Intro to Finance: Cost of Capital Weighted Average Cost of Capital WACC wdRd1T wpRp weRe

What This Is

The Weighted Average Cost of Capital (WACC) is a crucial concept in finance that represents the minimum return required by a company's investors to maintain their investment. It's a weighted average of the costs of debt and equity, where the weights are the proportions of debt and equity in the company's capital structure. For example, let's consider Apple Inc. with a market value of $2 trillion, $500 billion in debt, and $1.5 trillion in equity. Assuming a 30% debt-to-equity ratio, a 6% cost of debt, and a 10% cost of equity, Apple's WACC would be approximately 7.5%.

Key Formulas & Symbols

• WACC = wd×Rd(1‑T) + wp×Rp + we×Re where:
• WACC = Weighted Average Cost of Capital
• wd = Proportion of debt in the capital structure
• Rd = Cost of debt
• T = Corporate tax rate
• wp = Proportion of preferred stock in the capital structure
• Rp = Cost of preferred stock
• we = Proportion of equity in the capital structure
• Re = Cost of equity
• Cost of debt (Rd) = Rd = (1 + Rd)^n / (1 + Rd)^n - 1 where Rd is the periodic interest rate, n is the number of periods, and Rd is the cost of debt.
• Cost of equity (Re) = Re = Rf + β × (Rm - Rf) where Rf is the risk-free rate, β is the beta of the stock, Rm is the market return, and Re is the cost of equity.
• Beta (β) = β = Cov(Ri, Rm) / σm^2 where Ri is the return on the stock, Rm is the market return, σm is the market volatility, and Cov is the covariance.
• Market value of equity (MVE) = MVE = Number of shares × Current stock price
• Market value of debt (MVD) = MVD = Face value of debt × (1 + Coupon rate)^n / (1 + Coupon rate)^n - 1

Step-by-Step Calculation

1. Determine the proportions of debt, preferred stock, and equity in the capital structure.
2. Calculate the cost of debt using the formula Rd = (1 + Rd)^n / (1 + Rd)^n - 1.
3. Calculate the cost of preferred stock using the market value of preferred stock and its face value.
4. Calculate the cost of equity using the formula Re = Rf + β × (Rm - Rf).
5. Calculate the WACC using the formula WACC = wd×Rd(1‑T) + wp×Rp + we×Re.
6. Verify that the WACC is reasonable by checking that it's between the cost of debt and the cost of equity.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market values to reflect the current market conditions.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR is the rate at which the NPV equals zero, while NPV ranking is based on the magnitude of the NPV.
• Mistake: Ignoring the tax effect on debt.
• Correction: Include the tax effect on debt to accurately calculate the WACC.
• Mistake: Using an incorrect beta value.
• Correction: Use a reliable source to obtain the beta value, such as a financial database or a reputable research firm.

Exam / CFA Tips

• Tip: Be prepared to calculate WACC using different scenarios, such as changes in the capital structure or interest rates.
• Tip: Understand the concept of beta and its impact on the cost of equity.
• Tip: Be aware of the tax effect on debt and its impact on the WACC.

Quick Practice Problem

Apple Inc. has a market value of $2 trillion, $500 billion in debt, and $1.5 trillion in equity. Assuming a 30% debt-to-equity ratio, a 6% cost of debt, and a 10% cost of equity, what is Apple's WACC?

Answer: 7.5% Explanation: Using the formula WACC = wd×Rd(1‑T) + wp×Rp + we×Re, we can calculate Apple's WACC as follows:

WACC = 0.3 × 0.06 × (1 - 0.21) + 0 × 0.08 + 0.7 × 0.10 = 0.075

Last-Minute Cram Sheet

• ⚠️ The WACC is a weighted average of the costs of debt and equity.
• ⚠️ The cost of debt is calculated using the formula Rd = (1 + Rd)^n / (1 + Rd)^n - 1.
• ⚠️ The cost of equity is calculated using the formula Re = Rf + β × (Rm - Rf).
• ⚠️ The beta value is used to calculate the cost of equity.
• ⚠️ The tax effect on debt is included in the WACC calculation.
• ⚠️ The WACC is used to evaluate investment opportunities.
• ⚠️ The WACC is a key input in the capital asset pricing model (CAPM).
• ⚠️ The WACC is used to calculate the present value of future cash flows.
• ⚠️ The WACC is a key concept in corporate finance.