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%. Answer the following questions. (SHOW YOUR WORK. Correct answers with no formulas/calculations receive no credit)

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

Price is ascertained as the present value of future dividend income. This comprise of first stage growth for 3 years at 10% and at 5% infinitely thereafter. Price at the end of first stage = D(n+1)/(r-g2) where D(n+1) is the dividend in 1st year of second stage, g2= growth rate in that stage and r= required rate of return. This is further discounted to arrive at current price by adding the present value of dividend stream in first stage.

(a ): Price of stock today (P0) = $31.14

(b ): Price at t=10 = $53.51

(c) : Price at t=1 = $35.81

Calculations as below.