Practice Problem – Dividend Discount Model

Practice Question

Intro to Finance
Equity Valuation
Dividend Discount Model
Short Answer

LVMH Inc. is expecting a period of intense growth, so it has decided to retain more of its earnings to help finance their expected growth. Therefore, LVMH Inc. has reduced its annual dividend by 10% a year for the next three years. After that it will maintain a constant dividend of $0.75 a share. The company just paid a dividend of $1.80 per share. What is the market value of this stock if the required rate of return is 13%?

Answer +
Correct Answer: $7.48
Explanation +
Step 1: Calculate Future Dividends

- D₀ = 1.80
- D₁ = 1.80 × 0.90 = 1.62
- D₂ = 1.62 × 0.90 = 1.458
- D₃ = 1.458 × 0.90 = 1.3122
- D₄ = 0.75 (constant thereafter)

Step 2: Calculate Present Value of Each Dividend

Using the formula PV = D / (1 + r)ⁿ with r = 13%:

  • PV₁ = 1.62 / (1.13) ≈ 1.43
  • PV₂ = 1.458 / (1.13)² ≈ 1.14
  • PV₃ = 1.3122 / (1.13)³ ≈ 0.91

Step 3: Calculate PV of Perpetuity (Starting in Year 4)

Value at Year 3: PV = 0.75 / 0.13 ≈ 5.7692
Discount back to present: 5.7692 / (1.13)³ ≈ 4.00

Step 4: Add Everything Up

Total Present Value = 1.43 + 1.14 + 0.91 + 4.00 = $7.48

Conclusion

The market value of LVMH Inc.'s stock is approximately $7.48.