ABC company. paid a dividend of $2 on its stock. The growth rate of dividends is...

ABC company. paid a dividend of $2 on its stock. The growth rate of dividends is expected to be a constant 4 percent per year, indefinitely. Investors require an 12 percent return on the stock for the first year, a 11percent return in the second year, a 10 percent return for the next four years and an 9 percent return thereafter. What is the current price for the stock?

Expert Solution

The formula for Constant dividend growth model is

Stock Price at the end of 3rd year= Dividend for 4th year / (Required rate of Return - Growth Rate)

We need to discount the dividends and find the present value of the stock

Dividend after year 1 => 2 (1+ Constant growth rate) => 2 (1 + 0.04) = 2.08

Dividend after year 2 => 2.08 (1+ Constant growth rate) => 2.08 (1 + 0.04) = 2.1632

Dividend after year 3 => 2.1632 (1+ Constant growth rate) => 2.1632 (1 + 0.04) = 2.2497

Dividend after year 4 => 2.2497 (1+ Constant growth rate) => 2.2497 (1 + 0.04) = 2.3396

Stock Price at the end of 3rd year= Dividend for 4th year / (Required rate of Return - Growth Rate)

= 2.3396 / (0.09 - 0.04)

= 46.792

Stock price today = Pv of Dividend after year 1 + Pv of Dividend after year 2 + Pv of Dividend after year 3 + Pv of Stock after year 3

= 2.08 / (1 + 0.12) + 2.1632 / (1 + 0.11)^2 + 2.2497 / (1 + 0.1)^3 + 46.792 / (1 + 0.1)^3

= 40.90

The current stock price should be $40.90

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jeff jeffy answered 1 year ago

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