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 $0.50 coming 3 years from today. The dividend should grow rapidly - at a rate of 28% per year - during Years 4 and 5, but after Year 5, growth should be a constant 8% per year. If the required return on Computech is 18%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

Hi, first we need to find the value of dividend 4, 5 and 6, ths las one we will use to find the perpetuity value of this stock (since it will grow at 8% from year 5). So, let´s go ahead and find D4, D5 and D6

[tex]D4=0.50*(1+0.28)=0.64\\D5=0.64*(1+0.28)=0.8192\\D6=0.8192*(1+0.28)=0.884736[/tex]

Now, we need to find the price of this stock, for that we have to bring to present value all those cash flows.

[tex]Price=\frac{D3}{(1+0.18)^{3} } +\frac{D4}{(1+0.18)^{4} } +\frac{D5}{(1+0.18)^{5} } +\frac{D6}{(r-g)} (\frac{1}{(1+0.18)^{5} } )[/tex]

Where:

r = required return of Computech

g= growth rate from year 5 (8%)

Everything should look like this.

[tex]Price=\frac{0.5}{(1+0.18)^{3} } +\frac{0.64}{(1+0.18)^{4} } +\frac{0.8192}{(1+0.18)^{5} } +\frac{0.884736}{(0.18-0.08)} (\frac{1}{(1+0.18)^{5} } )[/tex]

Therefore:

[tex]Price= 4.86[/tex]

So, today´s value of this stock is $4.86