Question

a company just gave out a divided of $7 per share and you estimate that the divided would increase 10% annually for the next four years Year 1-4), then at 6% for the two years after that (Year 5-6) and finally setting at a 4% annual perpetual increase (Year 6- forever) if the required rated is 12.5%, calculate the price of the stock

Answer 1

Solution:

Calculation of share price:

Since the growth rate is constant after 6th years,hence first we have to find the share price(Terminal Value) at the end of 6th year

Dividend for each year is:

D1=$7*(1.10)=$7.70

D2=$7.7(1.10)=$8.47

D3=$8.47*(1.10)=$9.317

D4=$9.317(1.10)=$10.25

D5=$10.25*(1.06)=$10.86

D6=$10.86(1.06)=$11.51

D7=$11.51(1.04)=$11.97

Terminal Value=D7/Required rate-Growth rate

=$11.97/12.5%-4%

=$140.82

Now, we have to calculate the present value of dividend for each year and terminal value(i.e Stock's Price) using required rate at discount rate:

=$7.70/(1+0.125)^1+$8.47/(1+0.125)^2+$9.317/(1+0.125)^3+$10.25/(1+0.125)^4+$10.86/(1+0.125)^5+($11.51+$140.82)/(1+0.125)^6

=$107.65

Thus price of the stock is $107.65