Question

A firm's most recent annual dividend was $2.25. It is assumed that the firm will grow at an abnormal rate of 19% per year for the next 5 years. Beyond year 5, the firm is expected to grow at a more sustainable rate of 6% in perpetuity. If the required rate of return for the firm is 12%, what is the current value of the firm's stock? (show all work)

Answer 1

The value of the stock 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 + 1 / (1 + required rate of return)⁵ [ ( Dividend in year 5 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 2.25 x 1.19) / 1.12¹ + ($ 2.25 x 1.19²) / 1.12² + ($ 2.25 x 1.19³) / 1.12³ + ($ 2.25 x 1.19⁴) / 1.12⁴ + ($ 2.25 x 1.19⁵) / 1.12⁵ + 1 / 1.12⁵ [ ( $ 2.25 x 1.19⁵ x 1.06) / ( 0.12 - 0.06) ]

= $ 2.6775 / 1.12¹ + $ 3.186225 / 1.12² + $ 3.79160775 / 1.12³ + $ 4.512013223 / 1.12⁴ + $ 5.369295735 / 1.12⁵ + 1 / 1.12⁵ x [ ( $ 94.85755798 ) ]

= $ 67.37 Approximately

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