Computech Corporation is expanding rapidly and currently needs to retain all of

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 $1.75 coming 3 years from today. The dividend should grow rapidly-at a rate of 41% 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 17%, what is the value of the stock today? Round your answer to the nearest cent. Do not round your intermediate calculations.

Explanation / Answer

Solution :- Dividend at the end of three years (D3) = $ 1.75

Dividend at the end of four years (D4) = 1.75 + 41 % of 1.75 = $ 2.4675

Dividend at the end of five years (D5) = 2.4675 + 41 % of 2.4675 = $ 3.479175

Dividend at the end of six years (D6) = 3.479175 + 7 % of 3.479175 = $ 3.72271725

Value of stock at the end of five years (V5) = Dividend at the end of six years / (Required return - Growth in dividend)

= 3.72271725 / (0.17 - 0.07)

= 3.72271725 / 0.10

= $ 37.2271725 (approx).

Value of stock today = 1.75 / (1 + 0.17)3 + 2.4675 / (1 + 0.17)4 + (3.479175 + 37.2271725) / (1 + 0.17)5

= 1.75 / (1.17)3 + 2.4675 / (1.17)4 + 40.7063475 / (1.17)5

= 1.75 / 1.601613 + 2.4675 / 1.873887 + 40.7063475 / 2.192448

= 1.0926 + 1.3168 + 18.5666

= $ 20.9760 (Rounded off to $ 20.98)

Conclusion :- Value of the stock today = $ 20.98 (approx).

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