Professor Bai is worried about his job security, and has started to venture into a new startup. Perhaps surprisingly, he is able to take his startup to IPO within a 5-year period (please allow me to dream). The firm has just announced its first dividend of $3/share and the firm’s dividend is expected to grow extremely fast for 4 years in a row at 30% each year. However, Professor Bai expects that the company will only grow at 5% after that forever (Professor Bai is vampire and lives forever!!). Expected return (discount rate) for stocks is 12%. Please use the dividend discount model to price the stock at t=0.

Price is sum of:

1. Present value of expected dividend payments during 1-4 years;

2. Present value of the expected market price at the end of the fourth year based on growth at 5%.

The present value of expected dividend payments during 1-4 years:

PV1 = 3*(1+0.30)*0.8929 = 3.90*0.8929 = $3.482

*0.8929 = 1/1.12

PV2 = 3.90*1.30*0.7972 = 5.07*0.7972 = $4.042

PV3 = 5.07*1.30*0.7118 = 6.591*0.7118 = $4.691

PV4 = 6.591*1.30*0.6355 = 8.5683*0.6355 = $5.445

Total = $17.661

Present value of the expected market price at the end of the fourth year:

Market price of the share at the end = 5th year dividend/(Required rate of return - growth rate)

5th year dividend = $8.5683*(1+growth rate) = $8.5683*(1+0.05) = $9

Market price of the share at the end = $9/(0.12-0.05) = $128.57

Present value of $128.57 is 128.57*0.6355(present value interest factor for year 4) = $81.7

So the price of share is $17.661+$81.7 = $99.37