Question

Carnes Cosmetics Co.'s stock price is $60, and it recently paid a $3.00 dividend. This dividend is expected to grow by 21% for the next 3 years, then grow forever at a constant rate, g; and rs = 15%. At what constant rate is the stock expected to grow after Year 3? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

D₀ = $ 3

D₁ = D₀ x (1+g) = $ 3 x 1.21 = $ 3.63

D₂ = D₁ x (1+g) = $ 3.63 x 1.21 = $ 4.3923

D₃ = D₂ x (1+g) = $ 4.3923 x 1.21 = $ 5.314683

D₄ = D₃ x (1+g) = $ 5.314683 x (1+g)

Price of share in year 3, P₃ can be computed using dividend discount model as,

P₃ = D₄/(r-g)

r = cost of capital = 15 % or 0.15

g = Constant growth rate of dividend

P₃ = $ 5.314683 x (1+g) / (0.15 – g)

Current stock price, P = D₁/ (1+r) + D₂/ (1+r) ² + D₃/ (1+r) ³ + P₃/ (1+r) ³

$ 60 = $ 3.63/ (1+0.15) + $ 4.3923/ (1+0.15) ² + $ 5.314683/ (1+0.15) ³ + P₃/ (1+0.15) ³

       = $ 3.63/ (1.15) + $ 4.3923/ (1.15) ² + $ 1.662928/ (1.15) ³ + P₃/ (1.15) ³

        = $ 3.63/ 1.15 + $ 4.3923/ 1.3225 + $ 1.662928/ 1.520875 + P₃/ 1.520875

        = $ 3.15652173913043 + $ 3.32120982986768 + $ 3.49449034273034 + P₃/ 1.520875

        = $ 9.97222191172845 + P₃/ 1.520875

P₃/ 1.520875 = $ 60 - $ 9.97222191172845 = $ 50.02777808827155

P₃ = 1.520875 x $ 50.02777808827155 = $ 76.085997

$ 5.314683 x (1+g) / (0.15 – g) = $ 76.085997

$ 5.314683 x (1+g) = $ 76.085997 x (0.15 – g)

$ 5.314683 + $ 5.314683 g = $ 76.085997 x 0.15 - $ 76.085997g

$ 5.314683 + $ 5.314683 g = $ 11.41289955 - $ 76.085997g

$ 5.314683 g + $ 76.085997g = $ 11.41289955 - $ 5.314683

$ 81.40068 g = $ 6.09821655

g = $ 6.09821655/$ 81.40068 = 0.0749160393991795 or 7.49 %

The stock is expected to grow at a constant rate of 7.49 % after year 3.