Question

Pina Clothiers Ltd.’s current dividend is $4.80. Dividends are expected to grow by 9 percent for years 1 to 3, 4 percent for years 4 to 7, and 3 percent thereafter. The required rate of return on the stock is 12 percent. What is the current stock price for Pina? (Round intermediate calculations to 4 decimal places, e.g. 45.1771 and final answer to 2 decimal places, e.g. 45.17.)

Stock price

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

= ($ 4.80 x 1.09) / 1.12 + ($ 4.80 x 1.09²) / 1.12² + ($ 4.80 x 1.09³) / 1.12³ + ($ 4.80 x 1.09³ x 1.04) / 1.12⁴ + ($ 4.80 x 1.09³ x 1.04²) / 1.12⁵ + ($ 4.80 x 1.09³ x 1.04³) / 1.12⁶ + ($ 4.80 x 1.09³ x 1.04⁴) / 1.12⁷ + 1 / 1.12⁷ x [ ($ 4.80 x 1.09³ x 1.04⁴ x 1.03) / (0.12 - 0.03) ]

= $ 5.232 / 1.12 + $ 5.7029 / 1.12² + $ 6.2161 / 1.12³ + $ 6.4648 / 1.12⁴ + $ 6.7234 / 1.12⁵ + $ 6.9923 / 1.12⁶ + $ 7.2720 / 1.12⁷ + $ 83.2240 / 1.12⁷

= $ 5.232 / 1.12 + $ 5.7029 / 1.12² + $ 6.2161 / 1.12³ + $ 6.4648 / 1.12⁴ + $ 6.7234 / 1.12⁵ + $ 6.9923 / 1.12⁶ + $ 90.4960 / 1.12⁷

= $ 66.04 Approximately

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