Introductory Corporate Finance: Cost of Capital Cost of Common Equity Dividend Growth Model re D₁ P₀ g CAPM re Rf β Rm Rf Bond Yield Plus Risk Premium BYPRP

What This Is

The cost of common equity is a crucial concept in corporate finance, as it represents the minimum return required by shareholders to maintain their investment in a company. It is essential to estimate the cost of common equity accurately, as it affects the weighted average cost of capital (WACC) and, consequently, the firm's valuation and investment decisions. For instance, consider Tesla, Inc. (TSLA), which has a market capitalization of $1 trillion. If we assume a dividend yield of 0.5% and a growth rate of 15%, the cost of common equity using the dividend growth model would be approximately 6.5%.

Key Formulas & Models

• re = D₁ / P₀ + g – cost of common equity using the dividend growth model; D₁ is the next year's dividend, P₀ is the current price, and g is the growth rate.
• re = Rf + β × (Rm – Rf) – cost of common equity using the Capital Asset Pricing Model (CAPM); Rf is the risk-free rate, β is the beta coefficient, and Rm is the market return.
• re = r + (D/P) × (1 + g) – cost of common equity using the bond yield plus risk premium (BYPRP) model; r is the bond yield, D/P is the dividend payout ratio, and g is the growth rate.
• β = Cov(Ri, Rm) / σm² – beta coefficient; Cov(Ri, Rm) is the covariance between the stock's return and the market return, and σm² is the variance of the market return.
• Rf = (1 + r)^(1/n) - 1 – risk-free rate; r is the annual bond yield, and n is the number of compounding periods.
• Rm = (1 + Rm)^(1/n) - 1 – market return; Rm is the annual market return, and n is the number of compounding periods.
• g = (1 + r)^(1/n) - 1 – growth rate; r is the annual growth rate, and n is the number of compounding periods.

Step-by-Step Calculation

1. Estimate the risk-free rate (Rf) using a 10-year Treasury bond yield or a similar benchmark.
2. Estimate the market return (Rm) using historical data or a market index (e.g., S&P 500).
3. Estimate the beta coefficient (β) using historical stock price data or a beta estimate from a financial database.
4. Calculate the cost of common equity using the CAPM formula: re = Rf + β × (Rm – Rf).
5. Alternatively, use the dividend growth model: re = D₁ / P₀ + g, where D₁ is the next year's dividend, P₀ is the current price, and g is the growth rate.
6. For the BYPRP model, calculate the bond yield (r) and the dividend payout ratio (D/P), then use the formula: re = r + (D/P) × (1 + g).

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 the company's assets and liabilities.
• Mistake: Ignoring flotation costs when calculating WACC.
• Correction: Include flotation costs in the WACC calculation, as they represent the costs associated with issuing new debt or equity.
• Mistake: Confusing sunk cost with opportunity cost.
• Correction: Distinguish between sunk costs (irrecoverable expenses) and opportunity costs (foregone benefits), as they have different implications for investment decisions.

Exam / CFA Tips

• Be prepared to calculate the cost of common equity using different models (CAPM, dividend growth, BYPRP).
• Understand the assumptions and limitations of each model.
• Be aware of common mistakes, such as using book value instead of market value for WACC.
• Practice calculating the cost of common equity using real-world examples and data.

Quick Practice Problem

A company has a market capitalization of $10 billion, a dividend payout ratio of 40%, and a growth rate of 10%. What is the cost of common equity using the dividend growth model?

Answer: 4.2% Explanation: re = D₁ / P₀ + g = 0.4 × $400M / $10B + 0.1 = 4.2%

Last-Minute Cram Sheet

• Cost of common equity: re = D₁ / P₀ + g (dividend growth model) or re = Rf + β × (Rm – Rf) (CAPM).
• Beta coefficient: β = Cov(Ri, Rm) / σm².
• Risk-free rate: Rf = (1 + r)^(1/n) - 1.
• Market return: Rm = (1 + Rm)^(1/n) - 1.
• Growth rate: g = (1 + r)^(1/n) - 1.
• BYPRP model: re = r + (D/P) × (1 + g).
• ⚠️ 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.
• ⚠️ WACC = wd × rd(1-T) + wps × rps + we × re, where wd, wps, and we are the weights of debt, preferred stock, and equity, respectively.
• ⚠️ Flotation costs are ignored in WACC calculations, but they should be included in the cost of capital.
• ⚠️ Sunk costs are irrecoverable expenses, while opportunity costs are foregone benefits.