A firm is worth $1,400, has a 35% tax rate, total debt of $600, an unlevered return of 15%, and a cost of debt of 9%. What is the cost of equity?

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The cost of equity can be calculated using the Modigliani-Miller Proposition II with taxes, which states that the cost of equity (Re) is equal to the unlevered cost of equity (Ru) plus the debt-to-equity ratio (D/E) times the spread between the unlevered cost of equity and the cost of debt (Rd), all adjusted for the tax rate (Tc). The formula is: Re = Ru + (D/E)(1 - Tc)(Ru - Rd).Given:- Firm value (V) = $1,400- Total debt (D) = $600- Unlevered return (Ru) = 15% or 0.15- Cost of debt (Rd) = 9% or 0.09- Tax rate (Tc) = 35% or 0.35First, calculate the equity value (E) of the firm: E = V - D = $1,400 - $600 = $800.Then, calculate the debt-to-equity ratio (D/E): D/E = $600 / $800 = 0.75.Now, apply the formula: Re = 0.15 + (0.75)(1 - 0.35)(0.15 - 0.09) = 0.15 + (0.75)(0.65)(0.06) = 0.15 + 0.02925 = 0.17925 or 17.93%.

A Firm Is Worth $1,400, Has a 35% Tax Rate