Intro to Finance: Valuation - Stock Valuation, Dividend Discount Model DDM Gordon Growth Model

What This Is

The Dividend Discount Model (DDM) and Gordon Growth Model are fundamental tools in stock valuation. They help investors estimate a stock's intrinsic value by discounting future dividend payments. For example, consider Apple (AAPL) with a current stock price of $150 and a dividend yield of 1.2%. Using the DDM, we can estimate the intrinsic value of AAPL.

Key Formulas & Symbols

• DDM = ?(D1 / (1 + r)^n) where D1 = first dividend payment, r = required rate of return, n = number of periods.
• D1 = current dividend per share
• r = required rate of return (e.g., cost of equity)
• n = number of periods (e.g., years)
• Gordon Growth Model = D1 / (r - g) where g = expected growth rate of dividends.
• D1 = current dividend per share
• r = required rate of return (e.g., cost of equity)
• g = expected growth rate of dividends
• r = WACC + (? * (Rm - Rf)) where WACC = weighted average cost of capital,-= beta, Rm = market return, Rf = risk-free rate.
• WACC = weighted average cost of capital
• ? = beta (systematic risk)
• Rm = market return
• Rf = risk-free rate
• ? = (Cov(Ri, Rm) / ?m^2) where Cov(Ri, Rm) = covariance between stock and market returns, ?m^2 = variance of market returns.
• Cov(Ri, Rm) = covariance between stock and market returns
• ?m^2 = variance of market returns
• WACC = (E/V * Re) + (D/V * Rd * (1 - Tc)) where E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, Tc = corporate tax rate.
• E = market value of equity
• V = total market value
• Re = cost of equity
• D = market value of debt
• Rd = cost of debt
• Tc = corporate tax rate

Step-by-Step Calculation

1. Estimate the required rate of return (r) using the CAPM formula: r = WACC + (? * (Rm - Rf)).
2. Estimate the expected growth rate of dividends (g) using historical data or industry averages.
3. Calculate the dividend discount model (DDM) using the formula: DDM = ?(D1 / (1 + r)^n).
4. Calculate the Gordon growth model using the formula: Gordon Growth Model = D1 / (r - g).
5. Compare the calculated intrinsic value with the current stock price to determine if the stock is undervalued or overvalued.

Common Mistakes

• Mistake: Using the wrong required rate of return (r) in the DDM.
• Correction: Use the correct required rate of return (r) based on the company's risk profile and market conditions.
• Mistake: Assuming the expected growth rate of dividends (g) is constant over time.
• Correction: Estimate the expected growth rate of dividends (g) using historical data or industry averages, and consider the potential for changes in growth rates over time.
• Mistake: Failing to consider the impact of taxes on the cost of debt (Rd).
• Correction: Include the impact of taxes on the cost of debt (Rd) when calculating the weighted average cost of capital (WACC).

Exam / CFA Tips

• Tip: Be prepared to calculate the required rate of return (r) using the CAPM formula, and to estimate the expected growth rate of dividends (g) using historical data or industry averages.
• Tip: Consider the impact of taxes on the cost of debt (Rd) when calculating the weighted average cost of capital (WACC).
• Tip: Be prepared to compare the calculated intrinsic value with the current stock price to determine if the stock is undervalued or overvalued.

Quick Practice Problem

Tesla (TSLA) has a current stock price of $500 and a dividend yield of 0.5%. If the required rate of return (r) is 10% and the expected growth rate of dividends (g) is 5%, what is the intrinsic value of TSLA using the Gordon growth model?

Answer: $625. Explanation: Gordon Growth Model = D1 / (r - g) = $2.50 / (0.10 - 0.05) = $625.

Last-Minute Cram Sheet

• The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• The Gordon growth model assumes a constant growth rate of dividends over time.
• WACC = (E/V * Re) + (D/V * Rd * (1 - Tc)).
• ? = (Cov(Ri, Rm) / ?m^2).
• The required rate of return (r) is calculated using the CAPM formula: r = WACC + (? * (Rm - Rf)).
• The expected growth rate of dividends (g) is estimated using historical data or industry averages.
• The intrinsic value of a stock is calculated using the DDM or Gordon growth model.
• The DDM assumes a constant dividend payout ratio over time.
• The Gordon growth model is a special case of the DDM where g = D1 / P0.