Question

A stock just paid an annual dividend of $2.7. The dividend is expected to grow by 8% per year for the next 3 years. The growth rate of dividends will then fall steadily (linearly) from 8% after 3 years to 5% in year 6.

The required rate of return is 12%.

1.What is the stock price if the dividend growth rate will stay 0.05 (5%) forever after 6 years?

2.In 6 years, the P/E ratio is expected to be 20 and the payout ratio to be 80%. What is the stock price when using the P/E ratio?

Answer 1

1. g1=8%
g2 =7%
g3=6%
g4=5%
g5=5%
Dividend in year 7 =D0*(1+g1)^3*(1+g2)*(1+g3)*(1+g4)*(1+g5)=2.7*(1+8%)^3*(1+7%)*(1+6%)*(1+5%)*(1+5%)=4.523077
Stock Price in year 6 =Dividend in year 7/(Required Rate-growth) =4.523077/(12%-5%) =64.62

2. EPS in year 6 =Dividend per share in year 6/(1-Pay Out Ratio) =2.7*(1+8%)^3*(1+7%)*(1+6%)*(1+5%)/80% =5.06318
Stock Price =P/E*EPS =20*5.06318=101.26