Question

Your firm is financed 100% with equity and has a cost of equity capital of 15%. You are considering your first debt issue, which would change your capital structure to 29% debt and 71% equity. If your cost of debt is 7%, what will be your new cost of equity? Assume no change in your firm's WACC due to the change in capital structures.

Answer 1

The new cost of equity for a firm changing its capital structure to include debt is calculated using the original cost of equity, the cost of debt, and the proposed debt-to-equity ratio, based on Modigliani and Miller Proposition II.

Step-by-step explanation:

The question seeks to determine the new cost of equity after a firm, initially financed 100% by equity, shifts its capital structure to include debt. According to the Modigliani and Miller Proposition II, the cost of equity increases with financial leverage because equity becomes riskier to compensate for the additional debt risk.

To calculate the new cost of equity, we need the original cost of equity, which is 15%, the cost of debt, which is 7%, and the proposed debt-to-equity ratio from the new capital structure. With no change in the firm's weighted average cost of capital (WACC), we can use the formula:

Cost of Equitynew = Cost of Equityoriginal + (Cost of Equityoriginal - Cost of Debt) * (Debt/Equity)

Replacing the given values, we calculate:
Cost of Equitynew = 15% + (15% - 7%) * (29/71)

By computing these, the firm can arrive at its new cost of equity after issuing debt. It is important to note that the cost of debt is lower than the cost of equity due to the tax shield effect of debt and debt holders' priority over equity holders in claiming the firm's assets.