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Finanças. November 7. Topics covered. CAPM for cost of capital Estimation of beta. Risk and cost of capital. Previously: Determine the timing and the size of cash flows Now: determine the discount rate for risky cash flows The discount rate can be computed from the CAPM.

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November 7

QDai for FEUNL

Topics covered

  • CAPM for cost of capital

  • Estimation of beta

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Risk and cost of capital

  • Previously: Determine the timing and the size of cash flows

  • Now: determine the discount rate for risky cash flows

  • The discount rate can be computed from the CAPM

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Pay cash dividend

Invest in project

Choices of a firm with extra cash

Shareholder invests in financial asset

Firm withexcess cash

A firm with excess cash can either pay a dividend or make a capital investment

Shareholder’s Terminal Value

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Capital budgeting rule

  • The discount rate of a project

  • The expected return

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Cost of capital

  • Example

    • Suppose the stock of a company has a beta of 2.5. The firm is 100-percent equity financed.

    • Assume a risk-free rate of 5-percent and a market risk premium of 10-percent.

    • What is the appropriate discount rate for an expansion of this firm?

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Project b

Project’s Estimated Cash Flows Next Year


NPV at 30%
















Example (continued)

Suppose the company is evaluating the following non-mutually exclusive projects. Each costs $100 and lasts one year.

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Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects




Firm’s risk (beta)

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Estimation of beta

  • Beta: Sensitivity of a stock’s return to the return on the market portfolio.

  • Market Portfolio: Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.

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Stability of Beta

  • Many analysts argue that betas are generally stable for firms remaining in the same industry.

  • That’s not to say that a firm’s beta can’t change.

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Using an Industry Beta

  • It is frequently argued that one can better estimate a firm’s beta by involving the whole industry.

  • If you believe that the operations of the firm are similar to the operations of the rest of the industry,

  • If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry

  • Adjustments

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Determinants of beta

  • Cylicality of revenues

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Determinants of beta

  • Operating leverage

    • how sensitive a firm is to its fixed costs.

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Operating Leverage



 Volume


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Determinants of beta

  • Financial leverage

    • Operating leverage

    • Financial leverage

    • The relationship between the betas of the firm’s debt, equity, and assets is given by:

    • The beta of debt

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Financial Leverage and Beta: Example

Consider a company which is currently all-equity and has a beta of 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 0.90. However, assuming a zero beta for its debt, its equity beta would become:

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Financial leverage and beta

  • Conclusion

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Extension of the basic model

  • The firm vs the project

    • The risk of a project

    • The project should be discounted with

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The firm vs the project

A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value.

Project IRR

Hurdle rate

Firm’s risk (beta)

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The firm vs the project

Suppose the Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4%; the market risk premium is 10% and the firm’s beta is 1.3.

17% = 4% + 1.3 × [14% – 4%]

This is a breakdown of the company’s investment projects:

1/3 Automotive retailer b = 2.0

1/3 Computer Hard Drive Mfr. b = 1.3

1/3 Electric Utility b = 0.6

average b of assets = 1.3

When evaluating a new electrical generation investment, which cost of capital should be used?

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Capital Budgeting & Project Risk


Project IRR


Investments in hard drives or auto retailing should have higher discount rates.



Project’s risk (b)




r = 4% + 0.6×(14% – 4% ) = 10% 10% reflects the opportunity cost of capital on an investment in electrical generation, given the unique risk of the project.

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Extention of the basic model

  • The Weighted Average Cost of Capital

  • It is because interest expense is tax-deductible that we multiply the last term by

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  • Example: a firms with a debt-equity ratio of 0.6, a cost of debt of 15.15%, and a cost of equity of 20%. The corporate tax rate is 34%.

  • Debt to value ratio=6/(10+6)=0.375

  • Equity to value ratio=1-0.375=0.625

  • rwacc=0.625*20%+0.375*15.15%*(1-0.34)


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Steps to calculate WACC

Cost of equity

Cost of debt

Calculate WACC

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