Question

A company plans to pay a dividend of $0.50 per share next year rising by $0.25 per year until it reaches $2.50, at which point it will remain flat forever. If the discount rate is 9% per year, what is the present value of the dividends, i.e. the value of a share of stock?

Answer 1

The value is computed as shown below:

= Dividend in year 1 / (1 + discount rate)¹ + Dividend in year 2 / (1 + discount rate)² + Dividend in year 3 / (1 + discount rate)³ + Dividend in year 4 / (1 + discount rate)⁴ + Dividend in year 5 / (1 + discount rate)⁵ + Dividend in year 6 / (1 + discount rate)⁶ + Dividend in year 7 / (1 + discount rate)⁷ + Dividend in year 8 / (1 + discount rate)⁸ + Dividend in year 9 / (1 + discount rate)⁹ + 1 / (1 + discount rate)⁹ x [ (Dividend in year 9 / discount rate) ]

= $ 0.50 / 1.09 + $ 0.75 / 1.09² + $ 1 / 1.09³ + $ 1.25 / 1.09⁴ + $ 1.50 / 1.09⁵ + $ 1.75 / 1.09⁶ + $ 2 / 1.09⁷ + $ 2.25 / 1.09⁸ + $ 2.50 / 1.09⁹ + 1 / 1.09⁹ x [ ($ 2.50 / 0.09) ]

= $ 0.50 / 1.09 + $ 0.75 / 1.09² + $ 1 / 1.09³ + $ 1.25 / 1.09⁴ + $ 1.50 / 1.09⁵ + $ 1.75 / 1.09⁶ + $ 2 / 1.09⁷ + $ 2.25 / 1.09⁸ + $ 2.50 / 1.09⁹ + 27.77777778 / 1.09⁹

= $ 0.50 / 1.09 + $ 0.75 / 1.09² + $ 1 / 1.09³ + $ 1.25 / 1.09⁴ + $ 1.50 / 1.09⁵ + $ 1.75 / 1.09⁶ + $ 2 / 1.09⁷ + $ 2.25 / 1.09⁸ + $ 30.27777778 / 1.09⁹

= $ 20.93 Approximately

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