Question

Mobray Corp. is experiencing rapid growth. Dividends are expected to grow at 26 percent per year during the next three years, 16 percent over the following year, and then 4 percent per year indefinitely. The required return on this stock is 10 percent, and the stock currently sells for $64 per share. What is the projected dividend for the coming year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Please help me how to solve this question. thank you so much!!

Answer 1

Let the dividend in year n be D_n

Let Dividend this year be D₀

Growth in Year 1 to 3 = g₁ = 26%

Hence, D₁ = D₀(1+g₁) = D₀(1+0.26)

D₂ = D₁(1+g₁) = D₀(1+0.26)²

D₃ = D₂(1+g₁) = D₀(1+0.26)³

Growth in year 4 = g₂ = 16%

Hence, D₄ = D₃(1+g₂) = D₀(1+0.26)³(1+0.16)

Growth after year 4 = g = 4%

Hence, D₅ = D₄(1+g) = D₀(1+0.26)³(1+0.16)(1+0.04)

Required Return = r = 10%

Using Gordon's Growth formula,

Price of Stock in Year 4 = P₄ = D₅/(r - g) = D₀(1+0.26)³(1+0.16)(1+0.04)/(0.10 - 0.04)

Price of Stock now = P₀ = D₁/(1+r) + D₂/(1+r)² + D₃/(1+r)³ + D₄/(1+r)⁴ + P₄/(1+r)⁴

Given, P0 = $64

=> 64 = D₁/(1+r) + D₂/(1+r)² + D₃/(1+r)³ + D₄/(1+r)⁴ + P₄/(1+r)⁴

=> 64 = D₀(1+0.26)/(1+0.10) + D₀(1+0.26)²/(1+0.10)² + D₀(1+0.26)³/(1+0.10)³ + D₀(1+0.26)³(1+0.16)/(1+0.10)⁴ + (D₀(1+0.26)³(1+0.16)(1+0.04)/(0.10 - 0.04))/(1+0.10)⁴

=> 64 = 33.02D₀

=> D₀ = 64/33.02 = $1.94

=> D₁ = D₀(1+g₁) = D₀(1+0.26) = 1.94(1+0.26) = $2.44

Hence, Dividend next year = $2.44