Question

The risk-free rate is 3.41% and the market risk premium is 5.72%. A stock with a β of 1.53 just paid a dividend of $1.35. The dividend is expected to grow at 23.75% for five years and then grow at 3.84% forever. What is the value of the stock?

Answer 1

Required return=risk free rate+Beta*market risk premium

=3.41+(5.72*1.53)=12.1616%

D1=(1.35*1.2375)=1.670625

D2=(1.670625*1.2375)=2.06739844

D3=(2.06739844*1.2375)=2.55840557

D4=(2.55840557*1.2375)=3.16602689

D5=(3.16602689*1.2375)=3.91795828

Value after year 5=(D5*Growth rate)/(Required return-Growth rate)

=(3.91795828*1.0384)/(0.121616-0.0384)

=48.8897313

Hence value of stock=Future dividend and value*Present value of discounting factor(rate%,time period)

=1.670625/1.121616+2.06739844/1.121616^2+2.55840557/1.121616^3+3.16602689/1.121616^4+3.91795828/1.121616^5+48.8897313/1.121616^5

=$36.7(Approx).