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 $0.50 coming 3 years from today. The dividend should grow rapidly - at a rate of 45% 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 16%, 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

Solution :-

Required Return ( ke ) = 16%

Dividend in Year 3 ( D3 ) = $0.50

D4 = $0.50 * ( 1 + 0.45 ) = $0.725

D5 = $0.725 * ( 1 + 0.45 ) = $1.051

Growth after Year 5 = 6%

P5 = D5 * ( 1 + g ) / (ke - g )

P5 = $1.051 * ( 1 + 0.06 ) / ( 0.16 - 0.06 )

P5 = $11.14

Now Value of Stock = D3 / ( 1 + ke )³ + D4 / ( 1 + ke )⁴ + ( D5 + P5 ) / ( 1 + ke )⁵

Value of Stock = $0.50 / ( 1 + 0.16 )³ + $0.725 / ( 1 + 0.16 )⁴ + ( $1.05125 + $11.14 ) / ( 1 + 0.16 )⁵

= ( $0.50 * 0.641 ) + ( $0.725 * 0.552 ) + ( $12.19 * 0.476 )

= $6.525

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