Question

Carnes Cosmetics Co.'s stock price is $58, and it recently paid a $1.50 dividend. This dividend is expected to grow by 23% for the next 3 years, then grow forever at a constant rate, g; and r_s = 10%. 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 in the question

Current market price=58

Last paid dividend=1.5

Growth rate for initial 3 years=23%

Forever Growth rate after 3 years = let’s assume X

Rate of return on stock=10%

Now we know as per divided discount mode

Market price=Discounted value of dividends

And present value of stable dividend growth rate is

= Expected dividend next year/ (Cost of equity-Growth rate)

Hence

58=1.5*(1+0.23)/(1.1) + 1.5*(1+0.23)^2/(1.1)^2 + 1.5*(1+0.23)^3/(1.1)^3 + 1.5*(1.23)^3(1+g)/(0.1-g)*1/(1.1)^3

58=5.65+ 2.10*(1+g) / (0.1-g)

52.35=2.10(1+g)/(0.1-g)

52.35 (0.1-g)=2.10+2.10g

5.235-2.10=2.10g+52.35g

g=5.76%

Hence growth rate after 3 years is 5.76%