Question

Purple Inc. recently paid a common stock dividend of $3.00 (D₀ = $3.00). They expect their dividends to grow by 9% per year for 2 years. In year 3, they expect their dividends to start growing at a constant 4% per year forever. You require a 12% return on this stock. What is the most you would be willing to pay for this stock?

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 + 1 / ( 1 + required rate of return)² [ ( Dividend in year 2 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 3 x 1.09) / 1.12 + ($ 3 x 1.09²) / 1.12² + 1 / 1.12² [ ( $ 3 x 1.09² x 1.04) / ( 0.12 - 0.04) ]

= $ 3.27 / 1.12 + $ 3.5643 / 1.12² + 1 / 1.12² [ ( $ 46.3359 ) ]

= $ 42.70 Approximately

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