Question

K’s Fashions is growing quickly. Dividends are expected to increase by 15 percent annually for the next three years, with the growth rate falling off to a constant 5 percent thereafter. The required return is 16 percent and the company just paid a $3.80 annual dividend. What is the current share price?

Answer 1

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

`P_3 = (D_4)/(k-g)`

`P_3 = (6.068)/(0.16 - 0.05)`

P₃ = $55.166

The current share price, P₀is

`P_0 = (D_1)/(1+k)+(D_2)/((1+k)^2)+(D_3+P_3)/((1+k)^3)`

`P_0 = (4.37)/(1+0.16)+(5.026)/((1+0.16)^2)+(5.770 +55.166)/((1+0.16)^3)`

P₀ = $46.54