Question

Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $2.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 65% per year - during Years 4 and 5. After Year 5, the company should grow at a constant rate of 10% per year. If the required return on the stock is 15%, what is the value of the stock today (assume the market is in equilibrium with the required return equal to the expected return)?

Answer 1

The value 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 x [ (Dividend in year 6) / (required rate of return - growth rate) ]

= $ 2 / 1.15³ + ($ 2 x 1.65) / 1.15⁴ + ($ 2 x 1.65²) / 1.15⁵ + 1 / 1.15⁵ x [ ($ 2 x 1.65² x 1.10) / (0.15 - 0.10) ]

= $ 2 / 1.15³ + $ 3.30 / 1.15⁴ + $ 5.445 / 1.15⁵ + $ 1 / 1.15⁵ x [ ($ 119.79) ]

= $ 2 / 1.15³ + $ 3.30 / 1.15⁴ + $ 125.235 / 1.15⁵

= $ 65.47 Approximately

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