# Weighted Average Cost of Capital (WACC)

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Weighted Average Cost of Capital (WACC)
Chapter 12 Weighted Average Cost of Capital (WACC)

Motivation You’ve just moved up to the C-suite of a large, publicly traded company, and are faced with a decision on whether to accept a proposed capital improvement project. Easy enough, right? Find the NPV of the pro forma cash flows, and accept if it is positive. But what discount rate do you use?

Motivation The discount rate depends on the riskiness of the project under consideration. Furthermore, the project will have a positive (expected) NPV only if its return exceeds what the financial markets offer on investments of similar risk. This minimum required return (i.e., investment hurdle) is the cost of capital for the project. This chapter deals with approaches to estimate a project’s cost of capital.

Motivation Note that the cost of capital depends primarily on the use of the funds, and not the source. Someone offering to lend your firm money at a ridiculously low rate doesn’t take a bad project and make it golden; you’re still tying up funds that would (should) otherwise go to your investors at a higher rate of return.

Questions for Ch 12 What is the weighted average cost of capital (WACC) for a firm, and why is it often used as a discount rate to evaluate projects? How does one calculate the cost of common stock (equity) and the cost of preferred stock for a firm? How does one calculate the cost of debt for a firm? How does one calculate the WACC for a firm? What are some limitations of using a firm’s WACC as a discount rate when evaluating a project? What are some alternatives?

What is WACC? The weighted average cost of capital (WACC) for a firm is a weighted average of the current costs of the different types of financing that a firm has used to finance the purchase of its assets. When the WACC is calculated, the cost of each type of financing is weighted according to the fraction of the total firm value represented by that type of financing. The “value” is the market value, where possible. Using accounting, or book, value for anything other than short-term debt is problematic, at best. If a liability class (e.g., long-term debt) isn’t publicly traded, then one should observe yield on similar, publicly traded debt and then estimate the market value of the privately held debt using this yield as the discount rate.

What is WACC? The WACC is often used as a discount rate in evaluating projects because it is not possible to directly estimate the appropriate discount rate for many projects. Also, having a single discount rate reduces inconsistencies that can arise when different analysts in the firm use different methods to estimate the discount rate and can also limit the ability of analysts to manipulate discount rates to favor pet projects.

What is WACC? Note, however, that the firm’s WACC is the overall required return on the firm as a whole. It is the appropriate discount rate to use for cash flows similar in risk to the overall firm.

Estimating the Cost of Equity
The cost of equity can be estimated using the CAPM/SML or the dividend-growth formula (either constant-growth or multistage-growth). The cost of preferred stock can be calculated using the perpetuity model for the present value of cash flows.

Estimating RE – Dividend Growth
Under the constant-growth dividend growth model, P0=D1/(RE-g), where RE is the required return on equity. FYI, most notation uses ke for return on equity, kd for debt, etc.; I’ll switch around. This can be rearranged to RE=D1/P0+g. For publicly-traded stocks, current price is observable, as is current dividend; the dividend growth rate can be observed/estimated.

Estimating RE – Dividend Growth
Estimating dividend growth rate: use an arithmetic or geometric average over several years, or both. Alternatively, use the earnings growth rate projected by analysts are a proxy for dividend growth.

Estimating RE – Dividend Growth
The problem with the dividend-growth model approach is that cost of equity is sensitive to the estimated growth rate, and the latter is necessarily subject to error. In addition, there is no explicit consideration of project risk in this approach; for one thing, dividends are a firm-wide phenomenon… what are the implications of using dividend growth to evaluate a risky tech R&D venture?

Estimating RE – SML Using the security market line (SML) we can write the expected return on a company’s equity, E(Re), as: For the purposes of calculating WACC, we drop the expectations. If we have a risk-free rate, an estimate of the market risk premium, and an estimate of the relevant beta, we can calculate a firm’s cost of equity.

Estimating RE – SML Advantages: (1) Explicitly adjusts for risk; (2) It is applicable to companies other than just those with steady dividend growth, and thus, it may be useful in a wider variety of circumstances. Disadvantages: (1) Requires that two things be estimated, the market risk premium and the beta coefficient; (2) We are relying on the past to predict the future (though this is also true with the dividend growth model).

Question 3: Calculating Cost of Equity
Stock in CDB Industries has a beta of The market risk premium is 7%, and T-bills are currently yielding 3.5%. CDB’s most recent dividend was \$1.80 per share, and dividends are expected to grow at a 5% annual rate indefinitely. If the stock sells for \$47 per share, what is your best estimate of CDB’s cost of equity?

Estimating the Cost of Debt
The cost of debt can be calculated by solving for the yield to maturity of the debt using the bond pricing model, computing the effective annual yield, and adjusting for taxes. Cost of debt is often directly observed, through YTM of traded bonds – either the firm’s bonds, or bonds from firms with a similar risk profile (i.e., credit rating). Note that we look at YTM, and not the coupon rate for bonds, which is irrelevant.

Estimating the Cost of Debt
Cost of preferred stock is straightforward to solve for: RP=D/P0, from the formula for a perpetuity. When calculating the WACC for a leveraged firm, we must take into account that interest on debt is tax-deductible. This is NOT true for dividends. What this implies is that after-tax cost of debt to the firm is (1-t)×RD, where t is the firm’s marginal corporate income tax rate.

Question 6: Calculating Cost of Debt
ICU Window, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with seven years to maturity that is quoted at 108% of face value. The issue makes semiannual payments and has an embedded cost of 6.1% annually. What is ICU’s pretax cost of debt? If the tax rate is 38%, what is the aftertax cost of debt?

WACC=xdebtkDebt pretax(1-t)+xpskps+xeke
Estimating WACC The WACC is estimated using either a ‘traditional’ formula, or more generalized formula, where the cost of each individual type of financing is estimated using the appropriate method. Traditional WACC formula: WACC=xdebtkDebt pretax(1-t)+xpskps+xeke Here x denotes the share of firm value for debt, preferred stock, and equity, respectively; k denotes the return on debt, preferred stock, and equity. General formula:

Estimating WACC The “x’s” are called capital structure weights. Sometimes they are given explicitly, but more often they are reported as “debt-to-equity ratio”, “leverage”, or “gearing”. You need to be a little bit careful here; if a company has a Debt/Equity ratio of 1/3, then it has an equity weight of 3/(1+3), or 75%, and debt weight of (1/1+3), or 25%.

Question 10: Taxes and WACC
Benjamin Manufacturing has a target debt-equity ratio of Its cost of equity is 12 percent, and its cost of debt is 7 percent. If the tax rate is 35 percent, what is the company’s WACC?

Issues with WACC When a firm uses a single rate to discount the cash flows for all of its projects, some project cash flows will be discounted using a rate that is too high and other project cash flows will be discounted using a rate that is too low. This can result in the firm rejecting some positive NPV projects and accepting some negative NPV projects.

Issues with WACC It will bias the firm toward accepting more risky projects and cause the firm to create less value for stockholders than it would have if the appropriate discount rates had been used. Specifically, high beta projects will have higher returns, and will thus tend to exceed the WACC; however, these same projects may still lie below the SML. That is, the projects have higher returns… but not high enough to be profitable in expectation.

Issues with WACC An alternative is to identify a firm that engages in business activities that are similar to those associated with the project under consideration and that has publicly traded stock. The returns from this “pure-play” firm’s stock can then be used to estimate the equity beta for the project.

Issues with WACC In instances where pure-play firms are not available, another alternative is for the financial manager to classify projects according to their systematic risks and use a different discount rate for each class of project.