A stock pays dividends of $1.00 at t = 1. (D1 is provided here, not D0) It is growing at 25% between t =1 and t = 2, after which the growth rate drops to 12%, and will continue at that rate into the future. If the discount rate for this stock is 14%, what should be the value of the stock at t = 0? Hint: Make a diagram indicating ranges of the growth rates and the resulting dividends.
$53.04 |
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$21.74 |
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$55.70 |
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$58.41 |
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$61.16 |
Dividend at year 1 = 1
Dividend at year 2 = 1 * 1.25 = 1.25
Dividend at year 3 = 1.25 * 1.12 = 1.4
Present value at year 2 using dividend discount model = D1 / required rate - growth rate
Present value at year 2 = 1.4 / 0.14 - 0.12
Present value at year 2 = 1.4 / 0.02
Present value at year 2 = 70
Present value of 70 today = 70 / ( 1 + 0.14 )2
Present value of 70 today = $53.86273
Present value of year 2 dividend = 1.25 / ( 1 + 0.14)2
Present value of year 2 dividend = $0.9618
Present value of year 1 dividend = 1 / ( 1 + 0.14)
Present value of year 1 dividend = 0.87719
Value of stock = 0.87719 + 0.9618 + 53.86273
Value of stock = $55.70
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