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 $ 1 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

Last Earnings, E0 = $1,000,000

Growth rate for next 5 years is 30% and a constant growth rate (g) of 4% thereafter

E1 = $1,000,000 * 1.30 = $1,300,000
E2 = $1,300,000 * 1.30 = $1,690,000
E3 = $1,690,000 * 1.30 = $2,197,000
E4 = $2,197,000 * 1.30 = $2,856,100
E5 = $2,856,100 * 1.30 = $3,712,930
E6 = $3,712,930 * 1.04 = $3,861,447.20

Required Return, rs = 7%

Value of Earnings at the end of Year 5 = E6 / (rs - g)
Value of Earnings at the end of Year 5 = $3,861,447.20 / (0.07 - 0.04)
Value of Earnings at the end of Year 5 = $3,861,447.20 / 0.03
Value of Earnings at the end of Year 5 = $128,714,906.667

Present Value of Earnings = $1,300,000/1.07 + $1,690,000/1.07^2 + $2,197,000/1.07^3 + $2,856,100/1.07^4 + $3,712,930/1.07^5 + $128,714,906.667/1.07^5
Present Value of Earnings = $101,082,593