Question

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 $0.75 coming 3 years from today. The dividend should grow rapidly - at a rate of 48% per year - during Years 4 and 5, but after Year 5, growth should be a constant 7% per year. If the required return on Computech is 13%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

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Answer 1

Given about Commputech Corporation,

Computech to begin paying dividends, beginning with a dividend of $0.75 coming 3 years from today

So, D3 = $0.75

growth rate for next 2 year = 48%

So, D4 = D3*1.48 = 0.75*1.48 = $1.11

D5 = D4*1.48 = 1.11*1.48 = $1.6428

thereafter growth rate g = 7%

required return on Computech rs = 13%

So, price of stock at year 5 using constant dividend growth model is

P5 = D5*(1+g)/(rs-g) = 1.6428*(1.07)/(0.13-0.07) = $29.2966

So, price of stock today is sum of PV of future dividends and P5 discounted at rs

P0 = D3/(1+rs)^3 + D4/(1+rs)^4 + D5/(1+rs)^5 + P5/(1+rs)^5

P0 = 0.75/1.13^3 + 1.11/1.13^4 + 1.6428/1.13^5 + 29.2966/1.13^5 = $17.99

value of the stock today = $17.99