Question

A stock pays dividends of $1.00 at t =
1. **(D _{1} is provided here, not
D_{0})** 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 |
||

$21.74 |
||

$55.70 |
||

$58.41 |
||

$61.16 |

Answer #1

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**

A stock pays dividends of $1.00 at t = 1 (t = 1 NOT t =
0). Dividends are expected to grow at a
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NOT t = 0) (hint: there is more than one way to do this
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