# Best Practices for Estimating the Company-Specific Risk Premium

## (Part I of IV)

This is a four-part article that sets forth best practices for estimating the company-specific risk premium. The identification and quantification of alpha—or the subject-specific risk component—is sometimes a controversial issue in the private company valuation. This discussion summarizes best practices on what is included in—or should be considered in—the analysis of this K_{e} alpha component (or unsystematic risk component). These best practices discussion is presented in four parts. The first part of the discussion focuses on the factors that analysts may consider in developing the alpha estimate when selecting a K_{e} for a private company valuation. The second part describes the differences between systematic risk and unsystematic risk in the private company valuation. The third part presents the empirical evidence that analysts may consider when estimating the company-specific risk as part of the private company cost of capital measurement. Finally, the fourth part of this discussion summarizes best practices related to the functional analysis in developing the company-specific risk premium estimate.

**Introduction**

Valuation analysts, forensic accountants, financial advisors, industry consultants, economists, or other professionals (collectively referred to here as “analysts”) are often called on to value a private company, business ownership interest, security, or intangible asset. These valuations may be performed for transaction, taxation, financing, business/personal financial planning, litigation, financial accounting, and other purposes. Particularly regarding controversy-related valuations, analysts may serve as either consulting experts or testifying experts.

These analysts apply generally accepted business valuation approaches and methods to value the private company or associated business interest. These generally accepted business valuation approaches include the income approach, the market approach, and the asset-based approach. The generally accepted income approach valuation methods include the discounted cash flow method (sometimes called the yield capitalization method) and the direct capitalization method.

All income approach business valuation methods typically include the application of either a present value discount rate (sometimes called the yield capitalization rate) or a direct capitalization rate. Depending on the measure of income included in the private company valuation, the corresponding discount rate or capitalization rate may be (1) a weighted average cost of capital, (2) a cost of equity capital (K_{e}), or (3) some other opportunity cost or expected rate of return measurement.

When the K_{e} is one component of the discount rate or capitalization rate, there are several generally accepted methods that analysts may apply to measure the private company K_{e}. Several of these methods are summarized in this discussion.

One consideration of just about every K_{e} measurement method is a component related to investment-specific (or subject-specific) risk. This subject-specific risk component is called by many names in the professional literature, including unsystematic risk, asymptomatic risk, nondiversifiable risk, nonsystematic risk, project-specific risk, residual risk, investment-specific risk, and company-specific risk.

In the professional literature, this subject-specific risk component is sometimes called alpha—or the remaining component of risk that is not measured by the other K_{e} components. Whatever name is applied to this risk component, it does relate to a nondiversifiable element of risk. This type of risk is one consideration in the analyst’s selection of the discount rate or capitalization rate to be applied in the private company valuation.

The identification and quantification of alpha—or the subject-specific risk component—is sometimes a controversial issue in the private company valuation. For transaction, taxation, litigation, or for many other valuation purposes, the subject-specific risk is sometimes the source of disagreement between analysts working for either party. Further, the subject-specific risk is sometimes the explanation for any material difference in the private company values concluded by different analysts.

This discussion summarizes best practices on what is included in—or should be considered in—the analysis of this K_{e} alpha component (or unsystematic risk component). These best practices discussion is presented in four parts. The first part of the discussion focuses on the factors that analysts may consider in developing the alpha estimate when selecting a K_{e} for a private company valuation. The second part describes the differences between systematic risk and unsystematic risk in the private company valuation. The third part presents the empirical evidence that analysts may consider when estimating the company-specific risk as part of the private company cost of capital measurement. Finally, the fourth part of this discussion summarizes best practices related to the functional analysis in developing the company-specific risk premium estimate.

**The Private Company Cost of Capital**

The K_{e} is the expected rate of return that an equity investor expects on the capital invested in a particular investment. Equity investors expect to earn a certain return on investment in order to be attracted to that particular investment. In economic terms, the K_{e} for a particular investment is the opportunity cost of capital. That is, the K_{e} is the opportunity cost to the investor—or the rate of return that the investor forgoes by not investing the same amount of funds in the next best alternative investment available at a comparable level of risk.

The K_{e} is a forward-looking expectation of investment return. The K_{e} is the rate of return that the investor expects to receive in the future on that investment. The K_{e} incorporates the following expectations regarding the investment return:

- The “real” rate of return—The amount of return that an investor would expect to earn on a risk-free investment.
- The expected inflation rate—The anticipated depreciation in purchasing power while the investor’s wealth is tied up in the particular investment (i.e., during the expected investment holding period).
- The risk-related return—The return component related to the uncertainty as to when and how much current period income (or capital appreciation) the investor will receive from the particular investment.

The K_{e} metric enables the investor to convert (or to discount) an estimate of expected future income to a present value. This present value procedure allows the investor to (1) make informed pricing decisions with respect to the purchase or sale of the private company and (2) compare one investment opportunity to alternative investment opportunities.

There are several generally accepted K_{e} measurement methods (often called K_{e} measurement “models”). Most of the K_{e} measurement models include the following components: (1) a risk-free rate of return (R_{f}); (2) a general equity risk premium (ERP); (3) an industry-related risk premium (IRP); (4) a size-related risk premium (S_{p}); and (5) an unsystematic risk premium. This discussion generally refers to that unsystematic risk premium as the company-specific risk premium(CSRP).

For the first four above-listed K_{e} components, there are generally accepted data sources that analysts can access to quantify that particular return component. For the fifth above-listed K_{e} component (i.e., the unsystematic risk premium), there is no easily identifiable data source that analysts can access to specifically quantify that particular return component. Of course, there is no empirical data source available as a reference for the subject-specific risk measurement. This is because the subject-specific risk is, by definition, unique to the individual private company.

There are numerous qualitative factors that analysts can consider, and there are several quantitative proxies that analysts can consider developing the fifth K_{e} component estimate. Ultimately, the estimate of the private company unsystematic risk component is a matter of the analyst’s professional judgment.

For purposes of this discussion, the CSRP is referred to and explained in the context of the valuation of a private company ownership interest (e.g., corporation common stock, limited liability company member capital, partnership capital, etc.). That is, the consideration and estimation of a company-specific risk premium is discussed. The CSRP concept may also be considered in the context of other types of investments. For example, when valuing real estate or tangible personal property (e.g., the operating assets of the private company), analysts may consider a property-specific risk premium in the measurement of the discount rate or direct capitalization rate.

The S_{p} and the CSRP are sometimes referred to collectively as the “alpha” or “a” component of investment risk. Alpha is sometimes defined as the excess return on an investment above the rate of return that is predicted by the application of the capital asset pricing model (CAPM).

The term alpha is often attributed to the academic research of Michael Jensen. Jensen taught finance at the University of Rochester between 1967 and 1988. During that time period, Jensen compared the rates of return actually earned on diversified investment portfolios to the rates of return that were predicted by the CAPM. The formula for this comparison—or this measurement of what is often called “Jensen’s alpha”—follows:

a = R_{i} – [R_{f} + β × (R_{m} – R_{f})]

where:

a = Jensen’s alpha

R_{i} = Actual rate of return on the investment

R_{f} = Risk-free rate of return

(R_{m} – R_{f}) = Long-term equity risk premium (measurement of the overall equity risk premium)

β = Industry beta

The investment portfolio’s actual rate of return in excess of the CAPM-predicted rate of return may be positive, negative, or zero. The CAPM measures the risk-adjusted rates of return on investment securities (i.e., the CAPM accounts for the risk of the security). If the security is efficiently priced, then the actual return on investment will be same as the CAPM-predicted return on investment. The alpha in that case (i.e., the actual rate of return equals the expected rate of return) will be zero. If, however, the equity security actually earns a higher rate of return than the CAPM-predicted rate of return, then it will have a positive alpha. A negative alpha indicates that the portfolio did not earn its CAPM-predicted expected rate of return.

While capital markets are typically considered to be efficient (and, therefore, an alpha should theoretically not be observed in the actual application of the CAPM), Jensen noted that an alpha was observable—and measurable.

The discussion below describes several of the generally accepted models that may be applied to measure the private company K_{e}.

Parts II through IV will summarize the empirical evidence that analysts may consider to estimate the CSRP in the private company K_{e} measurement, present several benchmarking procedures—or best practices—that analysts may consider in developing the CSRP estimate, and summarize best practices related to the functional analysis in developing the CSRP estimate.

**Cost of Capital Measurement Models**

Investors and finance professionals have developed numerous models for analyzing and measuring the K_{e} component of an investment in a private company. These K_{e} measurement models include: (1) the dividend yield plus capital gain model (also called the discounted cash flow (DCF) model); (2) the arbitrage pricing theory (APT) model; (3) the Fama-French multi-factor model; (4) the CAPM; (5) the modified capital asset pricing model (MCAPM); (6) the build-up model (BUM); (7) the Duff & Phelps risk premium report model (RPM); (8) the R_{f} plus risk premium model; (9) the Gordon growth model; and (10) many other models.

The following discussion focuses on the application of the BUM, the CAPM, the MCAPM, and the RPM to measure the K_{e} for the purpose of valuing a private company.

This discussion of developing the CSRP estimate applies to all of the above-listed K_{e} models. Due to space constraints, this discussion focuses primarily on the BUM, CAPM, MCAPM, and RPM. However, analysts should be aware that the CSRP (or unsystematic risk premium) is a consideration in just about every discount rate and capitalization rate measurement. And the CSRP is a consideration in just about every private company valuation.

In each K_{e} measurement model, the R_{f} is the rate of return available on a security that the market generally regards as free from the risk of default. Additionally, the R_{f} serves as an inflation adjustment mechanism.[1] Typically, analysts measure the R_{f} by reference to the 20-year U.S. Treasury bond. This is because the 20-year U.S. Treasury bond is often used as the empirical benchmark in the measurement of the general ERP.

In most K_{e} measurement models, the ERP is the incremental rate of return that the investor expects to receive as compensation for the risk of investing in equity investments (e.g., stocks) instead of investing in a risk-free asset. Conceptually, the ERP should be forward-looking. However, most data sources available to measure the ERP actually rely on historical market returns.

One proxy to measure the ERP for U.S. stocks is the Standard and Poor’s (S&P) 500 index. This index is based on the market capitalizations of 500 large companies with common stock listings on either (1) the New York Stock Exchange (NYSE), (2) the National Association of Securities Dealers Automated Quotations (Nasdaq), or (3) the CBOE BZX Exchange.

In many K_{e} measurement models, the ERP is generally calculated as follows:

ERP = R_{m} – R_{f}

where:

ERP = Equity risk premium

R_{m} = Expected rate of return on the stock market

R_{f} = Risk-free rate of return

**Build-Up Model**

The BUM is an additive model that incorporates the various risk factor components of the K_{e,} including (1) an R_{f}, (2) an ERP, (3) an IRP, (4) an S_{p}, and (5) a CSRP.

In the BUM, the K_{e} is generally calculated as follows:[2]

K_{e} = R_{f} + ERP + IRP + S_{p} + CSRP

where:

K_{e} = Cost of equity capital

R_{f} = Risk-free rate of return

ERP = Equity risk premium

IRP = Industry risk premium

S_{p} = Size-related risk premium

CSRP = Company-specific risk premium

**Capital Asset Pricing Model**

According to the textbook *Understanding Business Valuation*, the CAPM was “originally developed in the context of portfolio theory as a way to measure the risk an individual stock contributes to a well-diversified portfolio.”[3]

Further, “CAPM has been modified to be used as a method of determining a discount rate, commonly used in the valuation of larger companies. It has little, if any, applicability to small- and medium-sized businesses …”[4]

The basic CAPM formula does not include an alpha component. This is because the basic CAPM is applicable to measure the expected rate of return of a well-diversified portfolio of publicly traded (i.e., perfectly liquid) securities. For that application, unsystematic risk can be diversified away. Accordingly, an investor in a well-diversified portfolio of publicly traded (i.e., perfectly liquid) securities would not expect to earn a CSRP.

In addition, the CAPM is based on a number of fundamental assumptions. Some of the fundamental assumptions underlying the development of—and the application of—the CAPM include the following:

- Financial markets are competitive and returns provide full range of investment opportunities.
- All investors plan to invest over the same time horizon.
- There are no distortionary income taxes or transaction costs.
- All investors can borrow and lend at the same risk-free rate.
- Investments are infinitely divisible.
- Investors can access all information and are equally well informed.
- The risk measure used remains constant (i.e., a nonvarying beta). That is, the market portfolio that is used to determine beta will consist of all publicly traded securities.
- The variance of returns is an adequate measurement of risk. That is, the CAPM assumes that investment rates of return will be normally distributed.

The above-listed fundamental assumptions of the CAPM typically do not apply in the private company valuation. Further, the fundamental assumptions of the CAPM do not always apply when estimating the K_{e} of a well-diversified portfolio of publicly traded securities. Analysts know this because alpha is still able to be observed in the public capital markets.

The basic CAPM formula is presented below:[5]

K_{e} = R_{f} + β × (R_{m} – R_{f})

where:

K_{e} = Cost of equity capital

R_{f} = Risk-free rate of return

(R_{m} – R_{f}) = Long-term equity risk premium (measurement of the overall equity risk premium)

β = Industry beta

**Modified Capital Asset Pricing Model**

The MCAPM measurement method expands the basic CAPM measurement method. The application of the MCAPM is appropriate for measuring the K_{e} that would be applicable to the private company valuation.

The MCAPM formula is presented below:[6]

K_{e} = R_{f} + β × (R_{m} – R_{f}) + S_{p} + CSRP

where:

K_{e} = Cost of equity capital

R_{f} = Risk-free rate of return

(R_{m} – R_{f}) = Long-term equity risk premium (measurement of the overall equity risk premium)

β = Industry beta

S_{p} = Size-related risk premium

CSRP = Company-specific risk premium (measurement of other risk factors)

Similar to the CAPM, in the application of the MCAPM, the long-term ERP is adjusted by an industry beta. Beta is a measure of the systematic risk (i.e., the systematic risk relative to the return measure of the overall equity market, such as the S&P 500 index) inherent in a company’s investment return.

Published betas for publicly traded stocks typically reflect the capital structure of each respective public company. These betas are often referred to as levered betas, or betas that reflect the amount of the debt/equity leverage in the public company’s capital structure.

**Duff & Phelps Risk Premium Report Model**

Duff & Phelps, LLC, annually publishes a measurement of the ERP based on the factors included in the *Risk Premium Report Study*. The *Risk Premium Report Study* is primarily intended to be used in the development of K_{e} estimates for private companies (1) that are financially healthy and (2) for which a “going-concern” premise of value is appropriate. The *Risk Premium Report Study* develops estimates of the ERP based on eight size factors.

The application of the *Risk Premium Report Study* to measure the K_{e} is often referred to as the risk premium report model (RPM).

The RPM also includes data that may be used to estimate the ERP based on three risk factors. A detailed explanation of the size factors and the risk factors presented in the *Risk Premium Report Study* is beyond the scope of this discussion.

The RPM provides regression formulas that may be used to estimate the ERP, and the risk premiums are “smoothed” across 25 portfolios of different sized companies. To calculate the ERP, the analysts can apply the corresponding regression equation. Alternatively, analysts can select the portfolio that most closely resembles the size—or the risk characteristic fundamental—of the private company.

Analysts rely on the subject investment (e.g., the private company) operating fundamentals and the corresponding regression equation to estimate the ERP over the R_{f} for the investment. Analysts may include a CSRP component to the indicated ERP to measure the investment’s K_{e}.

For example, let’s assume that the analyst is valuing an ownership interest in a private construction company as of June 2017. Let us assume that the company reports a historical five-year average net income of $0.7 million. Applying the RPM regression formulas, the applicable regression equation variables are as follows:[7]

- Constant of 14.722 percent
- Coefficient of -2.565 percent

The calculation of the ERP over the R_{f} in this example is (1) 14.722 percent plus (2) -2.565 percent multiplied by (3) the common logarithm (or Log_{10}) of $0.7 million. The resulting ERP over the R_{f} would equal 15.12 percent.

The RPM relies on an estimated ERP by Duff & Phelps in the calculation of the regression variables. Therefore, an ERP adjustment is needed. One frequently applied procedure for making this adjustment is to reconcile the difference between (1) the ERP used in other K_{e} models (e.g., the MCAPM) and (2) the estimated ERP by Duff & Phelps used to calculate the regression variables.

For example, let us continue with the above illustrative example. Let’s assume that (1) the “ex post” ERP that the analyst relies on in the application of the MCAPM is equal to 6.94 percent and (2) the Duff & Phelps estimated ERP used in the regression variable calculation is 5.00 percent. In this example, the RPM “ERP adjustment” would be 6.94 percent minus 5.00 percent, or 1.94 percent.

The estimated K_{e} in this example would be the (1) R_{f} (let’s assume 2.60 percent) plus (2) the ERP of 15.12 percent plus (3) the ERP adjustment of 1.94 percent plus (4) the CSRP (let’s assume 3 percent). Therefore, the estimated K_{e} would be 22.66 percent.

The MCAPM is one generally accepted model to measure the K_{e} for a private company. In the application of the MCAPM, analysts should understand both the conceptual basis for—and the empirical data considered in the measurement of—the S_{p} and the CSRP.

**Summary**

Analysts often apply income approach valuation methods in the valuation of a private company, business ownership interest, security, or intangible asset. The application of income approach valuation methods typically involves the selection of a present value discount rate or a direct capitalization rate. This first part of a four-part discussion summarizes several of the generally accepted cost of capital measurement models. Regarding a private company business valuation, one component of each cost of capital measurement is the consideration of the CSRP.

To understand both the conceptual foundation and the empirical evidence for the development of the CSRP, it is important to understand the concepts of systematic risk and unsystematic risk. These concepts are discussed in part two of this four-part discussion.

[1] 2018 Cost of Capital: Annual U.S. Guidance and Examples, Duff & Phelps Cost of Capital Navigator.

[2] Gary R. Trugman, *Understanding Business Valuation: A Practical Guide to Valuing Small to Medium Sized Businesses*, 5^{th} ed. (Hoboken, NJ: John Wiley & Sons, 2017)*,* 545.

[3] Ibid., 546.

[4] Ibid.

[5] Ibid.

[6] Ibid., 552.

[7] Duff & Phelps *2017 Valuation Handbook – U.S. Guide to Cost of Capital *(Hoboken, NJ: John Wiley & Sons, 2017), Exhibit A-3.

*Robert Reilly, **CPA, ASA, ABV, CVA, CFF, CMA,** is Managing Director of Willamette Management Associate’ Chicago offices. His practice includes business valuation, forensic analysis, and financial opinion services. *

*Mr. Reilly has performed the following types of valuation and economic analyses: economic event analyses, merger and acquisition valuations, divestiture and spin-off valuations, solvency and insolvency analyses, fairness and adequacy opinions, reasonably equivalent value analyses, ESOP formation and adequate consideration analyses, private inurement/excess benefit/intermediate sanctions opinions, acquisition purchase accounting allocations, reasonableness of compensation analyses, restructuring and reorganization analyses, tangible property/intangible property intercompany transfer price analyses, and lost profits/reasonable royalty/cost to cure economic damages analyses.*

*He has prepared these valuation and economic analyses for the following purposes: transaction pricing and structuring (merger, acquisition, liquidation, and divestiture); taxation planning and compliance (federal income, gift, estate, and generation-skipping tax; state and local property tax; transfer tax); financing securitization and collateralization; employee corporate ownership (ESOP employer stock transaction and compliance valuations); forensic analysis and dispute resolution; strategic planning and management information; bankruptcy and reorganization (recapitalization, reorganization, restructuring); financial accounting and public reporting; and regulatory compliance and corporate governance.*

*Mr. Reilly can be contacted at **(773) 399-4318 or by e-mail to rfreilly@willamette.com.*

*Connor Thurman is a senior associate with Willamette Management Associates. He performs the following types of valuation and economic analysis assignments: valuation of fractional ownership interests in businesses, forensic analysis, valuation of intangible assets and intellectual property, lost profits/economic damages analysis, and appraisal reviews.*

*Mr. Thurman prepares these valuation and forensic analyses for the following purposes: taxation planning and compliance (federal income, state and local property tax, transfer tax), forensic analysis and dispute resolution, marital dissolution, strategic information and corporate planning, ESOP transactions and financing, and ESOP-related litigation.*

*He performs these valuations for the following types of business entities and securities: closely held corporation business enterprises, closely held corporation noncontrolling ownership interests, various classes of common/preferred stock, general and limited partnership interests, professional service corporations, professional practices, and limited liability companies.*

*Mr. Thurman has performed these valuations for clients in the following industries: assisted living facilities, banking, coal power, electrical equipment manufacturers, electric utilities, food distribution, forestry products, grocery stores, logging, marijuana dispensaries, medical practices, natural gas distribution, natural gas power, natural gas transmission, oncology centers, railroads, real estate development, real estate holding, sawmills, telecommunications, transportation, travel agencies, and wineries.*

*Mr. Thurman can be contacted at (503) 243-7514 or by e-mail to cjthurman@willamette.com.*