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 $1.00 coming 3 years from today. The dividend should grow rapidly-at a rate of 46% per year-during Years 4 and 5; but after Year 5, growth should be a constant 5% per year. If the required return on Computech is 15%, what is the value of the stock today? Round your answer to the nearest cent. Do not round your intermediate calculations.

**?**

Answer #1

Given about Computech Corporation,

1st dividend is expected in 3 years

So, D3 = $1

The dividend should grow rapidly-at a rate of 46% per year-during Years 4 and 5

=> D4 = 1*1.46 = $1.46

D5 = 1.46*1.46 = $2.1316

thereafter growth rate is constant

g = 5%

required return on stock r = 15%

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

P5 = D5*(1+g)/(r-g) = 2.1316*1.05/(0.15-0.05) = $22.3818

So, Price of the stock today P0 is sum of PV of future dividends and P5 discounted at r

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

=> P0 = 1/1.15^3 + 1.46/1.15^4 + 2.1316/1.15^5 + 22.3818/1.15^5 = $13.68

So, Value of stock today is $13.68

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