Introductory Corporate Finance: Cost of Capital - Weighted Average Cost of Capital, WACC = wd rd(1 - T) + wps rps + we re

What This Is

The Weighted Average Cost of Capital (WACC) is a crucial concept in corporate finance that represents the minimum return required by investors to keep the company afloat. It's a weighted average of the costs of different sources of capital, such as debt and equity. For instance, let's consider Tesla, Inc. (TSLA), which has a market capitalization of $1 trillion, debt of $10 billion, and preferred stock of $5 billion. Assuming a market value of equity, debt, and preferred stock, and using the respective costs of capital, we can calculate Tesla's WACC.

Key Formulas & Models

• WACC = wd × rd(1-T) + wps × rps + we × re – weighted average cost of capital; used as discount rate.
• wd: weight of debt (market value of debt / total market value of capital)
• rd: cost of debt (interest rate on debt)
• T: corporate tax rate
• wps: weight of preferred stock (market value of preferred stock / total market value of capital)
• rps: cost of preferred stock (dividend yield on preferred stock)
• we: weight of equity (market value of equity / total market value of capital)
• re: cost of equity (required rate of return on equity)
• Market Value of Capital = Market Value of Equity + Market Value of Debt + Market Value of Preferred Stock
• Cost of Debt = Interest Rate on Debt
• Cost of Preferred Stock = Dividend Yield on Preferred Stock
• Cost of Equity = Required Rate of Return on Equity (e.g., CAPM: re = Rf +-× (Rm - Rf))
• ? (Beta) = Systematic Risk of the Company
• Rf = Risk-Free Rate
• Rm = Market Return

Step-by-Step Calculation

1. Determine the market value of each component of capital (equity, debt, and preferred stock).
2. Calculate the weight of each component (wd, wps, we).
3. Determine the cost of debt (rd), cost of preferred stock (rps), and cost of equity (re).
4. Plug the values into the WACC formula: WACC = wd × rd(1-T) + wps × rps + we × re
5. Verify the WACC calculation by ensuring that the weights add up to 1 (wd + wps + we = 1).

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value to reflect the current market conditions and avoid overestimating the WACC.
• Counterexample: If a company has a book value of $100 million and a market value of $500 million, using book value would result in a WACC of 10%, whereas using market value would result in a WACC of 5%.
• Mistake: Ignoring flotation costs when calculating WACC.
• Correction: Include flotation costs in the WACC calculation to reflect the true cost of capital.
• Counterexample: If a company issues $100 million in debt with a flotation cost of 2%, the WACC would increase by 2% due to the flotation cost.
• Mistake: Confusing sunk cost with opportunity cost.
• Correction: Use opportunity cost to reflect the true cost of capital, not sunk cost.
• Counterexample: If a company has a sunk cost of $10 million, using it as the cost of capital would result in a WACC of 10%, whereas using the opportunity cost would result in a WACC of 5%.

Exam / CFA Tips

• Tip: Be prepared to calculate WACC using different scenarios, such as changes in interest rates, tax rates, or capital structure.
• Tip: Understand the differences between M&M Proposition I (no taxes) and M&M Proposition II (with taxes) and how they affect WACC.
• Tip: Be able to explain the concept of WACC and its importance in corporate finance, including its use as a discount rate.

Quick Practice Problem

A company has EBIT of $10 million, interest of $2 million, and a tax rate of 25%. Calculate the Debt-Free Leverage (DFL).

Answer: DFL = (EBIT - Interest) / EBIT = ($10 million - $2 million) / $10 million = 0.8

Explanation: The DFL measures the company's ability to service its debt without using EBIT.

Last-Minute Cram Sheet

1. WACC = weighted average cost of capital.
2. WACC = wd × rd(1-T) + wps × rps + we × re
3. Market Value of Capital = Market Value of Equity + Market Value of Debt + Market Value of Preferred Stock.
4. Cost of Debt = Interest Rate on Debt.
5. Cost of Preferred Stock = Dividend Yield on Preferred Stock.
6. Cost of Equity = Required Rate of Return on Equity (e.g., CAPM: re = Rf +-× (Rm - Rf)).
7. ? (Beta) = Systematic Risk of the Company.
8. Rf = Risk-Free Rate.
9. Rm = Market Return.
10. In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.