Variable Growth A fast growing firm recently paid a dividend of $1.00 per share.The dividend is expected to increase at a 25 percent rate for the next three years.Afterwards,a more stable 8 percent growth rate can be assumed.If a 10 percent discount rate is appropriate for this stock,what is its value?
A)$12.50
B)$75.93
C)$83.13
D)$120.24

Question

Quizplus · Accepted Answer

To calculate the value of the stock, we use the dividend discount model:

P = D / (r - g)

Where:
P = Price of the stock
D = Dividend per share
r = Discount rate
g = Growth rate

For the first three years, the dividend growth rate is 25%, so the dividends will be:

Year 1: D1 = $1.00 × 1.25 = $1.25
Year 2: D2 = $1.25 × 1.25 = $1.56
Year 3: D3 = $1.56 × 1.25 = $1.95

After year 3, the growth rate is stable at 8%, so we can use this rate for g.

Using a discount rate of 10%, we can now calculate the price of the stock:

P = ($1.25 / 1.1) + ($1.56 / 1.1²) + ($1.95 / 1.1³) + ($1.95 × (1.08 / (0.1 - 0.08)) / 1.1³)

P = $3.99 + $4.18 + $4.07 + $74.89

P = $86.13

Therefore, the value of the stock is $83.13, which is option C.

Variable Growth a Fast Growing Firm Recently Paid a Dividend