NONCONSTANT GROWTH Carnes Cosmetics Cos stock price is 5199

NONCONSTANT GROWTH

Carnes Cosmetics Co.\'s stock price is $51.99, and it recently paid a $1.25 dividend. This dividend is expected to grow by 19% for the next 3 years, then grow forever at a constant rate, g; and r_s = 10%. 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.

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Solution

D1=(1.25*1.19)=$1.4875

D2=(1.4875*1.19)=$1.770125

D3=(1.770125*1.19)=$2.10644875

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

=(2.10644875(1+g))/(0.1-g)

Hence value of stock today=Future dividends*Present value of discounting factor(10%,time period)

51.99=$1.4875/1.1+$1.770125/1.1^2+$2.10644875/1.1^3+(2.10644875(1+g))/(0.1-g)/1.1^3

51.99=4.397792074+1.582606123(1+g)/(0.1-g)

(51.99-4.397792074)=[1.582606123+1.582606123g]/(0.1-g)

47.59220793(0.1-g)=1.582606123+1.582606123g

4.759220793-47.59220793g=1.582606123+1.582606123g

Hence g=(4.759220793-1.582606123)/(1.582606123+47.59220793)

which is equal to

=6.46%(Approx).4