Microtech Corporation is expanding rapidly and currently needs to retain all of its earnings, hence it does not pay dividends. However, investors expect Microtech 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 24% per year - during Years 4 and 5, but after Year 5 growth should be a constant 7% per year. If the required return on Microtech is 14%, what is the value of the stock today? Round your answer to two decimal places.

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)

Value of one share today is $ 28.80

Explanation:

D1 and D2 = 0

D3 = 2 coming at three years

Dividend grows at 24 % per year during Year 5 & Year 6.

D4 = 2 x 1.24 = 2.48

D5 = 2.48 x 1.24 = 3.072

D6 = 3.072 x 1.07 = 3.28704

Terminal value at the end of Year 5 = D6 / (Cost of equity - Costant growth rate)

Terminal value at the end of Year 5 = 3.28704 / (14 % - 7%) = 46.96

Value of Stock today will be = Present value of all dividends + Present value of terminal value at year 5

Present value of D1 & D2 = 0

Present value of D3 = 2 / (1.14) ^3 = 1.35

Present value of D4 = 2 / (1.14) ^4 = 1.47

Present value of D5 = 2 / (1.14) ^5 = 1.60

Present value of all dividends = 4.41

Present value of terminal value = 46.96 / (1.14) ^5 = 24.39

Value of one Share today = Present value of all dividends + Present value of terminal value

Value of one Share today = 4.41 + 24.39 = 28.80