In response to the article on appraisal arbitrage by Gaurav Jetley and Xinyu Ji of the Analysis Group, about which we’ve posted before, Villanova Law Professor Richard A. Booth now argues in  The Real Problem With Appraisal Arbitrage [via Social Science Research Network] that Jetley and Ji’s charge against the Delaware courts for overly indulging appraisal arbitrage is misdirected.  According to Professor Booth, while Jetley and Ji believe that the Delaware courts incentivize arbitrageurs by using a discount rate lower than the rate typically applied by investment bankers, Professor Booth argues that the bigger and more significant problem is that the Delaware courts additionally reduce the discount rate in the terminal period.  Nevertheless, after identifying what he believes is the Delaware courts’ truly faulty practice, Professor Booth offers up a full-throated defense of the appraisal remedy in general and arbitrage in particular.

Some Highlights of the Article

  • Professor Booth believes that Jetley and Ji’s criticism of the Delaware courts’ use of the so-called supply-side discount rate, rather than the historical rate of return, is overblown.  He agrees that the supply-side rate can inflate a valuation, but not by as great a magnitude as Jetley and Ji seem to believe.
  • In rebutting the argument that so-called arbs “are not themselves long-term common stock investors and should not be so compensated for the time value of their money,” he observes that “they have bought the stock they hold from legacy investors and thus should be entitled to the same package of rights enjoyed by such investors.”  If arbs’ rights were to be curtailed, that would cause stockholders who choose to sell out suffering an even bigger discount, which in turn would raise the price of deals for acquirors, because target stockholders “will be less confident that they will be paid based on the agreed amount when they want to be paid.”  In this respect, arbitrage actually serves the acquirors well.
  • Professor Booth critiques the presumption of fairness that some Delaware cases have accorded to the deal price:
    • First, the deal price may often be too low, as deal price sometimes depends on the percentage of shares bought.  Thus, dissenting stockholders may well be entitled to “higher and higher prices as the public float gets smaller and smaller,” which he finds consistent with the policy objective underlying appraisal: to compensate stockholders for being forced to sell out at a time and/or price not of their own choosing.
    • Second, Professor Booth cautions against according too much weight to the premium paid over market price, as a depressed stock price will naturally warrant a higher premium; in that case the premium is simply “compensation for a discount built into the market price.”
    • Finally, it is inherent in the concept of nearly any acquisition that a buyer is only willing to pay some lesser price than full fair value, in order to extract the expected value to be gained by redeploying the target company to its highest and best use; to that extent, he suggests, “deal price should always be a bit lower than going concern value [emphasis added],” prompting stockholders to hold out.
  • Given these factors, he finds that appraisal performs the valuable function of testing deal price against investor expectation based on CAPM.  He believes that appraisal thus helps drive price toward fairness, as a robust appraisal remedy will induce bidders to pay a fair price up front.  His critique of the court’s further reduction of the discount rate in the terminal period is intended to improve the appraisal process, not undermine it; he encourages the courts to embrace his reforms rather than “hide behind the aw-shucks notion that law-trained judges are ill-suited to address” questions of valuation, finance, and investment banking.

In summary, the author concludes that appraisal arbitrage has gotten a “bad rap” and that appraisal itself works best if arbitrage is made possible; he fears that absent arbitrage, buyers may rely on the hope that potential dissenters will simply decline to exercise any appraisal rights, allowing the bidder to get away with paying a reduced price.

Prior posts in our “Valuation Basics” series have examined the various components of the cost of equity capital under the Capital Asset Pricing Model (“CAPM”). In this post we continue our discussion of those components, focusing on the equity risk premium and its modifying coefficient, the beta.

The CAPM has become the Delaware Court of Chancery’s preferred method for calculating a company’s cost of equity (i.e., the rate of return an investor would demand in order to purchase the company’s stock). A company’s cost of equity under the CAPM is generally the sum of (1) a risk-free rate, plus (2) the equity risk premium adjusted by a beta, plus (3) a size risk premium.

The “equity risk premium” is the difference between the risk-free rate and the expected return from the market. That is, the equity risk premium predicts how a stock index will perform compared to a risk-free investment, such as a treasury bond. Because not all stocks listed on a particular index perform alike, an appraiser valuing a specific company typically adjusts the equity risk premium by a volatility metric called a “beta.” A company with a beta of 1.0 will have an equity risk premium in line with the market. A company with a beta higher than 1.0 will be more volatile than the market, and a company with a beta of less than 1.0 will be less volatile than the market.

Calculating the Equity Risk Premium

The Ibbotson SBBI Valuation Yearbook provides two methods for calculating the equity risk premium: historic and supply-side. The historic equity risk premium looks at stock market returns against risk-free returns dating back to 1926. The supply-side equity risk premium modifies the historic equity risk premium by adjusting the historic equity risk premium for any inflation included in the price-to-earnings ratio. The supply-side method thus produces a slightly lower equity risk premium than the historic method.

Although the historic equity risk premium is the more traditional method, in its recent appraisal opinions the Delaware Court of Chancery has embraced the supply-side equity risk premium as the prevailing methodology. In Global GT LP v. Golden Telecom, Inc., for example, the court adopted the supply-side method over the historic method because the weight of authority supported a rate of return that was closer to the supply-side equity risk premium.

Calculating Beta

Small variances in beta can lead to large discrepancies in the overall valuation of a company. For example, suppose an appraiser determines that, as of the merger date, the equity risk premium for Company X was 6%. A beta of 1.5 would increase that number to 9%. A beta of 0.5 would decrease that number to 3%. Assuming Company X had very little debt, this could lead to an almost 6% swing in the weighted average cost of capital. Not surprisingly, therefore, beta calculations are frequently contested in appraisal actions.

Although the historical market beta of a publicly traded company can be calculated by examining the covariance between the stock’s historical performance and that of the S&P 500, this method is often unreliable when calculating the beta of smaller public companies, where the stock may not trade in an efficient market. An alternative method for calculating beta is to use the published betas of guideline companies to select a beta for the subject company. Because the guideline companies have their own unique capital structures, however, the appraiser must “unlever” the guideline betas to remove the impact that the guideline company’s debt has on its beta. An unlevered beta is calculated using the following equation:

where LB is the levered beta of the guideline company; T is the tax rate of the guideline company; D is the percentage of the guideline company’s capital structure that is debt; and E is the percentage of the guideline company’s capital structure that is equity.

After selecting an appropriate unlevered beta for the subject company based on the unlevered betas of the guideline companies, the appraiser must “relever” the selected beta based on the capital structure of the subject company, using the following equation:

UB*[1 + (1 – T)*(D/E)]

where UB is the selected unlevered beta for the subject company; T is the tax rate of the subject company; D is the percentage of the subject company’s capital structure that is debt; and E is the percentage of the subject company’s capital structure that is equity. This levered beta is then applied to the equity risk premium as part of the calculation of the subject company’s cost of equity capital. This is a generally accepted method for calculating beta under the CAPM, although it is not the only method.


On May 12, 2014, the Delaware Court of Chancery issued its latest appraisal opinion, Laidler v. Hesco Bastion Environmental, Inc., addressing, among other things, the limitations on the use of merger price in an appraisal proceeding.

The petition for appraisal was brought by a former employee of Hesco Bastion USA, Inc. (“Hesco”), which manufactured and sold “Concertainer units” – deployable barriers designed to protect against flooding – in the United States. On January 26, 2012, Hesco was merged into its majority shareholder, the respondent, pursuant to a short-form merger. Immediately prior to the merger, the respondent held 90% of the outstanding equity of Hesco, and the petitioner held 10%. The petitioner refused to accept the $207.50 per share cash consideration offered by the respondent, and instead exercised appraisal rights.

Vice Chancellor Glasscock concluded that the fair value of the petitioner’s shares was $364.24 per share, a 75% increase over the merger consideration. In reaching his conclusion, the Vice Chancellor rejected the respondent’s position that the Court should consider the merger price as persuasive evidence of fair value because it was the result of an arm’s-length negotiation between the controlling shareholder and an independent director. The Court found that it was not an arm’s-length transaction subject to a full market check, but rather a short-form merger consummated by a controlling shareholder who set the merger price. “Under our case law,” the Court stated, “a statutory appraisal is the sole remedy to which the Petitioner is entitled, and to defer to an interested controlling shareholder’s determination of fair value in a transaction such as this would render that remedy illusory.”

Vice Chancellor Glasscock used a direct capitalization of cash flows (“DCCF”) valuation method to determine the fair value of the petitioner’s shares. The Vice Chancellor did not perform a traditional discounted cash flow (“DCF”) analysis because Hesco had not created management projections in its ordinary course of business. The Court relied on the DCCF analysis – which was the sole method applied by the petitioner’s valuation expert and one of the methods applied by the respondent’s valuation expert – determining a normalized figure for annual cash flows in perpetuity and then dividing those cash flows by a capitalization rate. To determine the company’s normalized annual cash flows, the Court averaged the company’s cash flows from the three years preceding the merger. To determine the capitalization rate, the Court subtracted the company’s long-term growth rate (4%) from its weighted average cost of capital (“WACC”) (21.83%). This appears to be the only Delaware case in which the Court based 100% of its valuation on a DCCF analysis.

The Court’s acceptance and application of a DCCF analysis may be significant. The DCCF analysis provides the Court with a methodology for valuing a company where there are no reliable management projections from which to craft a DCF analysis, and where the company is not sufficiently comparable to other companies for the Court to conduct a comparable companies or precedent transactions analysis. Rather than using the merger price as evidence of going concern value, the Court capitalized historical normalized cash flows in perpetuity to independently value the company as a going concern.

The Court’s acceptance of the buildup model to calculate the company’s WACC is also notable. What is the buildup model? The buildup model is similar to the Capital Asset Pricing Model (“CAPM”), except that it adjusts for industry risk by adding an industry-specific equity risk premium rather than using a beta, and also adds a company-specific equity risk premium. In In re Orchard Enterprises, Inc., (Del. Ch. July 18, 2012), then-Chancellor Strine was highly critical of the buildup model, finding that it was not “well accepted by mainstream corporate finance theory” because “its components involve a great deal of subjectivity.” Nevertheless, both parties’ experts used the buildup model in Laidler. The opinion in Laidler, therefore, should not be read as a signal that the Court of Chancery has abandoned the CAPM in favor of the buildup model.


In a prior post, we explained how the Capital Asset Pricing Model (“CAPM”) has become one of the frequently employed methods used by the Delaware Court of Chancery to calculate the cost of equity for the discount rate in a DCF analysis. In this post, we focus on one specific component of the CAPM: the equity size premium.

The equity size premium is a number added to the risk-free rate and the equity risk premium (modified by beta) to reflect additional returns on small companies. The argument is that investors may demand a higher rate of return on small companies than they do for large companies because of the increased risk associated with small company investments. The size premium supposedly quantifies the increased risk.

One method the courts have used to determine the size premium is to refer to the Ibbotson SBBI Valuation Yearbook. The Ibbotson tables, published by Morningstar, contain historical capital markets data that include, among other things, total returns and index values for stocks dating back to 1926. Morningstar recently discontinued the Ibbotson SBBI Valuation Yearbook, which means a court seeking to apply a small-size premium will have to look to other valuation materials for mergers occurring after 2013.

The Delaware Court of Chancery has used market capitalization as the benchmark for selecting a size premium. Thus, the court multiplies the amount of outstanding stock by the market price on the day prior to the merger and determines which Ibbotson decile the company falls under. The court then applies the appropriate size premium from the applicable Ibbotson table. The court may accept adjustments to the Ibbotson size premium if there is evidence of individual characteristics that distinguish the subject company from other companies within the same market capitalization decile.

Some valuation experts in appraisal cases have argued that the problem with this market capitalization approach is that it creates circularity based on the market price of the stock. The Delaware courts have acknowledged that the market price of a stock is not determinative of value in an appraisal proceeding because, among other things, the market price reflects a minority discount. The appraisal statute requires that the company be valued as a going concern, exclusive of any trading discounts. Moreover, the market price of a stock is an unreliable indicator of value when the market is inefficient (which is often the case for small companies) or when other factors affect market price. By relying on the market price to determine the size premium for the discount rate, these experts contend, the court is effectively incorporating that minority discount and inefficient market price into its valuation analysis in contravention of Section 262’s mandate that the company be valued as a going concern. An alternative approach to determine the company’s size for the purpose of ascertaining the small-size premium is to conduct an independent valuation of the company using a non-DCF method, such as a valuation based on comparable companies or precedent transactions. This alternative approach avoids the pitfalls of relying on an inefficient and discounted market price in calculating the company’s discount rate.

The discounted cash flow method, or “DCF”, has become the generally accepted method of valuation in Delaware’s Court of Chancery.  The DCF method seeks to value a company by discounting the company’s projected future cash flows to present value based on the perceived risk of investing capital in that company.  As recently summarized by Vice Chancellor Parsons in Merion Capital, L.P. v. 3M Cogent, Inc., C.A. No. 6247-VCP, “the DCF method involves three basic components: (1) cash flow projections; (2) a discount rate; and (3) a terminal value.”  Slight variances in those components, however, can result in radically different valuations.

Calculating the discount rate is often the most complex aspect of a DCF valuation.  When computing the discount rate, courts are asked to analyze “betas,” “risk premiums” and “size premiums” – terms that are casually thrown around in the valuation world but which are foreign to many lawyers and shareholders unfamiliar with the appraisal arena.

The purpose of the discount rate is to quantify the risk of investing capital in the subject company.  The most common method applied by the Delaware courts in determining the discount rate under a DCF analysis is the weighted average cost of capital, or “WACC.”  In computing a company’s WACC, an appraiser must first determine the company’s capital structure:  how much of the company is equity, and how much of it is debt?  The appraiser then multiplies the company’s “cost of equity” by the percentage of the capital structure that is equity and adds that number to the company’s after-tax “cost of debt” multiplied by the percentage of the capital structure that is debt.  Thus, if a company’s capital structure is 75% equity and 25% debt, its WACC would equal 0.75 times its cost of equity plus 0.25 times its after-tax cost of debt.

While this calculation appears to be fairly simple, the process of determining the company’s cost of equity and cost of debt often polarizes the parties in valuation cases.  The cost of debt typically is easier to calculate than the cost of equity.  In calculating the cost of debt, the court must determine what interest rate a lender would charge the company to borrow money over the long term.

In calculating the cost of equity, the court must determine what rate of return an investor would demand in order to purchase the company’s stock.  Last year, the Court of Chancery has indicated a preference for calculating the cost of equity using the Capital Asset Pricing Model, or “CAPM.”  See In re Appraisal of Orchard Enterprises., C.A. No. 5713-CS.  The CAPM calculates the cost of capital by taking a “risk-free rate,” which is the return that an investor would expect on an investment with no perceived risk, such as a treasury bond, and adding an “equity risk premium” to that rate.  The equity risk premium is the difference between the risk-free rate and the expected return from the market.  However, because not all stocks perform alike, the equity risk premium is adjusted by a coefficient called a “beta.”  The beta measures a stock’s volatility.  A stock with a beta of one will perform in line with the market, but a stock with a beta higher than one will be more volatile than the market and a stock with a beta of less than one will be less volatile than the market.  Finally, when a smaller company is being valued, a “size premium” is added to account for the additional return an investor will require to offset the additional risk of investing in a smaller company.  Although valuation experts sometimes have advocated for adding a company-specific risk premium as well, Delaware courts have generally resisted including such a premium as inconsistent with the conventional CAPM method.

The CAPM cost of equity is thus calculated as follows:

Cost of equity = Risk-free rate + (Equity risk premium x Beta) + Size risk premium

It is important to understand the different WACC variables discussed above when seeking an appraisal.  Even seemingly minor variances in the WACC’s discrete components can have a significant impact on the ultimate valuation of a shareholder’s stock.  Also, while the Court of Chancery has expressed a preference for calculating WACC using the CAPM for the time being, it has also indicated its willingness to adapt to developments in the financial and valuation communities.  Thus, the method for computing the discount rate in appraisal cases is not set in stone and may well evolve along with developments in the financial and economic fields.