirical Data!• Delaware Open MRI Radiology Associates

v. Howard B. Kessler, et al– “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.”

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Summary of Factor Models

• Excellent models to understand Size:CSR

• But, do not provide what the courts want:

– Empirical data on Total Risk and/or CSR

• If you want to make enemies, try to change something.

Woodrow Wilson, 28th President of the United States

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The Solution: Total Beta and the BPCSolving for the only unknown in the two equations, CSRP:

• TCOE = Rf + Tβ*ERP = Rf + β*ERP + SP + CSRP

Modified CAPM

Risk Allocation:• Combined Size:CSRP = (Tβ–β)*ERP

• CSRP = (Tβ–β)*ERP – SP

CAPMDamodaran BPC

“Market approach twist to developing a discount rate.”

Professors of Finance and Economics

Well–known appraisers

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The Calculator is:1) Empirical,2) Transparent,3) Real-time (or as close as possible),4) The only source (that appraisers typically rely upon) that captures total risk, and5) Empowering

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More Transparency

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Practical Advice

• This is clearly a great addition to what we have done in the past. We used to use Cost of Capital Quarterly to get an idea of the cost of equity by SIC code. We would adjust from there. Now, instead of using the entire industry, we can choose better guideline data as a starting point.

– Gary Trugman, CPA/ABV, MCBA, ASA

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Impeach Inferior Estimates of Cost of Capital Build-Up Method:SIC Code 8742 (Management Consulting Services, but really interested in litigation consulting)

• MANAGEMENT NETWORK GROUP INC• MAXIMUS INC

• NAVIGANT CONSULTING INC• OCEANIC EXPLORATION CO• PAREXEL INTERNATIONAL CORP• PDI INC• PHC INC/MA -CL A• QUANTUM GROUP INC• RAHAXI INC• REHABCARE GROUP INC• SOUTHWEST CASINO CORP• SPHERIX INC• SUNRISE SENIOR LIVING INC• TALEO CORP• TETRA TECH INC• THOMAS GROUP INC• TRI-ISTHMUS GROUP INC• TURNAROUND PARTNERS INC• TYSON FOODS INC -CL A• UNITEDHEALTH GROUP INC• VERSAR INC• WATSON WYATT WORLDWIDE INC

• ACCESS WORLDWIDE CMMNCTNS• ADVISORY BOARD CO• AON CORP• BEARINGPOINT INC• BUTLER NATIONAL CORP• CIRTRAN CORP• COMFORCE CORP• CORPORATE EXECUTIVE BRD CO• CROSS COUNTRY HEALTHCARE INC• DIAMOND MANAGEMENT & TECHNL• ELOYALTY CORP• EMCOR GROUP INC• EXPONENT INC

• FTI CONSULTING INC• GARTNER INC• HALLWOOD GROUP INC• HEWITT ASSOCIATES INC

• HURON CONSULTING GROUP INC• INVENTIV HEALTH INC

• LECG CORP

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The “Battle of the Experts” is Over Before it Even Began

Total Cost of Equity (TCOE) Litigation Consulting Firms

14.00%

14.50%

15.00%

15.50%

16.00%

16.50%

17.00%

17.50%

18.00%

18.50%

FCN ($2.7B) HURN ($1.0B) NCI ($600M) CRAI ($265M) Subject ($?)Subject: risk-free=4.16% (5/18/09); ERP = 6.5%; BUM = build-up method: IRP = -1.46%; SP = 5.81%; CSRP = 0.5% (Guess); BPC = Butler Pinkerton Calculator: 5-year-lookback; Market proxy = S&P 500

BPC

BPC

BPC

BPC

BUM

Empirical data

Guess

Out of thin air

More defensible

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Interesting Observation: “I Don’t Have any Good Guidelines!”• BUM with an IRP: You already have assumed “good”

guidelines – at least for systematic risk.– Use BPC to impeach inferior estimates of the cost of

capital• Broaden your search: Guidelines = guidance

– Joyce C. Hall v. Commissioner:• Hallmark Cards v. MCD, BUD, IBM, KO, AVP

• Many small publicly-traded companies.• Company-specific risk is just that – company specific.

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Practical Advice Related to Guidelines• Frankly, it was this analysis (reviewing Forms 10-K, etc.) that gave me the

best insight into the characteristics that affect risk in this industry. I don’t believe that you can reasonably assess company specific risk factors without an understanding and analysis of the benchmarks derived from the BPC.

• I much prefer BPC because it forces me to examine public company data about industry risk factors and value drivers which is available through public filings, press releases, analyst reports, etc. The data is much more comprehensive in nature than the limited data available for private companies. – James M. Skorheim, JD, CPA/ABV/CFF, CFE, CVA, CrFA

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Other BPC Applications: 

• First, we do a significant amount of Fair Value compliance work, and the BPC is a great tool for developing capital costs for hypothetical market participants. We've had general acceptance of this method in audit review, and it's a great time saver. 

• Second, in documenting a decision regarding discounts for lack of marketability, we regularly use QMDM as one of the methods considered.  The BPC enables us to develop actual market equity returns for smaller publicly traded companies, providing a lower limit for the expected return input in QMDM. – James B. Lurie, CPA/ABV, ASA, CBA, CVA, BVAL, CIRA

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Other BPC Applications (continued): 

• In using the market approach, the market multiples can be adjusted not only for size and growth, but also for the CSRP. Again, the judgment gap is narrowed. Finally, I have found that the variance between the values determined by the income and GPTC methods has been significantly reduced.– Donald P. Wisehart, ASA, CPA/ABV/CFF, CVA, MST

• There is a reason why your method (BPC) and our method (used to adjust public company multiples for CSR) are similar, that’s because both are actually the same method, developed a long time ago. – Vicentiu M. Covrig, Ph.D., CFA in an e-mail to Butler

There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.

– Niccolo Machiavelli, Italian philosopher

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Other BPC Applications (continued): 123R

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Other BPC Applications (continued): In Search of the “True” Beta Beta Source Market Proxy Period Frequency Adjustment

1 Bloomberg Over 20 domestic series Adjustable Adjustable (0.67*OLS Beta)+(0.33*1.0)

2 Compustat S&P 500 5 years Monthly None

3 Ibbotson S&P 500 5 years Monthly Adjusted toward peer group betaweighted by stat. significance

4 Value Line NYSE Composite 5 years Weekly 0.35+0.67*OLS Beta

5 Yahoo!Finance S&P 500 3 years Monthly None

6 BPC 6 domestic series Adjustable Weekly - default NoneAdjustable - manual

BPC rank 2nd Tied first 2nd Debatable

Sources: Table 6-11, SBBI Valuation Yearbook and definitions from Yahoo!Finance.

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1) Referenced in AICPA textbook written by G. Trugman, Understanding Business Valuation;

2) Referenced in PPC’s 19th Annual Guide to Business Valuations;

3) Referenced in CCH’s Business Valuation Guide;

4) E-book in collaboration with Morningstar;

5) Current Update in Valuations/part of training material for NACVA;

6) Part of HBS Case Study;

7) Numerous independent endorsements and testimonials;

8) Can be proven with the Sharpe ratio. It is just CAPM theory for the undiversified investor;

9) Goldman Sachs, Bank of America, Duff & Phelps;

10) Academic support;

11) More than 10 articles;

12) Numerous presentations;

13) Cost of Capital, 3rd edition

Total Beta:BPC and Peer Review

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Independent Select Testimonial

• Total beta is a widely accepted measure of risk in situations where investors are not well diversified.  The Butler-Pinkerton Calculator is a convenient and flexible tool for quickly arriving at an objective estimate of total beta and the company specific risk premium for a privately held company. – Keith Harvey, Ph.D., CFA (A finance professor

made aware of Mr. Kasper’s allegations)

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• We believe that the Butler-Pinkerton Calculator is a useful tool for appraisers who want a quantitative way to assess the maximum CSRP. What the Total Beta and calculator computes is the maximum or upper bound for the CSRP. A good appraisal should also use subjective techniques and judgment to determine the appropriate CSRP for the subject company.– Vicentiu M. Covrig, Ph.D., CFA and Daniel

McConaughy, ASA, Ph.D. (Finance professors made aware of Mr. Kasper’s allegations)

Another Select Testimonial

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Total Beta and The BPC: Why Not Now?• Subjective Factor Models Provide NO empirical data for

Total Risk or CSRP!– Any other source is subject to harsh criticism– BPC is not a solution in search of a problem

• BPC provides (moderately subjective) EMPIRICAL data:– Defend/support all assumptions/inputs

• No different than any other cost of capital input– Except the BPC provides real-time, transparency for

specific guidelines – Except the BPC empowers you to observe the

sensitivities in the calculations

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Questions to Consider:• If Total Beta and the BPC (which empirically

capture total risk) were developed first, would you abandon them to rely upon other databases (which only capture partial risk)?

• If Total Beta and the BPC were developed first, would you abandon them to rely upon the purely subjective factor models (which require a complete guess for a CSRP)?– One thing we do recognize is that the valuation profession can use

more tools grounded in market observations to help develop discount rates – Roger Grabowski; BV Update - November 2006

• Note: The BPC was commercialized in November 2007

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QuestionsMore questions during panel discussion:

Responses to Mr. Kasper’s criticisms in next session.

An important scientific innovation rarely makes its way rapidly winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and the growing generation is familiarized with the idea from the beginning.

– Max Planck, German physicist, founder of quantum theory

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The Butler Pinkerton Calculator: The Butler Pinkerton Calculator: Still (by far) the Best ChoiceStill (by far) the Best Choice

October 20, 2009

Peter J. Butler, CFA, ASA

Never let the search for the perfect get in the way of the perfectly good- John Elson, Time editor

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Whose Misunderstanding of Financial Theory is the Question• “We have argued that in equilibrium there will be a

simple linear relationship between the expected return and standard deviation of return for efficient combinations of risky assets. Thus far nothing has been said about such a relationship for individual assets. Typically the ER, σR values associated with single assets will lie above the capital market line, reflecting the inefficiency of undiversified holdings. Moreover, such points may be scattered throughout the feasible region, with no consistent relationship between their expected return and total risk (σR). However, there will be a consistent relationship between their expected returns and what might best be called systematic risk, as we will now show.”

William F. Sharpe (1964), “Capital asset prices: A theory of market equilibrium under conditions of risk,” Journal of Finance, 19 (3), p.436.

A Portfolio

Portfolio risk

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Are You on the Left-side or the “Right”-side?

• Correlated relative volatility v. Relative volatility

• Covariance v. Standard deviation• Well-diversified portfolio v. Stand-alone asset• Portfolio managers v. Appraisers• Partial risk v. Total risk• NO empirical data v. Empirical data• It’s your choice – I have made mine.

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Conclusion from Mr. Kasper’s Paper

• “Until the authors provide empirical evidence that total beta produces better estimates of actual public company returns…” – Why would we? – Mentioned in very first article that the technique does

not do this – Mr. Kasper missed it! – CSR is at least partially diversified away for publicly-

held stocks.• CSR, however, is priced for PRIVATE companies• Use Total Beta as a proxy for PRIVATE companies

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Other Observations (from today’s presentations): Instability of Beta

Dnacq Healthcare (DYII) Dryships (DRYS)

Beta Total Beta Beta Total Beta

Jan-08 Nov-08

Monday 0.34 10.72 Monday 2.88 4.33Tuesday 1.18 11.60 Tuesday 2.52 4.70Wednesday 0.60 12.05 Wednesday 2.41 4.39Thursday 0.60 12.93 Thursday 2.31 4.25Friday -0.47 11.92 Friday 2.18 3.93

Mean 0.45 11.84 Mean 2.46 4.32Median 0.60 11.92 Median 2.41 4.33

SD 0.60 0.80 SD 0.27 0.28CV 1.33 0.07 CV 0.11 0.06

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Other Findings (continued):• Statistical errors with beta (instability of beta) (continued)…

– Total beta (TCOE-side of Calculator) is relatively immune– BPC uses OLS beta to keep the following intact:

• β/R = s/m

• Other commercial sources use OLS regression– Recommendations: Calculations are very quick and easy

• Look at all 5 days of the trading week• Look at different look-back periods• T-stat greater than 80% (or whatever you so choose)• Select an appropriate R-square as a hurdle• Question: Maybe a low R-square captures exactly what it

should be capturing – a stock with low systematic risk?

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Summary:• All models are wrong, but some are useful.

George Box, statistician– Total beta and the BPC are very useful.– You can use them (or perform the calculations yourself) and be

subject to Mr. Kasper’s alleged criticisms or be subject to harsh criticisms from the Court.

• Your Choice!• It takes a model to beat a model.

Milton Friedman, Nobel Prize winning economist– Total beta and/or the BPC have beaten other models/databases that

require a complete guess for CSRP:1) Do not empirically capture total risk and 2) Are not transparent and empowering