Web Appendix 12D

# Web Appendix 12D - 19819_12Dw_p1-4.qxd 10:39 AM Page 12D-1...

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12D-1 As an alternative to the subjective approach, firms can use the CAPM to directly estimate the cost of capital for specific projects or divisions. To begin, recall from Chapter 8 that the Security Market Line equation expresses the risk/return relationship: r s 5 r RF 1 (RP M )b i As an example, consider the case of Erie Steel Company, an integrated steel producer oper- ating in the Great Lakes region. For simplicity, assume that Erie uses only equity capital, so its cost of equity is also its corporate cost of capital, or WACC. Erie’s beta 5 b 5 1.1; r RF 5 8%; and RP M 5 4%. Thus, Erie’s cost of equity and hence its WACC is 12.4 percent: r s 5 WACC 5 8% 1 (4%)1.1 5 12.4% This suggests that investors should be willing to give Erie money to invest in average-risk projects if the company expects to earn 12.4 percent or more on this money. Here again, by average risk we mean projects having risk similar to the firm’s existing assets. Therefore, as a first approximation, Erie should invest in capital projects if and only if those projects have an expected return of 12.4 percent or more. 1 Erie should use 12.4 percent as its hurdle rate for an average-risk project. Suppose, however, that taking on a particular project would cause a change in Erie’s beta coefficient, which, in turn, would change the company’s cost of equity. For example, suppose Erie is considering the construction of a fleet of barges to haul iron ore, and barge operations have betas of 1.5 rather than 1.1. Since the firm itself may be regarded as a “portfolio of assets,” and since the beta of any portfolio is a weighted average of the betas of its individual assets, taking on the barge project would cause the overall corporate beta to rise to somewhere between the original beta of 1.1 and the barge project’s beta of 1.5. The exact value of the new beta would depend on the relative size of the investment in barge operations versus Erie’s other assets. If 80 percent of Erie’s total funds ended up in basic steel operations with a beta of 1.1 and 20 percent in barge operations with a beta of 1.5, the new corporate beta would be 1.18: New beta 5 0.8(1.1) 1 0.2(1.5) 5 1.18 This increase in Erie’s beta coefficient would cause its stock price to decline unless the increased beta were offset by a higher expected rate of return . Specifically, taking on the new proj- ect would cause the overall corporate WACC to rise from the original 12.4 to 12.72 percent: r s 5 8%

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Web Appendix 12D - 19819_12Dw_p1-4.qxd 10:39 AM Page 12D-1...

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