Question

Company A announced that its current dividend is $10 per share (D0=$10). The dividend is expected to grow at a constant rate of 5 percent a year for the first 2 years and it will be 4 percent thereafter. The risk-free rate is 4 percent, the required rate of return on the market portfolio is 7 percent and the company's beta equals to 2. What is the expected price of the stock today (t=0)?

Answer 1

The formula for the Constant dividend growth model is

Stock Price= Dividend for next period / (Required rate of Return - Growth Rate)

The constant dividend growth model can be applied from 3rd year.

1st year dividend will be = D0 * (1 + growth rate)

= 10 * (1 + 0.05)

= 10.5

2nd year will be = 10.5 * (1 + 0.05)

= 11.025

3rd year dividend = 11.025 * (1 + 0.05)

= 11.57625

Required return as per CAPM = Risk-Free rate + Beta ( Market Return - Risk-Free Rate)

= 4 + 2(7 - 4)

= 10

Stock Price at the end of year 2 as per constant growth model = Dividend for year 3 / (Required rate of Return - Constant Growth Rate)

= 11.57625 / (0.10 - 0.04)

= 192.9375

Now we need to do the present value of year 1 and year 2 dividend along with the stock price at the end of year 2 to get the stock price now.

= 10.5(1 + Required Return)^1 + 11.025(1 + Required Return)^2 + 192.9375(1 + Required Return)^2

= 10.5(1 + 0.10)^1 + 11.025(1 + 0.10)^2 + 192.9375(1 + 0.10)^2

= 178.1095

The expected stock price for today is 178.1095

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