FNCE201 Corporate Finance Lecture 2: Advanced Cost of Capital Suggested Reading: Corporate Finance - Chapter 12 Ma Pengfei Lee Kong Chian School of Business Singapore Management University Class Outline and Learning Objectives ▪ Weighted Average Cost of Capital (WACC) ▪ Cost of equity ▪ Approaches to estimate the cost of equity ▪ Capital Asset Pricing Model (CAPM) ▪Estimate equity risk premium ▪Techniques in estimating Beta ▪ Cost of debt and preferred stock ▪ Approaches to estimate the cost of debt ▪ Component weights for WACC ▪ Project’s cost of capital ▪ Unlevered Beta Cost of Capital ▪ The rate of return that the suppliers of capital (bondholders and owners) require as compensation for their contribution of capital. ▪ It reflects the opportunity cost of the suppliers of capital (investors), who will not voluntarily invest in a firm unless its return meets or exceeds what they could earn elsewhere in an investment of comparable risk. ▪ Is a marginal cost i.e., the cost of raising additional capital since is used mainly to evaluate investment opportunities. Weighted Average Cost of Capital ▪ Capital is raised by issuing equity, debt, and hybrid instruments ▪ Each of these sources of capital has a cost referred to as its component cost of capital. ▪ The cost of capital is, therefore, a weighted average of the component costs of capital and is known as the weighted average cost of capital (WACC). ▪ WACC is also called the marginal cost of capital, since it is also the cost of raising additional capital, with the weights representing the proportion of each source of financing that is used. Weighted Average Cost of Capital ▪ rwacc = wE × rE + wD × rD × (1 − 𝜏C ) + wP × rP ▪ The weights wE , wD and wP, refer to the proportion of equity, debt and preferred stock, that the firm uses when it raises new funds. 𝜏C is the marginal tax rate, rE is the cost of equity, rD is the cost of debt, and rP is the cost of preferred stock. ▪ Interest on debt is tax-deductible, so rD must be adjusted downwards: ▪ Debt holders receive a return of rD, while the firm pays a net cost of rD(1 − 𝜏C ) ▪ Payments to owners are not tax-deductible, so the required rate of return on equity (whether rE or rP) is the equity cost of capital. Part 1 Cost of Equity Cost of Equity (rE) ▪ The cost of common equity (rE) is the rate of return required by the firm’s common shareholders. ▪ It is difficult to compute rE as there are no promised or pre-specified returns based on a financial contract. ▪ Three approaches to estimate rE: 1. Dividend discount model (DDM) 2. Bond yield plus risk premium 3. Capital asset pricing model (CAPM) Dividend Discount Model (DDM) ▪ Use the constant-growth DDM and re-write it to estimate rE: P0 = D1/(rE – g) => rE = D1/P0 + g ▪ g may be estimated by using third-party estimates of the firm’s dividend growth or computing the sustainable growth rate (SGR). ▪ SGR is the rate at which a company can maintain its growth without requiring additional financing from external sources. ▪ SGR the product of the historical ROE and the retention rate: g =(1 − D/EPS)× ROE ▪ D/EPS is the assumed stable dividend payout ratio. Example ▪ Brigham, Shome and Vinson (1985): cost of equity for utility industry firms ▪ Value Line provides estimates of dividend for the future 4 years, ROE, and retention rate (b) ▪ g = b × ROE ▪ DDM with Constant Long-Term Growth: Div1 Div2 Div3 Div4 1 P0 = + + + + 1 + rE (1 + rE )2 (1 + rE )3 (1 + rE )4 (1 + rE )4 ▪ We can then solve for rE Div4 (1 + 𝑔) rE − g Bond Yield Plus Risk Premium (BYPRP) ▪ Requires adding a premium to the firm’s yield on its debt: rE = rD + Risk Premium ▪ where rD is the before-tax cost of debt. ▪ This approach is based on the premise that the equity of the firm is riskier than its debt, but that these sources of capital move in tandem. ▪ The premium is often estimated using the historical spread between bond yields and stock yields. ▪ In a developed country, a typical risk premium is between 3 to 5 percent. Equity Risk Premiums for Electric Utilities ▪ Survey question: assuming a double A, long-term utility bond currently yields 12.5%, the common stock for the same company would be fairly priced relative to the bond if its expected return was [____]? Capital Asset Pricing Model (CAPM) ▪ The CAPM states that the expected return on equity is the sum of the risk-free interest rate and a premium for bearing market risk, as follows: E(ri) = rF + βi[E(rM) − rF] ▪ where rF is the risk-free rate, βi is the beta of stock i, E(rM) is the expected return on the market ▪ [E(rM) − rF] is the expected market risk premium or equity risk premium. ▪ Risk-free rate. A risk-free asset is one with no default risk. A common proxy for rF is the yield on a defaultfree government debt instrument. ▪ In general, the appropriate rF should be guided by the duration of the projected cash flows Example ▪ Suppose you estimate that Disney’s stock (DIS) has a volatility of 20% and a beta of 1.29. A similar process for Chipotle (CMG) yields a volatility of 30% and a beta of 0.55. If the risk-free interest rate is 3% and you estimate the market’s expected return to be 8%, calculate the equity cost of capital for Disney and Chipotle. Solution ▪ We expect the price for Disney’s stock to move by 1.29% for every 1% move of the market. Therefore, Disney’s risk premium will be 1.29 times the risk premium of the market, ▪ rDIS=3%+1.29×(8%−3%)=3%+6.45%=9.45% ▪ Chipotle has a lower beta of 0.55, ▪ rGMG=3%+0.55×(8%−3%)=3%+2.75%=5.75% ▪ B/c market risk cannot be diversified, it is market risk that determines the cost of capital; thus Disney has a higher cost of equity, even though it is less volatile. Expected Market Risk Premium ▪ Expected market risk premium. The premium that investors demand for investing in a market portfolio relative to rF: ▪ When using the CAPM to estimate rE, the beta is typically estimated relative to an equity market index. This means that the market risk premium, E(rM) − rF , is actually an estimate of the equity risk premium (ERP). ▪ Approaches to estimate ERP: 1. Historical ERP approach 2. Implied ERP approach 3. Survey approach Historical ERP ▪ Assumes that the realized ERP observed over a long period of time is a good indicator of the expected ERP. ▪ Requires historical data to compute the average rate of return of a country’s market portfolio (rM) and the average rate of return for rF. ▪ Typically obtained from external sources e.g., Ibbotson Associates, etc. Historical ERP ▪ Determining the Risk-Free Rate ▪ The yield on U.S. Treasury securities ▪ Surveys suggest most practitioners use 10- to 30-year treasuries ▪ Limitations of the historical ERP approach: ▪ Level of risk of the index may change over time. ▪ Risk aversion of investors may change over time. ▪ Estimates are sensitive to the method of estimation and the historical period covered. Implied Risk Premium Approach ▪ Also referred to as the DDM based approach. The simplest approach uses the constant-growth DDM to back out a value for rM from: P0 = D1/(rM − g) ▪ where P0 is the current value of the market index, D1 are the expected dividends next period on the index, and g is the expected growth rate of dividends. ▪ The implied ERP is obtained by subtracting rF from rM (used as a proxy for E(rM)). ▪ The advantage of the implied ERP is that it is marketdriven, up-to-date, and does not require historical data. It is however very much model dependent. Implied ERP for Singapore ▪ Source: http://www.market-risk-premia.com/sg.html Model Parameters Stock Beta (β) ▪ The stock beta is the sensitivity of stock returns to the returns of the market portfolio. It measures the market or systematic risk of the stock i.e., risk that cannot be diversified away. ▪ β is estimated from a regression of excess stock return against market risk premium: (ri - rF) = 𝛼ො + 𝛽መ (rM - rF) ▪ The R2 of the regression measures the goodness of fit of the regression. It estimates the proportion of the risk of the firm that can be explained by market risk. Cisco versus S&P 500, 2000–2017 Length of the Estimation Period ▪ While a longer estimation period provides more data, the firm’s risk characteristics may have changed over time. Stability of Beta Length of Estimation Period ▪ Deciding on the estimation period involves a trade-off between data richness captured by a long estimation period versus firm-specific changes that are better reflected with a shorter estimation period. ▪ A longer estimation periods is typically used for firms with a long and stable operating history, while a shorter estimation period is used for firms that have recently undergone significant structural changes or changes in their financial and operating leverage. Outliers ▪ Beta estimates from a regression are significantly affected by outlying observations. Determinants of Beta ▪ The beta of a firm or project is affected by business risk and financial risk. Both types of risk affect the uncertainty of the cash flows of the firm or project. ▪ Total Cost = Fixed Cost + Variable Cost ▪ The greater the fixed cost, the greater the risk. ▪ Business Risk: uncertainty of revenues (sales risk) and operating cost structure (operating risk). ▪ Financial Risk: uncertainty of net income and net cash flows attributed to the use of financing that has a fixed cost (i.e. debt and leases). Operating Leverage ▪ The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs. ▪ %Δin Profits ÷ %Δin Sales = 1 + Fixed Cost ÷ Profits = Operating Leverage ▪ Operating leverage increases as fixed costs rise ▪ Q: how much does the profit change if sales change by 10%, when ▪ Fixed Cost = 0 ▪ Fixed Cost > 0 ▪ Operating leverage magnifies the effect of cyclicality on beta. Operating Leverage and Beta ▪ Consider a project with expected annual revenues of $120 and costs of $50 in perpetuity. The costs are completely variable, so that the profit margin of the project will remain constant. ▪ Suppose the project has a beta of 1.0, the risk-free rate is 5%, and the expected return of the market is 10%. What is the value of this project? ▪ What would its value and beta be if the revenues continued to vary with a beta of 1.0, but the costs were instead completely fixed at $50 per year? Solution ▪ The expected cash flow of the project is $120 − $50 = $70 per year. Given a beta of 1.0, the appropriate cost of capital is r = 5% + 1.0(10% − 5%) = 10%. Thus, the value of the project if the costs are completely variable is: $70/10% = $700 Solution ▪ If the costs are fixed, then we can compute the value of the project by discounting the revenues and costs separately. ▪ The revenues still have a beta of 1.0, and thus a cost of capital of 10%, for a present value of: $120/10% = $1,200 ▪ The costs are fixed, we should discount them at the risk-free rate of 5%, so their present value is $50/5% = $1,000. ▪ Thus, with fixed costs the project has a value of only $1200 − $1000 = $200. What is the beta of the project? ▪ We can think of the project as a portfolio that is long the revenues and short the costs. The project’s beta is the weighted average of the revenue and cost betas: R C 1200 1000 βp = βR − βC = 1.0 − 0 = 6.0 R−C R −C 1200 − 1000 1200 − 1000 ▪ Given a beta of 6.0, the project’s cost of capital with fixed costs is r = 5% + 6.0 (10% − 5%) = 35%. ▪ The present value of the expected profits is then: $70/35% = $200 ▪ As this example shows, increasing the proportion of fixed versus variable costs can significantly increase a project’s beta (and reduce its value). Financial Leverage and Beta ▪ Operating leverage refers to the sensitivity to the firm’s fixed costs of production. ▪ Financial leverage is the sensitivity to a firm’s fixed costs of financing. ▪ If a firm raises it leverage, the return to equity will become more volatile (higher equity β). Part 2 Cost of Debt and Preferred Stock Cost of Debt (rD) ▪ The cost of debt financing to a firm when it takes out a bank loan or issues a bond. When the firm borrows from a bank, rD, is simply the interest rate charged. ▪ Estimating the before-tax cost of debt when the firm issues debt: 1. Yield-to-maturity (YTM). For long-term bonds that are widely traded and have no special features. 2. Debt-rating. For long-term bonds that do not trade on a regular basis but are rated. 3. Synthetic-rating. For long-term bonds that are not rated. Mainly for many smaller companies and most private businesses. YTM v.s. Returns ▪ Yield to maturity is the IRR an investor will earn from holding the bond to maturity and receiving its promised payments. ▪ If there is little risk the firm will default, yield to maturity is a reasonable estimate of investors’ expected rate of return. ▪ If there is significant risk of default, yield to maturity will overstate investors’ expected return. Default Risk ▪ Consider a one-year bond with YTM of y. For each $1 invested in the bond today, the issuer promises to pay $(1 + y) in one year. ▪ Suppose the bond will default with probability p, in which case bond holders receive only $(1 + y − L), where L is the expected loss per $1 of debt in the event of default. ▪ So the expected return of the bond is: ▪ rD = (1-p)× y + p× (y-L) = y - p× L ▪ = YTM – Prob(default) × Expected Loss Rate Annual Default Rates by Debt Rating (1983–2011) Rating: AAA AA A BBB BB B CCC CC−C Default Rate: Average 0.0% 0.1% 0.2% 0.5% 2.2% 5.5% 12.2% 14.1% In Recessions 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 48.0% 79.0% ▪ The average loss rate for unsecured debt is 60%. ▪ During average times the annual default rate for B rated bonds is 5.5%. ▪ So the expected return to B-rated bondholders during average times is 0.055 × 0.60 = 3.3% below the bond’s quoted yield. Debt Betas ▪ Alternatively, we can estimate the debt cost of capital using the CAPM . ▪ Debt betas are difficult to estimate because corporate bonds are traded infrequently. ▪ One approximation is to use estimates of betas of bond indices by rating category. By Rating A and above BBB BB B CCC Avg. Beta <0.05 0.10 0.17 0.26 0.31 By Maturity (BBB and above) 1-5 year 5-10 year 10-15 year >15 year Avg. Beta Blank 0.01 0.06 0.07 0.14 Example ▪ In mid-2015, homebuilder KB Home had outstanding 6-year bonds with a yield to maturity of 6% and a B rating. If corresponding risk-free rates were 1%, and the market risk premium is 5%, estimate the expected return of KB Home’s debt. Solution ▪ Given the low rating of debt, we know the yield to maturity of KB Home’s debt is likely to signification overstate its expected return. Using the average estimates in previous Table and an expected loss rate of 60%, we have: rD=6%−5.5%(0.60)=2.7% ▪ Alternatively, we can estimate the bond’s expected return using the CAPM and estimated beta of 0.26. In that case, rD =1%+0.26(5%)=2.3% ▪ Which both estimates approximation, they both confirm that the expected return of KB Home’s debt is well below its promised yield. Synthetic-rating Approach ▪ Uses a synthetic rating to find the credit spread based on the firm’s financial ratios e.g. interest coverage ratios: Cost of Preferred Stock ▪ A straight (i.e. nonconvertible) preferred stock pays the holder a fixed dividend each period (quarterly) forever. Because preferred stock are perpetual, its value is: PP = DP/rP ▪ where PP is the current preferred stock price per share, DP is the preferred stock dividend per share, and rP is the return on preferred stock. ▪ Rearranging this equation, we obtain the cost of preferred stock: rP = DP/PP ▪ The cost of preferred stock is not tax-adjusted because dividends on preferred stock are not tax deductible. Part 3 Component Weights for WACC Estimating the Component Weights ▪ Ideally, the weights to use when estimating the WACC should reflect the relative proportions of each source of capital that the firm intends to use in financing investment projects. The weights are called the target capital structure. ▪ The target capital structure cannot be observed but may be estimated by: ▪ Using the firm’s current capital structure at market value weights. ▪ Examining trends in the firm’s capital structure or statements made by management regarding capital structure. ▪ Using the capital structure of comparable firms. Estimating the Component Weights ▪ Weight of equity (wE). Based on market capitalization, which is the market price per share times the number of shares outstanding. ▪ Weight of debt (wD). Usually refers to interest-bearing debt and based on market value if available. However, market values are not easily available, so book values are typically used. Part 4 Project’s Cost of Capital Estimating Beta ▪ The beta for publicly traded firms can be estimated using easily accessible stock return data or obtained from external vendors. ▪ Estimating the beta for a firm that is not publicly traded or the beta for a project that is not the average or typical project of the publicly traded firm, is more difficult. ▪ To obtain a beta in these firms or projects, requires proxying the beta using information on the firm or project, combined with a beta of a publicly traded company. The Pure-Play Method ▪ This approach is used to estimate the beta for a project from the betas of comparable publicly traded firms, where a comparable firm is defined as a firm with similar business risks. ▪ The beta of the comparable is first “unlevered” by removing the effects of financial leverage, with the resulting beta known as the firm’s unlevered beta or asset beta, since it reflects the business risk of the firm’s assets. ▪ After the unlevered beta is obtained, it is adjusted for the capital structure of the project by “levering” this asset beta, to arrive at an estimate of the equity beta for the project. Asset/Unlevered Beta ▪ Since the firm’s risk is shared between creditors and owners, βA may be represented as the weighted average of the creditors’ market risk (βD) and the owners’ market risk (βE): ▪ 𝛽𝐴 (𝛽𝑈 ) = Debt Debt+Equity × 𝛽𝐷 + Equity Debt+Equity × 𝛽𝐸 ▪ βA removes the effects of financial leverage ▪ Further, assuming βD = 0, we obtain the unlevering formula ▪ 𝛽𝐴 = Equity Debt+Equity × 𝛽𝐸 = 𝛽𝐸 Debt/Equity+1 Asset/Unlevered Beta ▪ Rewriting equation in terms of βE, results in the levering formula: ▪ βE = βA[1 + Debt Equity ] ▪ The same unlevering and leveraging formulas may be used to estimate the asset beta and equity beta for a project. ▪ Note: to use this formula, we are assuming that the firm/project maintains a constant D/E ratio, the formula holds with the presence of tax. Example ▪ Consider Grand Sport, Inc., which is currently allequity financed and has a beta of 0.90: βA = βE = 0.90 ▪ The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity. ▪ Since the firm will remain in the same industry, its asset beta should remain βA = 0.90. ▪ However, assuming a zero beta for its debt, its equity beta would become twice as large: ▪ βA = 0.90 = 1 1+1 × βE ▪ βE = 0.90 × 2 = 1.80 Estimating βE Using Comparables 1. Estimate comparable firms’ βE and βD 2. Estimate their βA Debt Equity ▪ 𝛽𝐴 = ▪ Firms in the same industry should have same βA Debt+Equity × 𝛽𝐷 + Debt+Equity × 𝛽𝐸 3. Average βA across comparable firms 4. Use the average βA and the target firm’s actual leverage ratio to estimate βE Example ▪ Suppose a medical diagnostic firm has Debt-Equity ratio (D/E) of 0.2. The risk free rate is 5%. Company 2, which makes similar class of therapeutic drugs, has an equity beta of 2. Its D/E ratio is 0.4. The market risk premium is 7%. ▪ What should be the cost of equity for the diagnostic firm? Assume that the cost of debt for both firms is 6%. ▪ Hint: you need to solve debt beta using CAPM Solution E D a = e + d E+D E+D rd = r f + d [rm − r f ] .06 = .05 + d * .07 .01 d = = .14 .07 1 .4 a = *2+ * .14 1 + .4 1 + .4 = 1.47 E D a = e + d E+D E+D 1 .2 1.47 = * e + * .14 1 + .2 1 + .2 e = 1.736 re = r f + e [rm − r f ] = .05 + 1.736 * .07 = .1715 re = 17.15% Estimating the WACC for a Project 1. Estimate the project’s relative proportion of debt and equity financing. Use the average D/E ratios of comparable firms if the target D/E ratio is not available, and rewrite them in terms of wE and WD. 2. Estimate the after-tax cost of debt. Use the credit ratings and borrowing rates of the comparable firms to compute rD. Apply the corporate tax rate to find the after-tax cost of debt. 3. Unlever the project’s equity beta. Compute the unlevered beta of the comparable firms. Estimating the WACC for a Project 4. Compute the project’s equity beta. Find the average unlevered beta and lever it to the project’s target D/E ratio. 5. Estimate the project’s cost of equity. Use the CAPM to find rE based on the project’s βE obtained in step 4. 6. Calculate the project’s WACC. Input all the WACC variables to compute the project’s WACC: ▪ rWACC = 𝐸 𝐸+𝐷 × rE + 𝐷 𝐸+𝐷 × rD × (1 − 𝜏c) Online Discussion ▪ Read chapter 10 “Best Practices” in Estimating the Cost of Capital: An Update ▪ Robert F. Bruner, Kenneth M. Eades and Michael J.Schill, Case Studies in Finance: Managing for Corporate Value Creation, 8th International edition. ▪ Write some comments on what you have learned from it. Summary ▪ This class: ▪ Weighted Average cost of Capital (WACC) ▪ Cost of Equity ▪ Cost of Debt and Preferred Stock ▪ Component Weights for WACC ▪ Project’s Cost of Capital ▪ Next class: ▪ Capital structure
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