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 20% per year-during Years 4 and 5; but after Year 5, growth should be a constant 6% per year. If the required return on Computech is 18%, what is the value of the stock today? Round your answer to the nearest cent. Do not round your intermediate calculations.

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Answer 1

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) = $1.20 per share [$1 x 120%]

Dividend in Year 5 (D5) = $1.44 per share [$1.20 x 120%]

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

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

= $1.44(1 + 0.06) / (0.18 – 0.06)

= $1.53 / 0.12

= $12.72 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 + 0.18)³ + $1.20/(1 + 0.18)⁴ + $1.44/(1 + 0.18)⁵ + $12.7/(1 + 0.18)⁵

= [$1.00 / 1.64303] + [$1.20 / 1.93878] + [$1.44 / 2.28776] + [$12.72 / 2.28776]

= $0.61 + $0.62 + $0.63 + $5.56

= $7.42 per share

“Therefore, the value of the stock today = $7.42 per share”