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

D1=(1.75*1.21)=2.1175

D2=(2.1175*1.21)=2.562175

D3=(2.562175*1.21)=3.10023175

Value after year 3=(D3*Growth Rate)/(Required rate-Growth Rate)

=(3.10023175*(1+Growth rate)/(0.16-Growth rate)

Current price=Future dividends and value*Present value of discounting factor(rate%,time period)

44.32=2.1175/1.16+2.562175/1.16^2+3.10023175/1.16^3+(3.10023175*(1+Growth rate)/(0.16-Growth rate)/1.16^3

44.32=5.715731702+1.98618726(1+Growth rate)/(0.16-Growth rate)

(44.32-5.715731702)/1.98618726=(1+Growth rate)/(0.16-Growth rate)

(1+Growth rate)/(0.16-Growth rate)=19.4363689

1+Growth rate=19.4363689*(0.16-Growth rate)

1+Growth rate=3.109819025-19.4363689 Growth rate

Growth rate=(3.109819025-1)/(1+19.4363689)

=10.32%(Approx).