A project has an IRR of 16% and is being considered by a firm with $5 million in debt and $15 million in equity. Assuming the debt costs 12% (after-tax value), what is the most equity can cost for the project to be acceptable to the firm? (hint: set the IRR equal to WACC)

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Quizplus · Accepted Answer

The Weighted Average Cost of Capital (WACC) is calculated as the weighted sum of the cost of equity and the cost of debt. Given that the IRR (Internal Rate of Return) must equal the WACC for the project to be acceptable, we can set up the equation as follows: $$ WACC = \left(\frac{Equity}{Equity + Debt}\right) \times Cost\_of\_Equity + \left(\frac{Debt}{Equity + Debt}\right) \times Cost\_of\_Debt $$Given:- Equity = $15 million- Debt = $5 million- Cost of Debt = 12%- IRR (which we set equal to WACC) = 16%Substituting the given values:$$ 16\% = \left(\frac{15}{15 + 5}\right) \times Cost\_of\_Equity + \left(\frac{5}{15 + 5}\right) \times 12\% $$$$ 16\% = \left(\frac{15}{20}\right) \times Cost\_of\_Equity + \left(\frac{5}{20}\right) \times 12\% $$$$ 16\% = 0.75 \times Cost\_of\_Equity + 0.25 \times 12\% $$Solving for Cost_of_Equity:$$ 16\% = 0.75 \times Cost\_of\_Equity + 3\% $$$$ 13\% = 0.75 \times Cost\_of\_Equity $$$$ Cost\_of\_Equity = \frac{13\%}{0.75} = 17.33\% $$Therefore, the most equity can cost for the project to be acceptable to the firm is 17.33%.

A Project Has an IRR of 16% and Is Being