Final answer:
The firm's cost of equity is calculated using the WACC formula with the given variables: yield to maturity on debt, tax rate, WACC, and D/E ratio. After applying these variables to the formula and solving, the cost of equity is found to be approximately 12%, which is option b.
Step-by-step explanation:
The student's question relates to calculating the firm's cost of equity when the firm's yield to maturity on debt is 9%, the tax rate is 21%, weighted average cost of capital (WACC) is 9.56%, and the debt-to-equity (D/E) ratio is 1. To solve this, we use the WACC formula, which incorporates the cost of equity, cost of debt, and the D/E ratio, adjusted for taxes.
WACC is given by the formula: WACC = (E/V) × Re + (D/V) × Rd × (1 - Tc), where E = equity, V = E + D (total value of financing), Re = cost of equity, D = debt, Rd = cost of debt, and Tc = corporate tax rate.
Given that the D/E ratio is 1, it means E = D or equivalently E/V = D/V = 0.5 (50%). With this ratio, the formula simplifies to: 0.0956 = 0.5 × Re + 0.5 × 0.09 × (1 - 0.21). Solving for Re gives us the cost of equity, which is the answer to the student's question.
Substituting the values and solving for Re: 0.0956 = 0.5 × Re + 0.5 × 0.09 × 0.79, 0.0956 = 0.5 × Re + 0.03555, 0.0956 - 0.03555 = 0.5 × Re, 0.06005 = 0.5 × Re, Re = 0.1201 or 12.01%.
Therefore, the firm's cost of equity is closest to 12%, which corresponds with option b.