Our “Valuation Basics” series has focused on the various components of a discounted cash flow analysis under the income approach, which seeks to value a company based on the present value of its projected cash flows.  This post and those to follow in this series will now move away from the income approach and instead examine two “market” approaches: (1) the comparable companies method; and (2) the precedent transactions method.  Under these approaches, we look at how the market values similar companies in order to determine the value of the subject company.

The purpose of a comparable companies analysis is to derive a value for the subject company based on the stock price of similar publicly traded companies.  Accordingly, the first order of business is to select publicly traded companies that are “comparable” to the subject company.  No two companies are truly identical, so an appraiser must use her judgment to select companies that have sufficiently similar characteristics to the subject company from which meaningful valuation data can be extracted.  The more similar the selected companies are to the subject company, the more weight the court is likely to place on a comparable companies valuation.

After selecting the applicable comparable companies, valuation multiples are derived for each of the comparable companies by dividing their respective enterprise values (“EV”) by appropriate financial metrics, such as revenue or EBITDA.  The comparable companies’ stock price on the valuation date is used to calculate their enterprise value.  So, for example, assume that Comparable Company A has a stock price on the valuation date that yields an enterprise value of $2 billion.  Assume further that Comparable Company A has reported revenue for the last twelve months (“LTM”) of $500 million.  Comparable Company A’s LTM EV/revenue multiple would be 4.0.

Next, the valuation multiples of the comparable companies should be adjusted to account for differences between the comparable companies and the subject company.  For example, if the comparable companies have a large amount of outstanding debt but the subject company is debt free, the valuation expert might adjust the valuation multiples to account for the subject company’s more attractive balance sheet.  In our example, if the median LTM EV/revenue multiple of Comparable Companies A, B, C, and D is 3.8, the appraiser might select an LTM EV/revenue multiple of 4.0 to apply to the subject company if there are factors warranting an upward adjustment based on the subject company’s superior performance.

Once the appraiser has determined the correct valuation multiples, those multiples can be applied to the relevant financial metrics of the subject company to calculate the market value of invested capital of the subject company.  Using our example above, if the subject company had reported revenue of $750 million for the previous year, its market value of invested capital based on the LTM EV/revenue multiple of 4.0 would be $3 billion.  To derive the equity value of the subject company, the subject company’s interest-bearing debt should be subtracted.

Appraisal experts typically adjust a comparable companies valuation to account for the inherent minority trading discount reflected in the valuation multiples.  The stock price that is used to derive a comparable company’s enterprise value is based on transactions involving non-controlling ownership interests traded on the stock market.  Accordingly, the Delaware Court of Chancery has allowed appraisers to correct for this lack-of-control discount by adding a premium to the equity value derived from a comparable companies analysis.  While there is no set premium, the Delaware Court of Chancery has accepted as appropriate a premium of 30%.

In recent years, the Delaware Court of Chancery has become more exacting in its acceptance of comparable companies valuations in appraisal cases.   In cases where the court has rejected a comparable companies valuation proffered by a party’s expert, the court has often expressed its concern with the numerous subjective judgment calls made by the valuation expert in arriving at his comparable companies valuation.  Why did the expert choose some companies as comps but not others?  Why did the expert use certain multiples and not others?  Why did the expert adjust the selected multiple upward or downward rather than simply apply the mean or median multiple?  To address these concerns, valuation experts in appraisal cases should carefully describe in their expert reports not only the subjective judgment calls they made in conducting their comparable companies analysis, but also their principled basis for doing so.

In our next post in the Valuation Basics series, we will explain how the comparable transactions analysis differs from the comparable companies approach.

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.


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.

In a prior post we mentioned the three basic components of a discounted cash flow (“DCF”) valuation analysis — cash flow projections, a discount rate, and a terminal value — and explained how to calculate one of those components, the discount rate. In this post, we tackle another component, the terminal value.

In a typical DCF analysis, the appraiser will discount to present value the cash flows that the company projects it will receive over a discrete period. Because most companies’ financial projections forecast only a few years into the future, usually five years at most, an appraiser must add a “terminal value” to the projected cash flows in order to value all of the company’s future income beyond the initial near-term projections.

One common method applied by the courts in calculating that terminal value is the Gordon Growth Model. The first step of the Gordon Growth Model is to determine the company’s expected income for the year immediately following the initial discrete projection period. A “perpetuity growth rate” is applied to that projection income to estimate the company’s long-term growth. The perpetuity growth rate is determined based on a number of considerations, such as the company’s historical and expected future performance, the rate of inflation, and other factors. That amount is then capitalized using a capitalization rate that is equal to the discount rate minus the perpetuity growth rate. Thus, if Company A has a cost of capital of 10%, is expected to make $10,000,000 in normalized economic income in the year following its discrete projection period and is expected to grow past the discrete projection period at a rate of 5%, its terminal value would be $210,000,000, calculated as follows:

$10,000,000 * (1 + 0.05) =      $210,000,000

0.10 – 0.05

Because the terminal value is calculated as of the end of the discrete projection period, it must be further discounted to present value as of the valuation date.

A common misconception when calculating terminal value is that by applying a “perpetuity growth rate,” the court is assuming that a company will grow into perpetuity. As a practical matter, the perpetuity growth rate merely forecasts the company’s long-term growth, not its literal perpetual growth. When discounted to present value, most of a company’s terminal value is typically realized within the first ten to twenty years following the end of the discrete projection period.

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.