Question

Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends, beginning with a dividend of $1.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 17% per year - during Years 4 and 5, but after Year 5, growth should be a constant 7% per year. If the required return on Computech is 16%, what is the value of the stock today

Answer 1

$9.687

Step-by-step explanation:

Given:

Year 3 dividend = $1.00

Year4&5 growth rate = 17%

Constant rate = 7%

Required return rate = 16%

Year 4 dividend wil be:

D4 = 1.00 * 1+growth rate

= 1.00 * (1+0.17)

= $1.17

Year 5 dividend=

D5 = $1.17 * (1+0.17)

= $1.3689

Value of stock after year 5 will be given as:

`(D5 * (1+growth rate))/(required return - growth rate)`

`= (1.3689*(1+0.07))/(0.16-0.07)`

= $16.2747

For the current value of stock, we have:

Cv= Fd* Pv of discounting factor

Where Cv = current value of stock

Fd = future dividend

Pv = Present value of discounting factor

Therefore,

`C_v = (1.00)/(1.16^3) + (1.17)/(1.16^4) + (1.3689)/(1.16^5) + (16.2746)/(1.16^5)`

=$9.6871382455

≈ $9.687

The value of stock today =

$9.687