Understanding the Cost of Capital in the Income Approach

The cost of capital in the income approach is still one of the more misunderstood and inappropriately applied components of the valuation process.

By Kimberly Linebarger, Financial Analyst

When a marital dissolution includes the valuation of a business, the cost of capital utilized in the income approach is still one of the more misunderstood and inappropriately applied components of the valuation process. It is important that a lawyer in the family law arena has a basic understanding of the cost of capital in order to spot blatant errors in not only the opposing expert’s reports but in their own expert’s reports.

Lawyers need to read their own expert’s reports prior to depositions and request coherent backup of any inputs that do not seem clear; this is true for both the quantitative and qualitative factors. This is not the same as directing the appraiser’s conclusion of value, as independence of the expert’s opinion must always be maintained.

The Two Main Components of the Cost of Capital in the Income Approach

There are two main components to the income approach – the economic benefit, and the expected rate of return required to attract funds to the assets that will produce that economic benefit. The expected rate of return cannot be defined without first defining the benefit stream. In the context of a business, the economic benefit is produced from both the tangible and intangible assets of the firm. It is the future economic benefit stream that is expected from those assets that is the basis of the value of a business; to illustrate this point, Exhibit 1 presents a simplified balance sheet.

The balance sheet is as of a specific point in time, and at that given point in time, it will contain liability and equity holders who have previously supplied funds to the company, as well as the listed assets which are expected to produce an economic benefit back to those liability and equity holders. Generally, the assets on a balance sheet are presented in the order of the expected use of the assets. In other words, the expected amount of time to turn the assets into cash flow (economic benefit stream) increases as you move down the list of assets. The liabilities and equity are presented in the order of the right to claim the economic benefit stream that will be produced by the assets. There are of course a myriad of liability and equity instruments from which a company could choose to fund its operations, and each will fall within the spectrum of claims to the economic benefits.

In a business valuation of a privately held firm, we are most often focused on defining the value to the equity holders. This can be done in two ways: by determining the economic benefit expected to be distributed directly to them, most often referred to as the net cash flow to equity; or by looking at the expected benefit to both the debt capital and equity capital, which when combined is referred to as the invested capital, then subtracting out the debt portion to arrive at the equity interest (please see Exhibit 1 for illustration). Once we have determined the appropriate cash flow, either net cash flow to equity or invested capital, we can define the cost of capital applicable to the cash flow.

The second main component of the income approach is the expected rate of return. Each component of the capital of the firm will have a different required rate of return based on the inherent risk of that component. Exhibit 2 illustrates this relationship. The lower the degree of risk of receiving the future economic benefit, the lower the expected rate of return. The higher the degree of risk of receiving the future economic benefit, the higher the expected rate of return. In valuing a privately held company we often derive the value of the common equity portion of the firm’s capital, which most often has the highest degree of risk and thus the highest expected rate of return. “Risk can be defined as the degree of uncertainty (or lack thereof) of achieving future expectations at the times and in the amounts expected.” (1)

The expected rate of return that the market participants require in order to attract funds to a particular investment is referred to either as the cost of capital or the discount rate, and includes both the time value of money and risk. The main characteristics of the cost of capital include the following:

• A function of the investment not the investor.
• An expected rate of return; it is forward looking.
• Based on market value; not book value, par value, etc.
• Usually denominated in nominal terms (i.e., inclusive of inflation) instead of real terms. Also, this is the same for the projected net cash flow

The Two Most Commonly used Techniques to Estimate the Appropriate Discount

The two most commonly used techniques to estimate the appropriate discount rate for the previously determined economic benefit stream are the weighted average cost of capital (WACC), which is applied to the net cash flow to invested capital, and the cost of equity, which is applied to the net cash flow to equity.

The WACC is the blended overall expected rate of return for all of the components of the firm’s capital; i.e., interest-bearing debt and common equity. For a privately held company, the cost of debt is most often derived from the terms outlined in the specific debt instruments held by the firm. On the other hand, the cost of the common equity of a privately held company is not directly observable and it must be estimated. The estimate is based on market data from actively traded companies combined with quantitative and qualitative analysis of the subject company.

Models used to Estimate the Cost of Equity for a Privately Held Firm

The two foremost models used to estimate the cost of equity for a privately held firm are the capital asset pricing model (CAPM) and the Build-up Model (BUM). The basic equations are very similar and theoretically, they should arrive at the same estimate of the cost of equity. The main differentiating factor is how industry risk is incorporated in the equation.

There are two leading publishers of information used to determine the cost of equity. They are the Duff & Phelps Risk Premium Study (2) and Morningstar’s Ibbotson (3) data. Each publisher provides data to be used in both the CAPM and the BUM.

The equations and variables are as follows (4):

BUM: k_e = R_f + RP_m ± RP_i + RP_s ± RP_u

Expanded CAPM: k_e = R_f + (RP_m)β + RP_s ± RP_u

k_e = Expected (market required) rate of return on equity.

R_f = Risk-free rate is usually the yield to maturity on a 20-year U.S. Government security as of the valuation date.

RP_m = Equity risk premium (ERP) is defined as the extra return (over the expected yield on a risk-free security) investors expect to receive from an investment in a diversified portfolio of publicly traded common stocks.

β = Used in the CAPM, beta represents a security’s excess returns regressed against the market portfolio’s excess returns for a specific publicly traded company. Comparable company betas are used to arrive at an estimate of beta for a privately held company.

RP_i = Used in the BUM, the industry risk premium is the degree of risk assigned to the industry of the subject company as compared to the average risk of other companies in the same size category.

RP_s = Size premium is the extra return the market requires due to the increased risk inherent in small companies as compared to large companies.

RP_u = Company-specific risk premium is the extent that the subject company may be considered more or less risky than the population of companies from which the ERP, industry risk premium and size premium were drawn.

Cost of capital questions a family lawyer might consider when reading a business valuation include:

• Are the inputs, and thus the conclusion of value, well supported?
• Was the model(s) used to derive the cost of equity in conformance with a learned treatise?
• Was more than one source of data utilized?
• If more than one estimate was calculated do they coincide or are they divergent?
• Do the cash flow stream and the cost of capital match?
• Do the variables within the cost of capital match?
• Do the assumptions and ultimate conclusion make sense given the nature of the investment?

The Cost of Capital in the Income Approach and the Facts of each Business

Every business valuation engagement and the facts of each business valuation are different. This is why it is critical that the business appraisal have a coherent and substantiated conclusion of value. The main characteristics of the cost of capital within the expert’s report should be reviewed, not just to ensure they are internally consistent, but that they are also congruent with professionally established definitions. A basic understanding of the variables utilized in the income approach to determine the cost of capital will aid in the understanding of the expert’s report, determining if the cost of capital was developed using accepted business valuation methodologies, and whether the conclusion of value will hold up in court.

1.Judge David Laro, Dr. Shannon Pratt, Business Valuation & Federal Taxes, 2e, John Wiley & Sons,2011: P. 141.

2.  Duff & Phelps Risk Premium Study, please visit www.duffandphelps.com for more information.

3. Morningstar’s Ibbotson, please visit http://corporate.morningstar.com for more information.

4. Dr. Shannon Pratt and Roger Grabowski, Cost of Capital, 4e, John Wiley & Sons, 2010: Chapter 7 and 8.

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Kimberly Linebarger, ASA, AVA is a senior financial analyst with Shannon Pratt Valuations and is a contributing author to multiple publications on business valuation. www.shannonpratt.com..

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