A stock pays dividends of 100 at t 1 D1 is provided here no

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

$21.74

$55.70

$58.41

$61.16

Solution

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