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A share of stock is expected to pay a dividend of $1.25 in Year 1. $2.00 in Year 2. $3.25 in Year 3. $5.00 in Year...

Question

A share of stock is expected to pay a dividend of $1.25 in Year 1. $2.00 in Year 2. $3.25 in Year 3. $5.00 in Year...

A share of stock is expected to pay a dividend of $1.25 in Year 1. $2.00 in Year 2. $3.25 in Year 3. $5.00 in Year 4, and the
A share of stock is expected to pay a dividend of $1.25 in Year 1. $2.00 in Year 2. $3.25 in Year 3. $5.00 in Year 4, and then to grow at an annual rate of 5.0 percent per year. Investors require a 12.0 percent return for this stock. Given this information, determine what the price of this stock should be at Year 21. $199.00 $171.90 $208.95 $189.52 $180.50

Answers

Step-1, Calculation of Dividend per share in Year 21

Here, we’ve Dividend per share in Year 4 (D4) = $5.00 per share

Therefore, the Dividend per share in Year 21 = D4 x (1 + g)17

= $5.00 per share x (1 + 0.05)17

= $5.00 per share x (1.05)17

= $5.00 per share x 2.292018

= $11.4601 per share

Step-2, The Price of the stock at Year 21 (P21)

Dividend Growth Rate after 21 years (g) = 5.00% per year

Required Rate of Return (Ke) = 12.00%

Therefore, the Price of the stock at Year 21 (P21) = D21(1 + g) / (Ke – g)

= $11.4601(1 + 0.05) / (0.12 – 0.05)

= [$11.4601 x 1.05] / 0.07

= $12.0331 / 0.07

= $171.90 per share

“Hence, the Price of the stock at Year 21 (P21) will be $171.90”


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