Answer
Given,
current dividend, D₀ = $3.80, g₁ = g₂ = g₃ = 15%,
g = 5% and required return, k = 16%
Expected dividend, D₁= D₀ x (1 + g₁)
= $3.80 x (1.15) = $4.37
Expected dividend, D₂ = D₁ x (1 + g₂)
= $4.37 x (1.15) = $5.026
Expected dividend, D₃ = D₂ x (1 + g₃)
= $5.026 x (1.15) = $5.779
Expected dividend, D₄ = D₃ x (1 + g)
= $5.779 x (1.05) = $6.068
The price at the end of year 3, P₃ is
[tex]P_3 = \dfrac{D_4}{k-g}[/tex]
[tex]P_3 = \dfrac{6.068}{0.16 - 0.05}[/tex]
P₃ = $55.166
The current share price, P₀is
[tex]P_0 = \dfrac{D_1}{1+k}+\dfrac{D_2}{(1+k)^2}+\dfrac{D_3+P_3}{(1+k)^3}[/tex]
[tex]P_0 = \dfrac{4.37}{1+0.16}+\dfrac{5.026}{(1+0.16)^2}+\dfrac{5.770 +55.166}{(1+0.16)^3}[/tex]
P₀ = $46.54
