Question

The risk-free rate is 2.30% and the market risk premium is 6.49%. A stock with a β of 1.36 just paid a dividend of $2.92. The dividend is expected to grow at 23.49% for three years and then grow at 4.92% forever. What is the value of the stock?

Answer 1

Answer: The value of the stock is $78.60

Required return=Risk free rate +Beta*Market risk premium
=2.3% +1.36*6.49%=0.111264

Given that the stock just paid a dividend of $2.92 and the dividend is expected to grow at 23.49% for three years and then the constant growth rate will be 4.92% forever.
Dividend in year 1=(Dividend just paid)*(1+Growth rate)=2.92*(1+23.49%)=3.605908
Dividend in year 2=2.92*(1+23.49%)^2=4.452935789
Dividend in year 3=2.92*(1+23.49%)^3=5.498930406

Terminal value=(Dividend in year 3)*(1+Constant growth rate)/(Required return-Constant growth rate)
=(5.498930406)*(1+4.92%)/(0.111264-4.92%)
=5.769477782/0.062064
=92.96013441

Stock value=Present value of future cash flows
=3.605908/(1+0.111264)^1+4.452935789/(1+0.111264)^2+5.498930406/(1+0.111264)^3+92.96013441/(1+0.111264)^3
=3.244870706+3.605885581+4.007065922+67.73997108
=78.59779329 or $78.60 (Rounded to two decimal places)