Question

Carnes Cosmetics Co.'s stock price is $54, and it recently paid a $2.50 dividend. This dividend is expected to grow by 15% for the next 3 years, then grow forever at a constant rate, g; and r_s = 12%. 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=(2.5*1.15)=2.875

D2=(2.875*1.15)=3.30625

D3=(3.30625*1.15)=3.8021875

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

=(3.8021875*(1+Growth rate)/(0.12-Growth rate)

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

54=2.875/1.12+3.30625/1.12^2+3.8021875/1.12^3+(3.8021875*(1+Growth rate)/(0.12-Growth rate)/1.12^3

54=7.909008504+2.706321961(1+Growth rate)/(0.12-Growth rate)

(54-7.909008504)/2.706321961=(1+Growth rate)/(0.12-Growth rate)

(1+Growth rate)/(0.12-Growth rate)=17.03086039

1+Growth rate=17.03086039(0.12-Growth rate)

1+Growth rate=2.043703247-17.03086039 Growth rate

Growth rate=(2.043703247-1)/(17.03086039+1)

=5.79%(Approx)