Question

Q1) Last year, a company paid a dividend of $0.75 per share. Dividends for the next year, will increase by 167% and then by 50% in the following year. After that, dividends are expected to grow at a constant rate of 10% every year. If the required return for investments of similar risk is 15% and the market price of the stock is $55, would you buy the stock today? Explain your answer.

Answer 1

The problem can be solved by using Constant Dividend growth model

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

Dividend after end of year 1 = Dividend for last year + (Dividend for last year) * (Growth rate of year 1)

= (0.75) + (0.75)(167%)

= 2.0025

Dividend after end of year 2 = Dividend after end of year 1 + (Dividend after end of year 1) * (Growth rate of year 2)

= (2.0025) + (2.0025)(50%)

= 3.00375

Dividend after end of year 3 = Dividend after end of year 2 + (Dividend after end of year 2) * (Constant Growth rate)

= 3.00375 + (3.00375) * (10%)

= 3.304125

Intrinsic Stock price at the end of year 2 by applying constant growth model = Dividend after end of year 3 / (Required Rate of Return - Constant growth rate)

= 3.304125 / (15% - 10%)

= 66.0825

So now we will have to discount all the dividends and intrinsic value of stock to bring it to present value

Intrinsic value of the stock = Dividend after end of year 1/ (1 + Required rate of return) + Dividend after end of year 2 / (1 + Required rate of return)^2 + Intrinsic Value of stock at the end of year 2 / (1 + Required rate of return)^2

= 2.0025 / (1.15) + 3.00375 / (1.15)^2 + 66.0825 / (1.15)^2

= 53.9804

So the intrinsic value of the stock is $53.9804. The stock is selling at $55. It is overpriced. So shouldn't be bought.

It the stock was selling lower than intrinsic value, then the stock would have been under-priced, so an investor would have made profit by buying it.