Question

Corporate Finance I

You are running a hot Internet pharmacy 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 2% per year and continue at that level forever. Your company has just announced earnings of $1,000,000. What is the present value of all future earnings if the interest rate is 8%? (Assume all cash flows occur at the end of year.)

[Hint: this timeline consists of two parts, a growing annuity for five years and a growing perpetuity after that.]

Answer 1

Year 1 earning = 1000000*(1+30%) = 1000000*1.3=$1,300,000

g=30%

r=8%

PV of earning of first five years = A*(1-(1+g)^n/(1+r)^n)/(r-g)

=1300000*(1-(1+30%)^5/(1+8%)^5)/(8%-30%)

=1300000*(1-1.3^5/1.08^5)/(-22%)

=1300000*(1-3.7129/1.4693)/(-0.22)

=1300000*(1-2.5270)/(-0.22)

=1300000*(-1.5270)/(-0.22)

=$9022932.28

Earning of 6th Year = 100000*(1+30%)^6 = 1000000*1.3^6 = 1000000*4.8268 = $4826809

PV at the end of 5th year of perpetuity = Earning 6th year/ (r-g)= 4826809/(8%-2%)=4826809/6% = $80446816.67

Hence PV at the end of 0 year = 80446816.67/(1+8%)^5=80446816.67/1.08^5 = 80446816.67/1.4693=$54750751.68

Hence total PV = 9022932.28+54750751.68=$63773683.96