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# Calculating the Cost of Capital

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1. Calculating the Cost of Capital Chapter 11 Fin 325, Section 04 – Spring 2010 Washington State University

2. Weighted Average Cost of Capital • The WACC formula • E, P, D are market value of equity, preferred stock, and debt, respectively. • are cost of equity, cost of preferred stock, and cost of debt. • is the appropriate corporate tax rate. • Market values reflect investors’ assessment of what they would be willing to pay for various types of securities

3. Cost of Equity • Two methods for calculating the cost of equity: • CAPM • Constant Growth Model

4. Which Model is Better? • In the CAPM, βE estimates future systematic risk, but we calculate it based on historic data • Needs sufficient historic information • Past level of systematic (market) risk is a good indicator of future risk • Applies more accurately in most cases • The constant growth model assumes constant perpetual growth in dividends • Some type of simple or weighted average of the two methods might be appropriate

5. 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

6. Solution • CAPM method: iE = if + βE[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%

7. 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

8. Example • ADK has one million shares of preferred stock outstanding, which pays dividend of \$7 per year and currently trades at \$72 per share. What is ADK’s cost of preferred equity? iP = D/P0 = \$7 / \$72 = 9.72%

9. Cost of Debt • We estimate the before-tax cost of debt, and then calculate the after-tax cost of debt • Note that interest paid 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 rate of return

10. 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? (assuming annual compounding)

11. 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.

12. 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?

13. 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

14. 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%

15. The WACC for ADK Industries: = (.4925 x 10.75%) + (.3609 x 9.72%) + (.1466 x 8.26%)(1 - .3592) = 9.58%

16. 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 • 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

17. 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

18. 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

19. 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

20. 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