Question

In: Finance

17) Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence,...

17) 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 36% per year-during Years 4 and 5; but after Year 5, growth should be a constant 4% per year. If the required return on Computech is 12%, what is the value of the stock today? Round your answer to the nearest cent. Do not round your intermediate calculations.

Solutions

Expert Solution

Step-1, Dividend per share for Years 3,4 and 5

Dividend in Year 3 (D3) = $1.00 per share

Dividend in Year 4 (D4) = $1.3600 per share [$1.00 x 136%]

Dividend in Year 5 (D5) = $1.8496 per share [$1.3600 x 136%]

Step-2, Calculation of Stock Price in Year 5 (P5)

Dividend Growth Rate (g) = 4% per year

Required Rate of Return (Ke) = 12%

Therefore, the Stock Price in Year 5 = D5(1 + g) / (Ke – g)

= $1.8496(1 + 0.04) / (0.12 – 0.04)

= $1.9236 / 0.08

= $24.04 per share

Step-3, Value of the stock

The value of the stock today is the aggregate of present value of future dividends and Stock Price in Year 5

Intrinsic Value = D3/(1 + Ke)3 + D4/(1 + Ke)4 + D5/(1 + Ke)5 + P5/(1 + Ke)5

= $1.00/(1 + 0.12)3 + $1.3600/(1 + 0.12)4 + $1.8496/(1 + 0.12)5 + $24.04/(1 + 0.12)5

= [$1.00 / 1.40493] + [$1.3600 / 1.57352] + [$.8496 / 1.76234] + [$24.04 / 1.76234]

= $0.72 + $0.86 + $1.05 + $13.64

= $16.27 per share

“Therefore, the value of the stock today = $16.27 per share”


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