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 $2.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 18% per year - during Years 4 and 5, but after Year 5, growth should be a constant 10% per year. If the required return on Computech is 13%, what is the value of the stock today

23.83

Explanation:

Di = dividend in year i

D0 = D1 = D2 = 0

D3 = 2

D4 = D3 * (1+24%) = 2.48

D5 = D4 * (1+24%) = 3.0752

D6 = D5 * (1+7%) = 3.290464

require return r = 14%

g = 7% in the long run

So stock price in year 5 = D6/(r-g) = 3.290464/(14%-7%) = 47.0066

Current price = Present value of dividends and stock

= D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + D5/(1+r)^5 + Price in year 5/(1+r)^5

= 0 + 0 + 2/(1+14%)^3 + 2.48/(1+14%)^4 + 3.0752/(1+14%)^5 + 47.0066/(1+14%)^5

= 28.829219

= 28.83 (rounded to 2 decimals)

you have to put the parentheses like this:

in fact, you have to perform the operation inside parentheses first, and then proceed in order: