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Mitts Cosmetics Co
Mitts Cosmetics Co.'s stock price is $58.88, and it recently paid a $2 dividend. This dividend is expected to grow by 25% for the next 3 years, and then grow forever at a constant rate, g, and the required return on the stock is 12%. At what constant rate is the stock expected to grow after Year 3?
[Hint: you are recommended to draw a timeline to solve this problem]
Expert Solution
Computation of Constant Growth Rate:
Here,
D1 = $2*(1+0.25) = $2.5
D2 = $2.5*(1+0.25) = $3.125
D3 = $3.125*(1+0.25) = $3.90625
Value after year 3 = (D3*Growth rate)/(Required return-Growth rate)
=(3.90625*(1+g)/(0.12-g)
Current Stock Price = Future Dividend and Value*Present value of discounting factor(Rate%,Time period)
58.88 = 2.5/1.12+3.125/1.12^2+3.90625/1.12^3+(3.90625*(1+g)/(0.12-g)/1.12^3
58.88=7.5038+(3.90625*(1+g)/(0.12-g)*0.7118
(58.88-7.5038)=2.78039*(1+g)/(0.12-g)
(58.88-7.5038)/2.78039 = (1+g)/(0.12-g)
(1+g)/(0.12-g) = 18.48
(1+g)=18.48*(0.12-g)
1+g=2.22-18.48 g
g=(2.22-1)/(1+18.48)
g=6.25%
So, Constant Growth Rate is 6.25%.
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