Question

Carnes Cosmetics Co.'s stock price is $57, and it recently paid a $1.25 dividend. This dividend is expected to grow by 24% 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

Constant rate is computed as shown below:

Stock price = Dividend at end of year 1 / ( 1 + required rate of return )¹ + Dividend at end of year 2 / ( 1 + required rate of return )² + Dividend at end of year 3 / ( 1 + required rate of return )³ + 1 / ( 1 + required rate of return )³ [ Dividend at end of year 3 ( 1 + growth rate ) / ( required rate of return - growth rate ) ]

Dividend at end of year 1 is computed as follows:

= $ 1.25 x 1.24

= $ 1.55

Dividend at end of year 2 is computed as follows:

= $ 1.25 x 1.24²

= $ 1.922

Dividend at end of year 3 is computed as follows:

= $ 1.25 x 1.24³

= $ 2.38328

So the growth rate will be as follows:

$ 57 = $ 1.55 / 1.14¹ + $ 1.922 / 1.14² + $ 2.38328 / 1.14³ + 1 / 1.14³ [ ( 2.38328 ( 1 + growth rate ) / ( 0.14 - growth rate ) ]

By solving the above equation, growth rate will be equal to:

= 6.82% Approximately

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