Question

Consider the stock of SLB Inc., a growth stock that will pay no dividend the next year. Starting in year two, the company will pay a dividend of $3 and will increase it by 10% for the next three years. Afterwards, dividends will grow by 5% per year indefinitely. The stock has a required rate of return of 15%. a) What is the value (price) of the stock today (i.e. P0)? Show your work and formulas.b) What is the price of the stock at t=10, assuming the required rate of return (i.e. 15%) and the growth rate of dividends (i.e., 5%) do not change? Show your work and formulas.c) What is the price of the stock at t=1, assuming the required rate of return (i.e. 15%) and the growth rate of dividends (i.e., 5%) do not change? Show your work and formulas.

Answer 1

You need to calculate the stock price.

Price of any security today is the present value of all the incomes that security is going to generate in future discounted at required rate of return.

There is widely used formula to calculate the price of share whose dividend is contant, called gordan growth formula

GGn formula =

P0 = Price today , D1= Expected dividend , Ke = cost of capital , g is growth

Given Information

D2 = 3 , D3 = 3 x 1.10 = 3.30 , D4= 3.30 x 1.10 = 3.63 , D5= 3.63 x 1.10 = 3.9930

Required return 15%, Growth afterwars = 5%

a)
First Calculate the price of share at Time 4 with gordan growth constant from year 6 and onwards

P4 = D5 / ( Ke - G5)

= 3.9930 / ( 0.15 - 0.05)

= 3.9930 / 0.10

Price at Time 4 = 39.93

Now calculate the Present value of Dividend 2, 3 and 4 alongwith Price at Time 4

PV =

= 2.268431 + 2.16980357 + 2.07545428 + 22.83010710

= 29.34380595

Price of share = 29.34 approx.

b) Calculate share price at Time 10.

For this you reuiqred dividend at time 11

D11 = D5 (1.05)⁶

= 3.9930 x 1.34009564

= 5.351 approx

Price at time 10 = D11 / (Ke - g)

= 5.351 / (0.15 - 0.05)

= 5.351 / 0.10

PRice at Time 10 = 53.51 Approx

c) Stock price at time 1.

= You can pick the Equation from above point (a) get the present value of Dividends and price at Time 1.

=

= 33.74537684

= 33.75 Approx