Question

Non-constant dividend growth model: Compute the value of a share of common stock of Lexi's Cookie Company whose most recent dividend was $2.50 and is expected to grow at 9 percent per year for the next 5 years, after which the dividend growth rate will decrease to 3 percent per year indefinitely. Assume 8 percent required rate of return.

Answer 1

The value 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) ]

= ($ 2.50 x 1.09) / 1.08¹ + ($ 2.50 x 1.09²) / 1.08² + ($ 2.50 x 1.09³) / 1.08³ + ($ 2.50 x 1.09⁴) / 1.08⁴ + ($ 2.50 x 1.09⁵) / 1.08⁵ + 1 / 1.08⁵ [ ($ 2.50 x 1.09⁵ x 1.03) / ( 0.08 - 0.03) ]

= $ 2.725 / 1.08 + $ 2.97025 / 1.08² + $ 3.2375725 / 1.08³ + $ 3.528954025 / 1.08⁴ + $ 3.846559887 / 1.08⁵ + 1 / 1.08⁵ [ ($ 79.23913368) ]

= $ 2.725 / 1.08 + $ 2.97025 / 1.08² + $ 3.2375725 / 1.08³ + $ 3.528954025 / 1.08⁴ + $ 83.08569356 / 1.08⁵

= $ 66.78 Approximately

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