Case Studies & Papers

The following represent some case studies of pragmatic approaches Conn Valuation Services Ltd. has applied in real-world problems.  They are written in a quasi-academic style, however, they are meant to serve as a practical solution for financial measurement issues often encountered when attempting to merge financial theory with actual data.

Click on the title to view the case study in PDF format.

Ethics - Are the Courts Unintentionally Promoting Unethical Behavior In Business Valuators?

Are the Courts Unintentionally Promoting Unethical Behavior in Business Valuators? This article ponders the inherent role conflict faced by the Expert Witness / Business Valuator.  She owes a duty of absolute independence to the Court and yet is engaged by an Advocate who, in turn, has a strong bias in the ultimate legal outcome.  The exercise of professional integrity often requires experts of all types to be dedicated towards interests much larger than just those of the engaging party.  Often the roles of simultaneously serving the needs of society as well as the partisan interests of the Client will clash.  In the case of the Business Valuator, this role conflict is heightened because she will only be engaged by the Client on the tacit understanding that she can be of assistance to the Client’s interests and yet this very motivation runs contrary to the Court’s expectations. “The process of appraisal calling for the court to derive a single best estimate of value based on the ‘expert input’ of finance professionals paid to achieve diametrically opposite objectives” (Vice Chancellor Strine).  The problem is exacerbated by the fact the honest valuator cannot anticipate the outcome of her opinion – there is no way to sidestep all the due diligence and in depth analysis required.  This means that the Client must essentially engage the Expert on faith – usually incurring substantial fees before the final opinion can be disclosed.

This paper considers all of these competing motivations and cites a random selection of cases where the Courts have been increasingly skeptical of the Business Valuator’s ability to remain unbiased.  The concept of Limited Bias is introduced, founded upon the large number of cases where the opposing valuators have arrived at significantly divergent opinions of ultimate value.  The paper concludes that the system of a single court-appointed joint Business Valuator would hold many advantages over the existing practice and would realign the Expert’s motivation with the interests of the Court.

[As published in Journal of Business Valuation and Economic Loss Analysis, Volume 12, Issue 1 (de Gruyter retains all copyrights)]

Acquisitions & Divestitures – Reducing the Purchaser’s perceived risk will benefit both parties

This article considers why the Vendor’s predisposition towards non-disclosure may often work against him in negotiating the highest price in a business sale.  Finding effective ways of transferring perceived risk to the most appropriate party will increase net benefits to both Vendor and Purchaser.

Acquisitions & Divestitures – Valuing Acquired Tax Loss Carry-Forward Pools

This article examines some of the CRA rules with respect to ‘Acquisition of Control’ and considers those circumstances when the cumulative tax losses of the target firm may be deductible to the acquirer.  A simple methodology is suggested in arriving at an estimated value of the acquired taxes losses.

Cost of Capital - In Defence of the DCF Methodology

This paper is in reply to Messrs. Schwartz & Bryan’s “Campbell, Iridium and the Future of Valuation Litigation" as published by the American Bar Association's: Business Lawyer magazine.  The basic contention of that work is that paid professional valuation experts should not automatically be admitted to the financial litigation arena when there is sufficient Market Based evidence upon which the Court can draw its own conclusions of value.   The tacit complaint is that unscrupulous valuation professionals have been using the DCF method to achieve their own purposes and hinder the trier of fact.

The premise of my paper is that the DCF methodology is the point of origin upon which all other business valuation methods (including the Market Approach) is based.  Therefore let’s ban the unscrupulous valuator from giving expert testimony – not the DCF methodology.

[As published in The Value Examiner, May/June 2013] 

Chinese Translation (as translated by IACVA)

In Defence of DCF (NACVA Webinar of Oct. 23, 2013) - Power Point Slides

Cost of Capital - Importance of MM Propositions I & II in the valuation of private businesses

This paper is an overview of the famous Modigliani-Miller Propositions I and II and their impact upon the determination of a lower bound on costs of capital.  Fifty years have transpired since the introduction of MM I&II but these important theorems about capital structure irrelevance still have important implications in virtually every business valuation.  A practical example is given as to how MM I is based upon a no-arbitrage methodology.  

[As published in The Value Examiner (Cover article), March/April 2013] 

Cost of Capital - Convertible Bonds: Black Scholes vs. Binomial

This paper considers the usefulness of Black Scholes in the valution of a plain-vanilla Convertible Bond. The Black Scholes results are compared against a 128 step binomial model and sensitivity to changes in the underlying variables is tested. Ultimately, the conclusion reached is that, while Black Scholes is not useful in pricing anything but the most unrealistically simple of convertible securities, it does offer a reasonable and quick approximation to arriving at this basic starting point. In this sense, it can be used as a redundant check upon the base-case binomial model, before the more complex attributes are priced in.

Cost of Capital - EDITORIAL: Why All the Fuss about Total Beta?

This is my guest editorial as it appears in the January/February 2012 Value Examiner Magazine. It provides an overview of the two opposing points of view with respect to Total Beta and the Total Cost of Capital (TCOE) application. Ultimately my conclusion is that both sides suffer unavoidable weaknesses. The "Pro" side lacks empirical evidence supporting the assumed rate of non-systematic risk. And, the "Con" side continues to attempt to disprove TCOE via Modern Portfolio Theory (MPT) which, by definition, was advanced in order to measure systematic-risk only.

[As published in The Value Examiner, Jan/Feb 2012]

Cost of Capital - A Primer On the Nature of Idiosyncratic Risk and Volatility

This paper deals with the apparent contradiction between traditional portfolio theory that adamantly maintains that idiosyncratic (or Company-Specific or Non-Systematic) risk is not rewarded in the public security markets and yet, is still so prevalent in all the public data.Various methods of measuring the degree of idiosyncratic price movements in ex post securities data are discussed.

[Abridged version as published in The Value Examiner, Sept/Oct 2011]

Cost of Capital - Total Beta and TCOE: Why TCOE May Not Be Defensible

In consideration of the professional controversy that has been ranging since 2007 and the introduction of the Butler-Pinkerton Model, this paper attempts to assess the practical utility of Total Beta and the TCOE (Total Cost Of Equity) formula to the everyday practitioner. This paper employs pragmatic analogies and transparent empirical evidence to form its conclusions. [Abridged version as published in The Value Examiner (Cover article), Jan/Feb 2011]

Cost of Capital - Stock Price Volatility: Implications to Business Valuation

This paper examines the relationship between stock volatility, asset risk and cost of capital. Historic asset volatility profiles can provide important qualitative insight as to the relative riskiness of the target asset compared with other industry peers and the Market Index.

Cost of Capital - Risk Quantification; The Semi-Variance and Other Tools

This paper considers the nature of risk quantification in general and the comparison of two independent project cash flows in particular. The Semi-Variance and other statistical techniques are used in order to attain a better understanding of relative risk - even when Market indicators of the cost of capital are not available. The interdependency between estimate dispersion and the risk-adjusted discount rate is discussed.

Cost of Capital - Finding the Minimum Portfolio Variance using MS Excel

This paper is a demonstration of a practical approach to find the minimum portfolio variance of any combination of securities using Microsoft Excel © array functions.The benefits of diversification are highlighted.A Monte Carlo methodology is employed to provide an approximate proof of the minimum variance findings. 


Cost of Capital - A Rebuttal of Bulter-Schurman's Private Company Total Beta

This paper was written specifically as a rebuttal of the Butler-Schurman article: A Tale of Two Betas that appeared in the Jan/Feb issue of The Value Examiner (NACVA's professional magazine).In Tale of Two Betas Butler-Schurman propose the use of a private company total beta that takes into account the diversification of the entrepreneurial investor. This article points out the primary flaw with that scheme:the public markets would be expected to price idiosyncratic risk as if all investors were wholly undiversified whereas entrepreneurs would, for some inexplicable reason, take heed of their degree of diversification when purchasing private equity firms.

[As published in The Value Examiner, March/April 2011 Issue]

Cost of Capital - The Price-Earnings Ratio and its Common Misapplication in Business Valuations

This paper considers how widespread the P/E Ratio has become in the financial press and how unreliable this statistic is in all but a very few business valuation situations.

Cost of Capital - Capitalized Earnings Method vs. Discounted Cash Flow

This paper compares the single-period capitalized earnings method of business valuation against the discounted cash flow (DCF) approach.  How likely is it that one approach consistenly delivers a more accurate esimtate of value than the other?  A monte carlo simulation methodology is employed in addressing this question.

Cost of Capital - On The Practicality of Using A Single Point-Estimate of The Discount Rate in Long-Term Cash Flow Valuation

This paper ponders the outcome reliability of a single-point discount rate estimate that is really meant to reflect a range of discount rates that are expected to be incurred throughout the life of the underlying cash flows. The appendix speaks to the difficulty of imputing discount rates from only observing publicly available market data.

Cost of Capital - Junior Oil and Gas Firms Cost of Equity Approximation: A Continuation of the pragmatic use of the Sharpe Ratio employed June 2008;

This paper serves as an update to 'Approximating the minimum Cost of Equity for junior oil and gas firms during times of high commodity price uncertainty'. It re-examines the applicability of ex-post financial measures in the face of the severity of recent market declines.

Cost of Capital - Approximating the minimum Cost of Equity for junior oil and gas firms during times of high commodity price uncertainty

This paper considers the difficulty in applying traditional cost of capital techniques when annual stock price volatility for junior oil and gas plays commonly exceed 100%. The Sharpe Ratio is used to determine the Market price of risk and in turn set a minimum expected cost of equity.

Cost of Capital – Regressing Beta from Historical Stock Prices

This paper considered the effects of non-systematic price impacts on the accuracy of regressed stock betas.  The study design begins with a hypothetically ‘pure’ stock history, and then adds random noise in order to test the impacts on the resultant Betas.

Cost of Capital—R-Squared & the T Statistic as an indicator of Regressed Beta Accuracy

This paper is a continuation of “Sensitivity of Stock Betas to Non-Systematic Price Changes” and attempts to empirically show the predictive qualities of R-Squared and T Statistic hypothesis testing to the accuracy of regressed Betas.

Cost of Capital – Measuring the Error of Estimation in Grouped Stock Betas

This paper is the conclusion of a three-part series that deals with identifying, measuring and mitigating the impacts of non-systematic price distortions to regressed stock betas.

Cost of Capital—Use of Black’s Model in restructuring capital of income trust

This paper describes the application of Black’s interest rate-cap model in the equity restructuring of a mid-size income trust.  The conclusions show that derivative models can be successfully used as normative predictors of hybrid capital structures.

Cost of Capital - Misapplication of WACC in the assessment of Project Value

This paper identifies an oft repeated error in using firm-wide Weighted Average Cost of Capital to evaluate the price of target acquisitions or assess the value of new projects or assets.

Cost of Capital—Does the Implied Private Company Pricing Line Make Sense?

This paper is the first of three that addresses the Implied Private Company Pricing Line (IPCPL) as created by Messrs. Dohmeyer, Butler & Burkert and asks the question whether this methodology for pricing small private firm pre-tax risk rates makes any sense.  This paper deals with the issues of using Revenues as a yardstick for Risk and also the applicability of the double-Lehman Curve in the pricing of this type of risk.

[As published in The Value Examiner (Cover article), Jan/Feb 2016]

Cost of Capital—Does the Implied Private Company Pricing Line Make Sense - Part II?

This paper is the second of three that addresses the Implied Private Company Pricing Line (IPCPL) as created by Messrs. Dohmeyer, Butler & Burkert. This installment deals with the Gorshunov Chart and shows that a high correlation between the Operating Profit Margin and Price-to-Sales Margin does not imply any degree of correlation between Revenues and the Cost of Capital. Further, the paper uses IPCPL datasets to show that there is only a very weak association between Revenes and Enterprise Value.

[As published in The Value Examiner (Cover article), May/June 2016]

Cost of Capital—Does the Implied Private Company Pricing Line Make Sense - Part III?

This is the third and final critique of the Implied Private Company Pricing Line (IPCPL) created by Messrs. Dohmeyer, Butler & Burkert. This paper addresses what Conn sees as the third most significant failing of the IPCPL methodology - which is the use of an inordinately long (13 to 15 years) look-back period in the derivation of Data Point 1. In fairness to The Value Examiner, it should be noted that the IPCPL authors were invited to publish a rebuttal to both of the Part II and Part III critiques, but have thus far declined to do so.

[As published in The Value Examiner, Sep/Oct 2016]

Industry Specific—Modelling WTI Oil Price Movements and Markov Chains: Paper I 

This paper is the first in a series of two that ultimately are dedicated towards using Markov Probabilities as means of modelling future WTI oil prices.  This paper specifically asks the questions 'Do WTI Prices Move in a Markov Chain?'  The focus of this work is to test whether the past 26 years of WTI price movements demonstrate Markov properties via an intuitive statistical approach as well as via the application of the chi-square test.  Rudimentary characteristics of matrix algebra are discussed such the the sequel paper can deal entirely with the Monte Carlo modelling of the Markov probabilities. 

Industry Specific—Modelling WTI Oil Price Movements and Markov Chains: Paper II 

This is the conclusion of a two paper series that deals with modelling future WTI oil prices.  All the preliminary considerations of Markov probabilities are dealt with in Paper I.  This paper deals with the construction of the model.  An added complexity is the stochastic nature of volatility in WTI prices and a means of randomizing the degree of price volatility is introduced.  Future price paths are derived from the frequency distributions of prior price deltas.

Industry Specific—Method of modeling expected future growth in appreciating assets

This paper considers the indisputable fact that the future growth expectations of appreciating assets (specifically land, in this case) must be inherently reflected in their current market prices.  It offers one possible method of modeling this growth profile using the Gordon Growth Model. 

Industry Specific - Lease, Finance or Purchase Decisions: Commercial Aircraft

This paper describes how the three financing options available in acquiring commercial aircraft; Leasing, Borrowing or Purchasing Outright, often have significantly different after-tax (Canadian) financial implications.

Industry Specific—Use of Monte Carlo Simulation in Expected Cost/Revenue Planning

This short newsletter is a brief description of the usefulness of a Monte Carlo approach to the Best/Worst/Expected case Revenue & Cost planning exercise.  It is specifically targeted to the charter aviation operator and explains how simple random simulation can substantial improve the predictive qualities of your operational budgets.

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