A rapidly growing company just paid a dividend of $1.30 a share. For the next three years, the earnings growth rate is projected to be 15% each year, and then 5% each year thereafter. If the required rate of return is 8%, what is the value of the stock?

$59.36

Explanation:

Given that

Dividend per share = $1.30

Growth rate for next 3 years is  15%

Now

Dividend for year 1 is

= Dividend per share × (1 + growth rate)

= $1.30 × (1 + 0.15)

= $1.495

For dividend for year 2 is

= Dividend for year 1 × (1 + growth rate)

= $1.495 × (1 + 0.15)

= $1.719

For dividend for year 3 is

= Dividend for year 2 ×  (1 + growth rate)

= $1.719 × ( 1 + 0.15)

= $1.977

And,

Subsequent Growth rate = g2 = 5%

Now

Dividend for year 4 is  

= Dividend for year 2 × (1 + g2)

= $1.977 × (1 + 0.05)

= $2.076

Now

As per Gordon's Growth Rate Model

Price at year 3 is

= Dividend for year 4 ÷ (required rate of return - g2)

= $2.076 ÷ (0.08 - 0.05)

= $69.2

So, Value of the Stock is

= Dividend for year 1 ÷ (1 + required rate of return ) + Dividend for year 2  ÷ (1 + required rate of return)^2 + Dividend for year 3 ÷ (1 + required rate of return)^3 + Price at year 3 ÷ (1 + required rate of return)^3  

= $1.495 ÷ (1+0.08) + $1.719 ÷ (1+0.08)^2 + $1.977 ÷ (1+0.08)^3 + $69.2 (1 + 0.08)^3

= $59.36

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