estimating the weighted-average cost of capital

By L. Schall

This note explains how to estimate the discount rate (weighted average cost of capital, or WACC) for a firm or for a particular investment (e.g., a machine). Section I discusses the estimation of the WACC for a publicly traded company for which the analyst believes that the observable market value equals intrinsic value. In this case, the purpose of estimating the WACC is to determine the discount rate for computing the NPVs of newly proposed investments that have risk and financing similar to the existing company. Section II explains how to estimate the firm’s WACC if the purpose is to value a publicly traded company for which market value may significantly differ from intrinsic value, or to value a privately held company for which there is no observable market price. In this case, comparables (firms similar to the one being valued) are employed in the estimation procedure. Section III discusses the estimation of the WACC to be used as the discount rate to value a new project that has a risk that differs from that of the firm as a whole.

Part of the WACC estimation process involves the estimation of beta, a measure of a stock’s (or any asset’s) risk. In most cases, the beta for a stock should be obtained from an outside source that specializes in risk analysis and beta estimation (such as Bloomberg, BARRA, or Ibbotson Associates). In fact, a cost of capital estimate can also be purchased (for example, from Ibbotson Associates). Why then should a financial manager be concerned with the WACC estimation process? There are at least three reasons. First, most companies compute their own discount rates, depending on an external information source largely to obtain market betas and interest rates. It is the job of the company’s finance staff to use these data to compute discount rates for valuation purposes. This note explains how that is done. Second, a company’s management should be the most informed about the drivers of the firm’s business risk. Even if an outside consultant computes the company’s cost of capital, management will have to provide relevant information to enable that estimate. A financial manager who does not understand what a WACC is and how it is estimated will be at a loss in providing the key information required to generate a defensible WACC estimate. Third, knowledge of what constitutes “risk,” how it arises, and how it affects value (the WACC is a risk-adjusted discount rate for computing value), is essential in managing and controlling risk so that equity value is maximized.

I. THE WACC OF A CORRECTLY VALUED PUBLICLY TRADED FIRM

Suppose that management wants to compute the after-tax WACC for the company in order to evaluate new investments that will have similar business risk and financing as the company as it currently exists. Management believes that the prevailing market values of the company’s traded securities (equity, debt, etc.) are close to their intrinsic values.

The after-tax WAAC, , is defined as:

= (1  T) + [1]

, , are the current market values of the firm’s equity, debt and complex financing, respectively; and , , and T are the equity cost of capital (equity discount rate), the debt cost of capital (debt discount rate), the complex financing cost of capital (complex financing discount rate), and the firm’s tax rate, respectively. The firm’s tax rate T can often be determined from the company’s annual report or 10-K. If not, the tax rate could likely be obtained from an investment bank that follows the company, or from the company itself. In Sections I.1 and I.2 we discuss the estimation of the other terms in equation [1].

I.1. Determining the , , and : Market value data for the firm’s publicly traded securities are readily available by simply obtaining the market quotes and multiplying by the quantity of the security that is outstanding. If all the company’s securities are publicly traded, , , and are therefore easily computed quantities.

Valuing securities that are not publicly traded is more difficult. For securities that do not have option characteristics (convertible securities, for example, have embedded options), the valuation is a fairly straightforward exercise. For example, valuing a particular issue of non-traded non-convertible debt can be performed as follows. [a] Analyze the debt’s risk level by studying the underlying business risk and financial structure (debt to assets level) of the company, and the specific provisions in the debt agreement (priority, nature of collateral, etc.). Financial ratios are often used in such an analysis. [b] Given the findings in [a], rate the debt (e.g., comparable to Standard and Poor’s A or BBB) and determine the yield to maturity on debt with that rating and a similar term to maturity and pattern of interest and principal payments, where yields to maturity can be obtained from Bloomberg and various other sources. [c] Value the debt by discounting the debt’s promised future interest and principal payments using the yield to maturity estimated in [b]. To illustrate, suppose that the firm has a debt issue X that would justify a Standard & Poor’s rating of A, that matures in 5 years, and that pays interest semi-annually and all principal in 5 years. Assume that such debt would have a current yield to maturity of 8 percent. To value the X-debt, the debt’s promised interest and principal would be discounted using a discount rate of 8 percent.

The valuation of non-traded complex financing (financing other than common stock and non-convertible debt) depends on the type of financing. For example, preferred stock is rated very much the way debt is rated. So, imagine a non-callable, non-convertible preferred stock issue paying a fixed dividend and justifying a BB rating, and assume that a BB rating implies a prevailing market dividend yield (dividend/price) of 6 percent. The estimated value of the preferred would be the present value of the forecasted future dividend discounted at a 6 percent rate (price = [annual dividend/.06]).

Financing with option properties (convertibles, warrants, firm issued puts, etc.) must be valued using an option-pricing model. Option valuation will not be covered here.

I.2. Determining the Costs of Capital , and

Estimating Equity Rate: Equity discount rate (cost of capital) is typically estimated using the CAPM. The CAPM equation for the equity cost of capital for firm X is:

= + [] [2]

Rate is the market rate of return over the coming time period (e.g., a year), which is unknown now and has a probability distribution. Quantity in [2] is the mean of the probability distribution of ; is the “expected rate of return on the market.” Rate is the risk-free rate (usually estimated using the rate on a U.S. Government security). Parameter is the risk parameter (the beta) for stock X; it indicates the stock’s risk from an investor portfolio standpoint. Beta reflects the degree to which firm X’s stock moves with the overall stock market. Quantity [] in [2] is referred to as the “equity premium.” The equity premium is the amount by which the expected return on the entire market of risky securities exceeds the rate on a “riskless” asset (such as a U.S. Government security).

A publicly traded firm’s stock beta (), and the rates on U.S. Government securities, can be obtained from Bloomberg, Value Line, Standard & Poor’s, and other sources. The equity premium ([]) can be obtained from Ibbotson Associates (and other data services). So, for a given publicly traded stock, equation [2] is readily solved.

Stock betas are estimated using historical (past) stock price data. As a word of caution, the beta estimate for a particular firm’s stock (e.g., Intel common stock) will differ among information services that provide betas. This is because the services use different stock portfolios to represent the market (the S&P 500, the Wilshire 5000, the Value Line stock universe, etc.) and use different historical time periods to estimate betas.

Estimating Debt Rate : Rate is the interest rate that the company would have to pay on incremental borrowing (if there are multiple issues of debt, it is a value-weighted average of the incremental rate on each issue of debt). The rate on incremental debt of a particular debt issue is the yield to maturity on that debt. If the debt is publicly traded, that rate is observable. If the debt is not publicly traded, then an appropriate procedure would be the one described in Section I.1 above (rating the debt based on the company’s business risk and financing, and the debt’s particular characteristics, and then determining the prevailing yield to maturity on similar debt). The debt cost of capital can also be estimated using the CAPM (estimate the debt’s beta and plug into the CAPM formula).

Estimating Other Financing Rate : The procedure for estimating the cost of capital on complex financing depends on the nature of the complex financing. For non-callable, non-convertible preferred with a constant dividend, [dividend/market price] is the cost of capital. Complex financing with option characteristics (convertibles, etc.) should be evaluated using an option-pricing model. An investment or commercial bank can assist in estimating the incremental cost of a given type of complex financing.

I.3. Illustration

Main Corporation’s management wants to estimate the company’s after-tax WACC. Main is publicly traded and management believes that the market prices of the firm’s securities approximate their intrinsic values. Main’s financing (using market values) is = $300 million, = $150 million, and = $50 million. It is expected that the firm’s financial structure (financing proportions), capital costs, and tax rate (T) will not change significantly over time. Main’s marginal borrowing rate is 8% (so let = 8%), and the cost of capital for Main’s complex financing is 12% ( = 12%). The beta on the company’s stock, , equals 1.4. Suppose that the risk-free rate (based on U.S. Government treasury bills) is = 4%; and the equity premium [] = 8%. Main’s corporate tax rate T is 34%. What is Main’s after-tax WACC, ?

Solution: All of the needed data were provided above. We begin by computing the equity cost of capital using equation [2].

= + []

= 4% + 1.4 [8%]

= 15.2% [3]

By definition, the value of the firm, , equals the sum of the value of all the firm’s securities. Therefore, = + + = $300 million + $150 million + $50 million = $500 million. Using the information in Exhibit 1 below, we have:

= (1  T) +

= 15.2% + 8% (1  .34) + 12%

= 11.904% [4]

Exhibit 1. Main, Inc. Financial Data

Equity market value () / $300 million
Debt market value () / $150 million
Complex financing market value () / $50 million
Firm value () / $500 million
Equity cost of capital () / 15.2%
Debt cost of capital () / 8%
Complex financing cost of capital () / 12%
Corporate tax rate / 34%

II. ESTIMATING THE WACC TO VALUE A FIRM

Section I explained how to estimate the WACC for a firm that has publicly traded common stock that is assumed to be fairly valued in the market (i.e., market value is close to intrinsic value, so there is no need to estimate the stock’s intrinsic value). This section explains how to estimate the WACC if the intrinsic value of the common stock is assumed not to be known. This is a common problem for privately-held companies (for which there is no quoted stock price), and also for publicly traded firms in cases in which the analyst (appraiser) believes that the equity market value may be significantly different from intrinsic value. Business acquisitions often involve this issue (both buyer and seller will want an intrinsic value estimate) whether the acquired company is publicly-held or privately-held.

The approach for estimating the after-tax WACC presented here parallels that in Chapter 19 of Brealey & Myers 7th edition. To tie this discussion to that in Brealey & Myers, we assume a firm (Olive Corporation) that plans to have only debt and equity in its capital structure (no “complex financing”). Define , , as the current market values of Olive’s equity, debt and complex financing, respectively; and define , , and as Olive’s equity cost of capital, debt cost of capital, and the complex financing cost of capital, respectively. Rate signifies Olive’s opportunity cost of capital. T is Olive’s marginal corporate tax rate. The approach presented here entails the following three steps.

Step 1: Estimate Olive’s opportunity cost of capital. To do this, identify publicly traded companies that have an underlying business risk like that of Olive. We refer to these similar business risk companies as “comparables.” From data about Olive’s comparables, we infer Olive’s opportunity cost of capital (), which is the cost of capital that is appropriate to the underlying business risk of Olive and its comparables.

Step 2: Determine Olive’s target capital structure and debt cost of capital () and, using that information and the estimated from Step 1, determine Olive’s equity cost of capital ().

Step 3: Use the data from Steps 1 and 2 to compute Olive’s .

We will now discuss each of the three above steps in detail, using Olive to illustrate the concepts.

STEP 1: Estimate Olive’s Opportunity Cost of Capital r. Olive’s opportunity cost of capital, r, is defined as:

= + [5]

Rate is not the same as the after-tax WACC (in [1] above) because the (1  T) is absent in [5]. The Modigliani-Miller analysis implies that, for a given firm, r is independent of the firm’s capital structure (i.e., is the same for any financing proportions[/], [/], and [). So, depends on Olive’s business risk, not its financing method. The higher is Olive’s business risk, the higher is . The underlying business risk is determined by the probability distribution of Olive’s free cash flow (FCF).

Since we are unsure of the intrinsic market values of Olive’s equity and debt, we cannot at this point compute the proportions in [5]. So, what we do is to examine publiclytraded firms that have the same underlying business risk as does Olive, and then use the data about these comparable firms to estimate . Suppose that we identify three other companies (A, B, and C) that we regard as Olive’s comparables in terms of underlying business risk (you would prefer more than three if you can find them). Firms A, B and C have the characteristics shown in Exhibit 2 below. The estimate of is the average of the comparables’ r magnitudes. This average is = 12.2%.

To compute a comparable’s r (the last column in Exhibit 2), we use the approach described in Section I for publicly traded companies to determine each comparable’s [/], [/], [], , , and . (As shown below, to determine a comparable’s we use its and the CAPM.) We then substitute those six quantities into equation [5] to solve for that comparable’s r. Thus, using the data in Exhibit 2, we have:

= + = [.8] 12% + [.2] 8% + 0 = 11.2% [6a]

= + = [.6] 14% + [.4] 10% + 0 = 12.4% [6b]

= + = [.5] 16% + [.4] 9% + [.1] 14% = 13%[6c]

Notice from Exhibit 2 that Firms A, B and C do not have the same r, which they would if their business risk were identical. In practice, the best that we can usually do is to identify comparables with similar, but not identical, risk. That is what we are assuming here.

Exhibit 2. Data on Olive Corporation Comparables

[/] / [/] / [] / / / / / r
Firm A / .8 / .2 / 0 / 1.00 / 12% / 8% / n/a / 11.2%
Firm B / .6 / .4 / 0 / 1.25 / 14% / 10% / n/a / 12.4%
Firm C / .5 / .4 / .1 / 1.50 / 16% / 9% / 14% / 13.0%
Average* / 12.2%

* 12.2% = (11.2% + 12.4% + 13.0%)/3.

Above we showed how to each comparable’s opportunity cost of capital using the market data, and the estimated betas, shown in Exhibit 2. We did not address the issue of how one finds comparables, and we brushed over the determination of each comparable’s [/], [/], [], , , and . Let’s fill in some of these details.

Finding and Analyzing Comparables:For purposes here, a comparable is a publicly traded company that is very similar to Olive in terms of underlying business risk. Business risk is measured by the firm’s free cash flow (FCF) probability distribution. To identify comparables, a good place to start is Olive’s industry, since firms in a given industry are subject to similar supply and demand forces. We would also consider other industries with risk characteristics like Olive’s industry. For example, the sales of consumer products that are income sensitive and also appeal to consumers in the same income category may be highly correlated. The FCFs of some producers’ goods manufacturers are highly correlated because they depend on the general economy in similar ways.

Keep in mind that we want to estimate the discount rate (WACC) to discount Olive’s future FCF. This means that we want each comparable to have a future like that of Olive (not simply a similar past history). Current market values and discount rates for a comparable reflect investors’ perceptions about the comparable’s anticipated future performance.

Estimating a Comparable’s Capital Structure Parameters: Since the comparables are publicly traded, obtaining their , , and will not be difficult. Debt and complex financing that is not publicly traded can be valued on the basis of the firm’s business risk, capital structure, rating of the security (e.g., bond rating), and provisions in the financing agreement. On this, see Section I.1 above.

Estimating aComparable’s , and : We can apply the procedures that were presented in Section I.1 here, including the use of the CAPM to estimate each comparable’s equity cost of capital . So, the equity cost of capital rates , , and for firms A, B and C, respectively, would be computed in the following way. As in expression [3], assume that risk-free rate = 4% and equity premium [] = 8%. Assume that we also have obtained from an external source (Bloomberg, Ibbotson Associates, etc.) the beta estimates = 1.0, = 1.25, and = 1.5; these quantities are shown in Exhibit 2. Using the CAPM, it follows that the equity rates for comparables A, B and C are calculated as shown in equations [7a], 7b] and [7c].