Carnes Cosmetics Co.'s stock price is $38, and it recently paid a $1.25 dividend. This dividend is expected to grow by 22% for the next 3 years, then grow forever at a constant rate, g; and rs = 13%. 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.
%
Given about Carnes Cosmetics Co.'s
Current stock price P0 = $38
recently paid dividend D0 = $1.25
This dividend is expected to grow by 22% for the next 3 years,
So, D1 = 1.25*1.22 = $1.525
D2 = 1.525*1.22 = $1.8605
D3 = 1.8605*1.22 = $2.2698
then grow forever at a constant rate, g
Required return rs = 13%
So, price of stock at year 3 using constant dividend growth rate is
P3 = D3*(1+g)/(rs - g)
=> P3 = 2.2698*(1+g)/(0.13-g)
So, price today is sum of PV of future dividends and P3 discounted at rs
P0 = D1/(1+rs) + D2/(1+rs)^2 + D3/(1+rs)^3 + P3/(1+rs)^3
=> 38 = 1.525/1.13 + 1.8605/1.13^2 + 2.2698/1.13^3 + P3/1.13^3
=> 38 = 1.3496 + 1.4570 + 1.5731 + P3/1.4429
So, P3 = 33.6203*1.4429
using P3 = 2.2698*(1+g)/(0.13-g), we get
2.2698*(1+g)/(0.13-g) = 48.5106
1+g = 21.3721*(0.13-g)
g = 7.95%
So, constant growth rate = 7.95%
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