Question

A company pays dividends annually on Dec. 31. Yesterday's dividend was $1. Dividends are expected to grow for the next 2 years at 10% and then settle down to a longrun growth rate of 5% in perpetuity. Because of the initial riskiness of the company, investors required a 20% rate of return over the first 2 years, but only a 12% rate of return thereafter. What is the fair price for the stock today, January 1?

Answer 1

D₀ = $ 1

D₁ = D₀ x (1+g) = $ 1 x (1+0.1) = $ 1 x 1.1 = $ 1.1

D₂ = D₁ x (1+g) = $ 1.1 x (1+0.1) = $ 1.1 x 1.1 = $ 1.21

D₃ = D₂ x (1+g) = $ 1.1 x (1+0.05) = $ 1.21 x 1.05 = $ 1.2705

As per Dividend Discount Model, stock price in year 2 can be computed as:

P ₂ = D₃/(r – g)

r = cost of capital = 12 % or 0.12

g = Constant growth rate of dividend = 5 % or 0.05

     P ₂ = $ 1.2705/ (0.12 – 0.05)

      = $ 1.2705/ 0.07

      = $ 18.15

Current stock price P₀ = D₁ / (1+r) + D₂ / (1+r) ² + P₂ / (1+r) ²

  = $ 1.1 / (1+0.2) + $ 1.21 / (1+0.2) ² + $ 18.15/ (1+0.2) ²

= $ 1.1 / (1.2) + $ 1.21 / (1.2) ² + $ 18.15/ (1.2) ²

= $ 1.1 /1.2 + $ 1.21 / 1.44 + $ 18.15/ 1.44

= $ 0.916666666666667 + $ 0.840277777777778 + 12.6041666666667

= $ 14.361111111111100 or $ 14.36

Current stock price of the company is $ 14.36