Problem 9-14. Nonconstant growth Microtech Corporation is expanding rapidly and

Question

Problem 9-14. Nonconstant growth

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.

Explanation / 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)

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