Question

11. Suppose a firm is expected to increase dividends by 10% in one year and by 15% in two years. After that, dividends will increase at a rate of 6% per year indefinitely. If the current dividend is $1.05 and the required return is 7.5%, what is the price of the stock?

Answer 1

Current Dividend = $1.05

Dividend at the end of Year 1 - $1.05 * 1.10 = $ 1.155

Dividend at the end of Year 2 = $ 1.155 * 1.15 =  $ 1.32825

Dividend at the end of Year 3 = $ 1.32825* 1.06 =  $ 1.407945

Now as the growth rate is constant thereafter, it makes no sense to compute the future dividends. We need to compute the Present value of Infinite Cash Flows by using the below forumla

=Dividend at the end of year 3/(Rate of Return- Growth Rate)

=$ 1.407945/(7.5-6)%

=$ 93.863

To Compute the share price we need the following

1) Present Vlaue of D1

2) Present Vlaue of D2

3) Present Value of Infinite Cash Flows. (The above is derived at the end of year 2)

A summation of all the above would give us our required share price

=$ 1.155/(1.075)+ $ 1.32825/(1.075)^2 +$ 93.863/(1.075)^2

=$ 83.45

Therefore the share price today = $ 83.45

the Value of teh firm = Dividend at the end of Year 2