Question

Smith 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 $2.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 49% per year - during Years 4 and 5, but after Year 5, growth should be a constant 5% per year. If the required return on Smith is 12%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

The value of the stock is computed as shown below:

= Dividend in year 3 / (1 + required rate of return)³ + Dividend in year 4 / (1 + required rate of return)⁴ + Dividend in year 5 / (1 + required rate of return)⁵ + 1 / (1 + required rate of return)⁵ [ (Dividend in year 5 (1 + growth rate) / ( required rate of return - growth rate ) ]

= $ 2 / 1.12³ + ( $ 2 x 1.49 ) / 1.12⁴ + ( $ 2 x 1.49² ) / 1.12⁵ + 1 / 1.12⁵ [ ($ 2 x 1.49² x 1.05) / ( 0.12 - 0.05) ]

= $ 2 / 1.12³ + $ 2.98 / 1.12⁴ + $ 4.4402 / 1.12⁵ + $ 66.603 / 1.12⁵

= $ 43.63 Approximately

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