Question

Carnes Cosmetics Co.'s stock price is $44.32, and it recently paid a $1.75 dividend. This dividend is expected to grow by 21% for the next 3 years, then grow forever at a constant rate, g; and r_s = 16%. At what constant rate is the stock expected to grow after Year 3? Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

Given
D0 = 1.75
rs = 16%
growth fro first three years = 21%
Price = $44.32
D1 = 1.75*1.21 = 2.1175
D2 = 2.1175*1.21 = 2.562175
D3 = 2.562175*1.21 = 3.10023

Price = D1/(1+rs) + D2/(1+rs)² + D3/(1+rs)³ + D3*(1+g) /(rs - g)] /1.16^3
44.32 = 2.1175/1.16 + 2.5627175/1.16² + 3.10023 / 1.16³ + [3.10023*(1+g) / (0.16-g)] /1.16^3
44.32 = 1.82543 + 1.904 + 1.98619+ [3.10023*(1+g) / (0.16-g) ]/ 1.16^3
38.604 = [3.10023*(1+g) / (0.16-g)] / 1.16^3
60.2572 = [3.10023*(1+g) / (0.16-g)]

Solving for g we get

g = 10.32%

growth rate = 10.32%