Question

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

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%. Suppose that you borrow only \$45,000 in financing the project. According to MM proposition II, what is the firm's equity cost of capital?

(PLEASE provide formulas, Step-by-step process for all sections/parts, **don't use spreadsheet, I need to see the complete work out for all parts**)

Present value (equity cash flows - unlevered) = { (0.5) x \$90,000 + (0.5) x \$117,000 } / 1.15

= [\$45,000 + \$58500] / 1.15

= \$103500 / 1.15
= \$90,000

Given ,

Cost of capital of levered equity = Cost of capital of unlevered equity + premium proportional to debt-equity ratio

Numerically, rE = rU + D/E (rU - rD)
rE = .015 + [45000 / (90000 - 45000)] x (.15 - .05) = 0.25 or 25%

So, according to MM proposition II, the firm's equity cost of capital = 25%

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