Question

Purple Inc. recently paid a common stock dividend of $3.00
(D_{0} = $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 1.09^{2}) /
1.12^{2} + 1 / 1.12^{2} [ ( $ 3 x 1.09^{2}
x 1.04) / ( 0.12 - 0.04) ]

= $ 3.27 / 1.12 + $ 3.5643 / 1.12^{2} + 1 /
1.12^{2} [ ( $ 46.3359 ) ]

**= $ 42.70 Approximately**

Feel free to ask in case of any query relating to this question

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