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

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

P₃ = $55.166

The current share price, P₀is

P₀ = $46.54

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: