Practice Problem – Geometric Average Return

Practice Question

Intro to Finance
Equity Valuation
Dividend
Short Answer

A stock has year-end prices and dividends as below. What is the geometric average return?

Year 1: Price = $60.18, Dividend = $0
Year 2: Price = $73.66, Dividend = $0.60
Year 3: Price = $94.18, Dividend = $0.64
Year 4: Price = $89.35, Dividend = $0.72

Answer +
14.96%
Explanation +

Step 1: Calculate Total Returns Per Year

  • Year 1: R₁ = (73.66 + 0.60) / 60.18 - 1 ≈ 0.2339
  • Year 2: R₂ = (94.18 + 0.64) / 73.66 - 1 ≈ 0.2876
  • Year 3: R₃ = (89.35 + 0.72) / 94.18 - 1 ≈ -0.0436

Step 2: Convert to Growth Factors
1 + R₁ = 1.2339, 1 + R₂ = 1.2876, 1 + R₃ = 0.9564

Step 3: Geometric Average Formula
R₉ = (1.2339 × 1.2876 × 0.9564)^(1/3) - 1 ≈ 14.96%

Conclusion:
The geometric average return is approximately 14.96%.