You are considering the purchase of a common stock that just paid out a dividend of $2 (D₀) recently. You expect this stock to have annual growth rates of 40%, 30%, 30%, and 20%, respectively, for the next 4 years, and then to have a long-run constant growth rate of 8% thereafter, starting from year 5. If you require a 15% rate of return for this investment, then how much should you be willing to pay for this stock now? (12 marks)

40% 30% 30% 20% || g=8% ----->

0 1 2 3 4 5

+---------+---------+---------+---------+---------+----->

D₀=2

please show working as well.