Consider a project with free cash flows in one year of $90,000 in a weak economy

Question

Consider a project with free cash flows in one year of $90,000 in a weak economy or $117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is $80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%. Sisyphean Bolder Movers Incorporated has no debt, a total equity capitalization of $50 billion, and a beta of 2.0. Included in Sisyphean's assets are $12 billion in cash and risk-free securities. Required: Calculate Sisyphean's enterprise value and unlevered beta considering the fact that Sisyphean's cash is risk-free.

Explanation / Answer

Consider a project with free cash flows in one year of $90,000 in a weak economy or $117,000 in a strong economy, with each outcome being equally likely. The initial investment required for the project is $80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%.

PV(equity cash flows -unleverd) = [(0.5)*90,000+.5*117,000]/1.15 = $90,000

Given Re = Ru+D/e*(Ru-Rd)

Re =0.15+45,000/(90,000-45,000)(0.15-.05) =0.25 or 25%

Sisyphean Bolder Movers Incorporated has no debt, a total equity capitalization of $50 billion, and a beta of 2.0. Included in Sisyphean's assets are $12 billion in cash and risk-free securities. Required: Calculate Sisyphean's enterprise value and unlevered beta considering the fact that Sisyphean's cash is risk-free.

Calculate Sisyphean's enterprise value

Enterprise value = Market value-Cash = $50 billion-$12 billion = $8 billion

unlevered beta considering the fact that Sisyphean's cash is risk-free.

Beta u = E/(E+D)*BetaE+D/(E+D)*Beta D

Bu= 50/(50-12)*2-12/(50-12)*0 = 2.63

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