Steadybeta currently operates 3 projects, resulting in a beta of 1.27. It is considering a risky expansion project whose cash flow analysis indicates a beta of 2.3.
The project requires a capital commitment of $4.8 million and has an NPV of $2 million. The current risk-free rate is 5.6% and the market risk premium is 8.9%.
Steadybeta's current market capitalization is $17.2 million. If Steadybeta undertook the project, the required rate of return expected by its shareholders will be:
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A. B. C. D.C
19.5% The firm can be considered a portfolio of 4 projects. The beta of a portfolio equals the weighted average of the betas of the individual components. The weight of a component equals the fraction of the market value it comprises. Since the project has an NPV of $2 million, its market value equals $6.8 million and the market value after the project is undertaken will be $(17.2+6.8) = $24 million. Therefore, the beta of the firm after it undertakes the project equals 17.2/24*1.27 +
6.8/24*2.3 = 1.56. The required rate of return then equals 5.6% + 1.56*8.9% = 19.5%.