Question

Carnes Cosmetics Co.'s stock price is $60, and it recently paid a $3.00 dividend. This dividend is expected to grow by 18% for the next 3 years, then grow forever at a constant rate, g; and rs = 14%. 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

D1=(3*1.18)=3.54

D2=(3.54*1.18)=4.1772

D3=(4.1772*1.18)=4.929096

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

=(4.929096*(1+Growth rate))/(0.14-Growth rate)

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

60=3.54/1.14+4.1772/1.14^2+4.929096/1.14^3+(4.929096*(1+Growth rate))/(0.14-Growth rate)/1.14^3

60=9.646482318+3.326999401*(1+Growth rate))/(0.14-Growth rate)

(60-9.646482318)/3.326999401=(1+Growth rate))/(0.14-Growth rate)

(1+Growth rate))/(0.14-Growth rate)=15.13481417

1+Growth rate=15.13481417*(0.14-Growth rate)

1+Growth rate=2.118873984-15.13481417Growth rate

Growth rate=(2.118873984-1)/(1+15.13481417)

=6.93%(Approx).