Practice Problem – Dividend Discount Model

Practice Question

Intro to Finance
Equity Valuation
Dividend Discount Model
Short Answer

Golden State Inc. has a beta of 1.20. The risk-free rate is 6% and the expected return on the market portfolio is 14.5%. The company presently pays an annual dividend of $5 per share. However, investors expect all future dividends to experience a decline of 1% per annum for many years to come. What is the stock’s present market price per share, assuming the required rate of return is determined by the CAPM?

Answer +
Correct Answer: $28.77
Explanation +
Step 1: Calculate Required Rate of Return Using CAPM

Formula: r = Rf + β(Rm − Rf)

Substitute values: r = 0.06 + 1.20 × (0.145 − 0.06) = 0.06 + 0.102 = 0.162

The required rate of return is 16.2%.

Step 2: Use the Gordon Growth Model

Formula: P₀ = D₁ ÷ (r − g)

Where:

  • D₀ = 5
  • g = −0.01 → D₁ = D₀ × (1 + g) = 5 × 0.99 = 4.95
  • r = 0.162
Step 3: Calculate Price

P₀ = 4.95 ÷ (0.162 − (−0.01)) = 4.95 ÷ 0.172 ≈ 28.77

Final Answer:

The stock’s present market price per share is approximately $28.77.