Understanding Cost of Capital – Construction of Discount Rates

Part 3 in a Series

This is the third in a series of posts related to enhancing business owners’ understanding of cost of capital. The previous posts discussed Understanding Cost of Capital and Value Enhancement and Equity Capital vs. Invested Capital.

As noted in the second post, the construction of a discount rate is fundamentally a mechanical process of adding components of investment risk that match the risk related to investing funds into the subject company or expected economic benefit stream.  The components are identified within several well known and accepted financial models and leave little debate among financial analysts and valuators as to exactly what components should be considered. However, the difficulty and, thus, the complexity, arises in making a proper determination regarding the size of each of the components, as the higher the level of each component, the higher the overall discount rate and the lower the present value of any future economic benefit stream.

The mechanical process that serves as the basis for most discount rate determinations is best described and understood by looking to the most commonly-used financial models.

Common Models

While numerous formulas and theories have evolved that enable the determination of the risk rates, there are three primary models that have become more accepted and common in usage. All are based on the Capital Asset Pricing Model (CAPM) but, due to limitations with that model, two methods have become more commonly accepted in the valuation of privately held businesses and interests in those businesses. The formulas for these two methodologies are as follows:

Modified Capital Asset Model (MCAPM)

The MCAPM is primarily the same as the CAPM, excepting for the addition of additional risk factors for size and specific industry/company risk.

Build Up Model (BUM)

The BUM is the most common methodology employed by valuation practitioners to estimate the future cost of equity capital for a privately held business. In its most basic form, the method can be expressed in the following formula:

Comparing the Models

Note that the only difference between the two models is the use of beta in the MCAPM, whereas none is used in the BUM. In function, a beta measures systematic risk. Systematic risk is that risk of market movements of particular stock or equity instrument against market movements for the entire market.

Comparisons of such market movements are based on a factor of 1. If the specific stock or equity instrument moves in perfect alignment to the overall market, it will have a beta of 1. However, if the specific company is more volatile than the market, it would be seen as more risky and have a beta greater than 1. Less volatility would result in a beta of less than 1 because it would be perceived to be less risky than the overall market.

In the BUM, there is a presumed beta of 1. If the stock is felt to have greater volatility than the overall market, the additional risk is considered in the specific industry/company risk.

Using the Models to Develop Discount Rates

Due to the similarity between the two methodologies detailed above, the following specific analysis will focus on the BUM.

The rate used to discount the expected future cash flows to present value is the estimated rate of return currently available in the market on alternative investments with comparable risk. The estimate of the discount rate (required rate of return) is derived from market evidence and is the sum of:

  • A risk-free rate, and
  • A premium for risk, which is the sum of the following:
    • An equity risk premium, which is the expected premium over the risk-free rate that investors expect to earn by investing in a broad index of the common stock market (such as the Standard & Poor’s 500 stock composite average),
    • An additional premium for the additional risk associated with the small size of the company compared to the average size of comparable public companies in the marketplace, and
    • An additional premium for other risk factors specific to the company

The risk-free rate is developed by starting with the 20-year U.S. Treasury Bond yield as of the date of valuation. A premium is then added to compensate for differences between average market returns in the stock market and investments in “safer” Treasury bonds. This premium is taken from the Center for Research in Security Prices (CRSP) Deciles Size Premia Study, published annually in the Duff and Phelps (D&P) Valuation Handbook, using a supply-side model for estimating the equity risk premium.

The supply of stock market returns is generated by the productivity of the corporations in the real economy. The model is based on four types of earnings, three of which are supplied by companies (inflation, income return and growth in real earnings per share), and a fourth based on investors’ predictions of future growth in earnings as reflected by the price to earnings (P/E) ratio. The arithmetic average of the supply-side equity risk premium is 6.18%. This premium is added to the bond yield and produces an average market yield.

In the construction of a discount rate that properly compensates potential willing buyers for risks attendant to a specific equity interest, valuation analysts often add a risk premium for “size” for smaller companies. Risk premiums for size are broadly analyzed in the CRSP Deciles Size Premia Study, based on the market value of equity capital. Historical information (as published in the study) verifies that small companies (deemed to have a market capitalization between $1.963 million and $209.406 million) have earned higher rates of return than larger companies over long-term periods.  In its analysis, the CRSP Deciles Size Premia Study has determined that the additional small stock premium to be added to the average market rate of return is 5.6%.

Finally, in determining the adjustment for other risk factors that should be provided for the subject company, specific factors that add additional risk to the potential investment are considered. Typically, company-specific risk factors range between 1% and 5%, but higher adjustments may be valid when facts dictate. Each valuation study is fact-sensitive, and results can vary widely. The following example illustrates the computation of a discount rate under the BUM.

As discussed earlier in this post, and in previous posts in this series, the build-up model simply is an accumulation of investment risk measured in incremental assessments. The most often challenged aspect of this model is that risk element specific to the company under valuation or the expected economic benefit stream. The problems with this determination begin with the fact that the adjustment is clearly and wholly subjective, and continues with the perception that much of the risk inherent in that subjective determination is already considered in the size premium as well as other elements of the valuation process.

Future postings in this series will address additional topics to provide readers with a more detailed understanding of cost of capital and how to tailor business decision making to grow value. In the interim, should you have questions, or comments, please contact Bob Grossman at 412-338-9300.

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Bob Grossman

Bob Grossman

Bob, one of the firm’s founding partners, has over 40 years of experience in public accounting. He specializes in tax and valuation issues that affect businesses as well as their stakeholders and owners. Bob has extensive experience working with the Internal Revenue Services and also serves as an expert witness in litigation matters.

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