Question

Free Motion Enterprises paid a $2.20 per share annual dividend last week. Dividends are expected to increase by 3.75 percent annually. What is one share of this stock worth to you today if your required rate of return is 15 percent?

Answer 1

Using the Gordon Growth Model, one share of Free Motion Enterprises stock, which paid a $2.20 per share annual dividend and is expected to increase by 3.75% annually, is worth $20.29 today based on a 15% required rate of return.

Step-by-step explanation:

To determine the value of one share of Free Motion Enterprises stock based on the given dividend growth model, we can use the Gordon Growth Model (Dividend Discount Model). This model calculates the present value of an infinite series of future dividends that are expected to increase at a constant rate. Since the dividend is expected to grow perpetually at a rate of 3.75%, we'll use the formula:

Value of Stock = D1 / (k - g),

where D1 is the expected annual dividend next year, k is the required rate of return, and g is the growth rate of dividends. In this case, the expected dividend D1 is $2.20 increased by 3.75%, k is 15%, and g is 3.75%. Hence:

D1 = $2.20 × (1 + 3.75%) = $2.20 × 1.0375 = $2.2825,

Value of Stock = $2.2825 / (0.15 - 0.0375) = $2.2825 / 0.1125 = $20.29.

Therefore, using the Gordon Growth Model, one share of Free Motion Enterprises stock would be worth $20.29 today to an investor requiring a 15% rate of return.

Answer 2

$20.29

Step-by-step explanation:

The computation of the today share price is shown below:

= Next year dividend ÷ (Required rate of return - growth rate)

where,

Next year dividend

= $2.20 + $2.20 × 3.75%

= $2.20 + 0.0825

= $2.2825

The other items values would remain the same

So, the today price would be

= $2.2825 ÷ (15% - 3.75%)

= $2.2825 ÷ 11.25%

= $20.29