Question

A7X Corp. just paid a dividend of $1.40 per share. The dividends are expected to grow at 30 percent for the next 9 years and then level off to a growth rate of 8 percent indefinitely.

   

If the required return is 14 percent, what is the price of the stock today?

Multiple Choice

• $82.18

• $2.72

• $110.05

• $107.89

• $105.74

Answer 1

The price is computed as shown below:

= Dividend in year 1 / (1 + required rate of return)¹ + Dividend in year 2 / (1 + required rate of return)² + 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 + Dividend in year 6 / (1 + required rate of return)⁶ + Dividend in year 7 / (1 + required rate of return)⁷ + Dividend in year 8 / (1 + required rate of return)⁸ + Dividend in year 9 / (1 + required rate of return)⁹ + 1 / (1 + required rate of return)⁹ [ ( Dividend in year 9 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 1.40 x 1.30) / 1.14¹ +  ($ 1.40 x 1.30²) / 1.14² +  ($ 1.40 x 1.30³) / 1.14³ +  ($ 1.40 x 1.30⁴) / 1.14⁴ +  ($ 1.40 x 1.30⁵) / 1.14⁵ +  ($ 1.40 x 1.30⁶) / 1.14⁶ +  ($ 1.40 x 1.30⁷) / 1.14⁷ +  ($ 1.40 x 1.30⁸) / 1.14⁸ +  ($ 1.40 x 1.30⁹) / 1.14⁹ + 1 / 1.14⁹ x [ ($ 1.40 x 1.30⁹ x 1.08) / ( 0.14 - 0.08) ]

= $ 1.82 / 1.14¹ + $ 2.366 / 1.14² + $ 3.0758 / 1.14³ + $ 3.99854 / 1.14⁴ + $ 5.198102 / 1.14⁵ + $ 6.7575326 / 1.14⁶ + $ 8.78479238 / 1.14⁷ + $ 11.42023009 / 1.14⁸ + $ 14.84629912 / 1.14⁹ + $ 267.2333842 / 1.14⁹

= $ 107.89 Approximately

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