Question

XYZ common stock recently paid annual dividend in the amount of $1.75 per share. The analysts estimate of the firm's growth forecast over the next 6 years is 15%. You expect the firm to slow down in the long run and estimate the long-term growth rate after 6 years to be 8%. If the required rate of return on the stock is 10%, what is your estimate of the stock price?

Answer 1

The stock price is computed as shown below:

Dividend at end of year 1 is computed as follows:

= $ 1.75 x 1.15

= $ 2.0125

Dividend at end of year 2 is computed as follows:

= $ 1.75 x 1.15²

= $ 2.3144 Approximately

Dividend at end of year 3 is computed as follows:

= $ 1.75 x 1.15³

= $ 2.6615 Approximately

Dividend at end of year 4 is computed as follows:

= $ 1.75 x 1.15⁴

= $ 3.0608 Approximately

Dividend at end of year 5 is computed as follows:

= $ 1.75 x 1.15⁵

= $ 3.5199 Approximately

Dividend at end of year 6 is computed as follows:

= $ 1.75 x 1.15⁶

= $ 4.0479 Approximately

Dividend at end of year 7 is computed as follows:

= $ 4.0479 x 1.08

= $ 4.3717 Approximately

So the price will be:

= Dividend at end of year 1 / ( 1 + required rate of return )¹ + Dividend at end of year 2 / ( 1 + required rate of return )² + Dividend at end of year 3 / ( 1 + required rate of return )³ + Dividend at end of year 4 / ( 1 + required rate of return )⁴ + Dividend at end of year 5 / ( 1 + required rate of return )⁵ + Dividend at end of year 6 / ( 1 + required rate of return )⁶ + 1 / ( 1 + required rate of return )⁶ [ ( Dividend at end of year 7 ) / ( required rate of return - growth rate ) ]

= $ 2.0125 / 1.10¹ + $ 2.3144 / 1.10² + $ 2.6615 / 1.10³ + $ 3.0608 / 1.10⁴ + $ 3.5199 / 1.10⁵ + $ 4.0479 / 1.10⁶ + 1 / 1.10⁶ [ ( $ 4.3717 / ( 0.10 - 0.08 ) ]

= $ 135.69 Approximately

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