Question

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.

Answer 1

Answer:

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

Answer 2

Answer:

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)

Explanation: