Question

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
r_{s} = 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.

%

Answer #1

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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