1 Chapter 11 Calculating the Cost of Capital 2 Chapter 11 Learning Goals LG1: Grasp the basic intuition behind calculating the cost of capital and its relationship to the investor? required return LG2: Use the Weighted Average Cost of Capital (WACC) formula to calculate a project?s cost of capital LG3: Debate the firm?s choices in estimating the appropriate capital component costs of equity, preferred stock, and debt LG4: Calculate and justify appropriate weights used for WACC projections LG5: Clarify which parts of a firm-wide WACC can be used in calculating a project-specific WACC and which parts do not apply LG6: Note the tradeoff implicit in using either a firm-wide WACC or a divisional cost of capital approach LG7: Differentiate between the objective and subjective approaches to computing a divisional cost of capital LG8: Denote the impact that flotation costs have on capital budgeting decisions and adjust the WACC to reflect flotation costs 3 ? The WACC formula ? Note that the weights are based on market values rather than book values ? Market values reflect investors? assessment of what they would be willing to pay for various types of securities )1( CDPE TiDPE DiDPE PiDPE EW A C C 4 Calculating the Component Cost of Equity ? We have two methods for calculating the cost of equity: 1. CAPM 2. Constant Growth Model ? CAPM ])([ fMEfE iiEii 5 ? Constant Growth Model g P D i 0 1 E 6 ? Which one is better? ? In the CAPM, ?E estimates future systematic risk, but we calculate it based on historic data ? We can?t use the CAPM if we don?t have sufficient historic information or when we suspect that the past level of systematic (market) risk is not a good indicator of future risk ? The constant growth model assumes constant perpetual growth in dividends ? If this assumption is not approximately true for our firm then this model will not produce reliable estimates 7 ? Overall we should expect that the CAPM method for estimating iE will apply more accurately in most cases ? If the constant growth model applies it is a good idea to use both methods ? Some type of simple or weighted average of the two methods might be appropriate 8 Example ? Calculate the cost of equity for ADK Industries given the following information: ? ADK common stock price = $32.75 ? The next dividend is expected to be $1.54 per share ? ADK expects future dividends to grow by 6 percent per year indefinitely ? The risk-free rate is 3 percent ? The expected return on the market is 9 percent ? ADK has a beta of 1.3 9 ? CAPM method: iE = if + ?E[E(iM) ? if] = .03 + 1.3[.09 - .03] = 10.80% ? Constant growth model: ? iE = D1/P0 + g ? = $1.54/$32.75 + .06 ? = 10.70% ? The best estimate is (10.80 + 10.70)/2 = 10.75% 10 Calculating the Component Cost of Preferred Stock ? Preferred stock pays constant dividends forever, and so it can be valued as a perpetuity ? We can rearrange the perpetuity model to solve for iP: ? Note: this is the same as the constant growth model in which the value of the constant growth is g = 0 0P D iP 11 Example ? ADK has one million shares of 7% preferred stock outstanding which currently trades at $72 per share. What is ADK?s cost of preferred equity? iP = D/P0 = $7 / $72 = 9.72% 12 Calculating the Component Cost of Debt ? We first have to estimate the before-tax cost of debt, and then calculate the after-tax cost of debt ? Unlike the other forms of capital, interest on debt is tax deductible ? To find the before-tax cost of debt we find the Yield to Maturity on the firm?s existing debt ? YTM takes into account both the interest cash flows and the principal, and reflects debtholders? required return 13 Example ? ADK has 30,000 20-year, 8 percent bonds outstanding. If the bonds currently sell for 97.5 percent of par and the firm has a marginal tax rate of 35.92 percent, what is the cost of debt for ADK? Input 20 -975 80 1000 N I PV PMT FV Output 8.26 14 ? If the before-tax cost of debt is 8.26 percent, then the after-tax cost of debt is: 8.26% (1 - .3592) = 5.293% ? What tax rate do we use in the WACC calculation? ? We use the marginal rate, but that rate needs to reflect the weighted average of the marginal rates that would have been paid on the taxable income shielded by the interest deduction 15 Calculating the Weights ? We need to use the relevant market values of equity, preferred stock, and debt, represented by E, P, and D ? In the ADK example, the firm has 3 million share of common stock outstanding, one million shares of preferred stock, and 30,000 bonds. ? What are the relevant weights for ADK? 16 ? Equity has a total market value of 3,000,000 x $32.75 = $98,250,000 ? Preferred stock has a market value of 1,000,000 x $72 = $72,000,000 ? Debt has a market value of 30,000 x $975 = $29,250,000 17 ? For common equity: E/(E+P+D) = $98,250,000 / $199,500,000 = 49.25% ? For preferred stock: P/(E+P+D) = $72,000,000 / $199,500,000 = 36.09% ? For debt: D/(E+P+D) = $29,250,000 / $199,500,000 = 14.66% 18 ? We can now calculate the WACC for ADK Industries: WACC = (.4925 x 10.75%) + (.3609 x 9.72%) + (.1466 x 8.26%)(1 - .3592) = 9.58% 19 Firm WACC vs. Project WACC ? We have calculated the firm?s overall weighted average cost of capital ? This WACC will be appropriate to use in evaluating ?typical? projects ? If a new project is similar enough to existing projects, then the firm?s WACC is appropriate 20 ? If the project is significantly different, then the WACC used to evaluate the project must be different than the firm?s overall WACC ? If the new project is riskier than the firm?s average project, then a higher cost of capital should be used ? If the new project is safer, then a lower cost of capital should be used to evaluate the project 21 ? In adjusting the overall firm WACC for a specific project: ? For preferred stock and debt we generally use the overall firm?s cost of preferred stock and debt ? These sources represent fixed claims, and so for small projects debt and preferred are generally not materially affected by a project?s risk ? Most of the risk of new projects is transferred to common stockholders ? Stockholders will adjust their required returns, so the firm?s cost of equity will change 22 ? Adjusting the cost of equity ? New projects will not have a history of returns ? Without this data we can?t calculate a project- specific beta ? What if we can find publicly-traded firms engaged in the same line of business as our proposed project? ? These are called ?pure-play? firms, and we can use their betas as a proxy for our project beta ? It is not easy to find such firms, but if we find multiple pure plays we can take the average of their betas 23 ? What if we can?t find any pure-play proxies? ? Find firms that are engaged in multiple businesses, including ones like our proposed project, and ?back out? the impact of their other lines of business 24 Divisional WACC ? Ideally, firms would calculate a risk- appropriate WACC for every new project under consideration ? Time consuming ? Managers must often consider hundreds of new projects each year ? Instead, large firms often calculate a divisional WACC, which consumes less time and resources but achieves many of the benefits of project-specific WACCs 25 ? Why not use a firm-wide WACC to evaluate all projects ? Incorrect reject / accept decisions ? Reject most low-risk projects, both good and bad ? Firm becomes riskier over time 26 ? Subjective vs. Objective Approaches to Calculating Divisional WACCs ? Subjective approach ? If the projects are riskier than the firm average, adjust the WACC upward ? If the projects are safer than the firm average, adjust the WACC downward ? Biggest disadvantage: the amount of the adjustment is subjective 27 28 ? Objective approach: ? Compute the average beta per division, and use the CAPM to calculate the cost of equity for each division ? Use the divisional iE to calculate the divisional WACCs ? The subjective approach is used more often than the objective approach because it is easier to implement 29 30 Flotation Costs ? If a firm uses internally-generated sources of capital, such as retained earnings, then the firm doesn?t need to adjust for flotation costs ? If the firm funds a project using externally-generated capital, then they will have to pay the costs of underwriting the new issue ? The costs associated with issuing new securities are called flotation costs 31 ? There are two ways to integrate these costs: 1. Increase the projects WACC to reflect the flotation costs 2. Adjust the project?s initial investment upwards to reflect the true cost of the project ? This method violates the separation principle of capital budgeting, which states that the calculations of cash flows should remain independent of financing 32 ? Adjusting the WACC to reflect flotation costs: ? Subtract the flotation costs from the issue price of the new issue to reflect the net price ? Use this price to calculate the cost of capital ? For equity, we often use the constant growth model: g FP D i E 0 1 33 Example ? ADK?s common stock is selling for $32.75 per share, the next annual dividend is expected to be $1.54 per share, and the firm is expected to grow at 6 percent indefinitely. If ADK faces flotation costs of 20 percent on new equity issues, calculate the cost of new equity. 34 iE = D1 / (P0 ? F) + g = $1.54 / ($32.75 - $6.55) + .06 = 11.88% byerstev Chapter 11