Question

Carnes Cosmetics Co.'s stock price is $65.90, and it recently paid a $1.75 dividend. This dividend is expected to grow by 27% for the next 3 years, then grow forever at a constant rate, g; and rs = 15%. 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

Price of Stock = PV of Dividends + PV of Terminal Value
PV of Dividend =1.75*(1+27%)/(1+15%)+1.75*(1+27%)^2/(1+15%)^2+1.75*(1+27%)^3/(1+15%)^3 = 6.42386

PV of Terminal Value = 1.75*(1+27%)^3*(1+g)/(15%-g)*(1+15%)^3) = 2.3570(1+g)/(15%-g)

Price of Stock = PV of Dividends + PV of Terminal Value
65.90 = 6.42386+2.3570*(1+g)/(15%-g)
(65.90-6.42386)/2.3570 = (1+g)/(15%-g)
25.2338 = (1+g)/(15%-g)
25.2338*15% - 25.2338g = 15%+15%g
g = (25.2338*15%-15%)/(15%+25.2338) = 14.32%

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