Question

You are running a hot Internet company. Analysts predict that its earnings will grow at 30% per year for the next five years. After​ that, as competition​ increases, earnings growth is expected to slow to 4% per year and continue at that level forever. Your company has just announced earnings of $4 million. What is the present value of all future earnings if the interest rate is 7%​? ​(Assume all cash flows occur at the end of the​ year.)

Answer 1

Current Earnings = $ 4 million = E0

Initial Supernormal Growth Rate = 30 % and Final Perpetual Growth Rate = 4 %

Expected Future Earnings:

E1 = 1.3 x 4 = $ 5.2, E2 = 1.3 x 5.2 = $ 6.76, E3 = 6.76 x 1.3 = $ 8.788, E4 = 8.788 x 1.3 = $ 11.4244 and E5 = 11.4244 x 1.3 = $ 14.85172

Interest Rate = 7 %

Present Value of Supernormal Growth Earnings = PV1 = 5.2 / 1.07 + 6.76 / (1.07)^(2) + 8.788 / (1.07)^(3) + 11.4244 / (1.07)^(4) + 14.85172 / (1.07)^(5) = $ 37.2426 million

E6 = 14.85172 x 1.04 = $ 15.44579

Present value of Perpetual Growth Earnings = PV2 = [15.44579 / (0.07 - 0.04)] x [1/(1.07)^(5)] = $ 367.0878 million

Total Present Value of all Future Earnings = PV1 + PV2 = 37.2426 + 367.0878 = $ 404.3304 million