Intro to Finance: Capital Structure - Optimal Capital Structure, Minimize WACC Maximize Firm Value

What This Is

Optimal capital structure refers to the mix of debt and equity that minimizes a company's weighted average cost of capital (WACC) and maximizes its firm value. This concept is crucial in finance as it helps companies make informed decisions about how to finance their investments and operations. For example, consider Apple Inc., which has a market value of $2 trillion and a debt-to-equity ratio of 0.2. If Apple can reduce its WACC from 6.5% to 6.0% by adjusting its capital structure, it can potentially increase its firm value by $10 billion.

Key Formulas & Symbols

• WACC = (E/V x Re) + (D/V x Rd x (1 - T)) where WACC = weighted average cost of capital, E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, T = corporate tax rate.
• Cost of Equity (Re) = Rf +-× (Rm - Rf) where Re = cost of equity, Rf = risk-free rate,-= beta coefficient, Rm = market return.
• Cost of Debt (Rd) = Coupon Rate + (Default Risk Premium) where Rd = cost of debt, Coupon Rate = interest rate on debt, Default Risk Premium = additional return for default risk.
• Market Value of Equity (E) = Number of Shares × Current Stock Price where E = market value of equity, Number of Shares = outstanding shares, Current Stock Price = current stock price.
• Market Value of Debt (D) = Face Value × (1 + Coupon Rate) where D = market value of debt, Face Value = face value of debt, Coupon Rate = interest rate on debt.
• Debt-to-Equity Ratio (D/E) = D/E = D/V where D/E = debt-to-equity ratio, D = market value of debt, V = total market value.
• Firm Value (FV) = Present Value of Expected Future Cash Flows where FV = firm value, Present Value = present value of expected future cash flows.

Step-by-Step Calculation

1. Estimate the cost of equity (Re) using the CAPM formula: Re = Rf +-× (Rm - Rf).
2. Estimate the cost of debt (Rd) using the formula: Rd = Coupon Rate + (Default Risk Premium).
3. Calculate the market value of equity (E) and market value of debt (D) using the formulas: E = Number of Shares × Current Stock Price and D = Face Value × (1 + Coupon Rate).
4. Calculate the weighted average cost of capital (WACC) using the formula: WACC = (E/V x Re) + (D/V x Rd x (1 - T)).
5. Determine the optimal capital structure by minimizing WACC and maximizing firm value.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value for WACC as it reflects the current market price of equity and debt.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR is the rate of return on investment, while NPV is the present value of expected future cash flows.
• Mistake: Ignoring default risk premium when estimating cost of debt.
• Correction: Include default risk premium in the cost of debt estimate to reflect the risk of default.

Exam / CFA Tips

• Tip: Be prepared to estimate cost of equity and cost of debt using different methods, such as CAPM and bond yield.
• Tip: Understand the difference between WACC and cost of capital for individual securities.
• Tip: Be able to calculate firm value using different methods, such as DCF and market capitalization.

Quick Practice Problem

Apple Inc. has a market value of $2 trillion, a debt-to-equity ratio of 0.2, and a cost of equity of 8%. If the corporate tax rate is 20%, what is Apple's WACC?

Answer: WACC = 6.4% Explanation: WACC = (0.8 x 8%) + (0.2 x 4% x (1 - 0.2)) = 6.4%

Last-Minute Cram Sheet

• The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• WACC = (E/V x Re) + (D/V x Rd x (1 - T)).
• Cost of Equity (Re) = Rf +-× (Rm - Rf).
• Cost of Debt (Rd) = Coupon Rate + (Default Risk Premium).
• Market Value of Equity (E) = Number of Shares × Current Stock Price.
• Market Value of Debt (D) = Face Value × (1 + Coupon Rate).
• Debt-to-Equity Ratio (D/E) = D/E = D/V.
• Firm Value (FV) = Present Value of Expected Future Cash Flows.
• The weighted average cost of capital (WACC) is not the same as the cost of capital for individual securities.
• The cost of debt (Rd) includes default risk premium.