Big Time Cell Phone Corporation just announced a cut in their annual dividend from $3.01 to $2.10 per share (year 1 dividend). Big Time has announced the investment in a new indestructible smart phone. Prior to this announcement, analysts believe dividends would grow at 2.50% into the foreseeable future, and the stock was priced at $18.66. After the announcement, the expectation is that dividends will now grow at a 3.90% rate.

Question

What is the new price of the stock after the announcement?

Answer 1

To calculate the new price of the stock after the announcement of the dividend decrease and the change in growth rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:

$$P_0=\frac{D_1}{r-g}$$

Where:

• $P_0$ = Price of the stock today
• $D_1$ = Dividend in the next year
• $r$ = Required rate of return
• $g$ = Growth rate of dividends

Step 1: Identify the inputs

1. Next Year Dividend ($D_1$): The dividend will be $2.10 per share.
2. Growth Rate ($g$): The new growth rate is 3.90% or 0.039.
3. To use the Gordon Growth Model, we also need the required return ($r$). We can assume it remains constant based on its original price.

Step 2: Calculate the required return ($r$)

The original dividend was $3.01, and the stock was priced at $18.66 with an expected growth rate of 2.50%. We can find the required return using the original data:

$$P_0=\frac{D_1}{r-g}$$

We can rearrange this to solve for $r$:

$$r=\frac{D_1}{P_0}+g$$

Using $D_1=3.01$, $P_0=18.66$, and $g=0.025$:

$$r=\frac{3.01}{18.66}+0.025$$

Calculating $\frac{3.01}{18.66}$:

$$\frac{3.01}{18.66}\approx 0.1613$$

So,

$$r\approx 0.1613+0.025\approx 0.1863=18.63$$

Step 3: Use the new growth rate to find the new stock price

Now that we have $r$ and the new $g$, we can calculate the new price using $D_1=2.10$ and $g=0.039$:

$$P_0=\frac{2.10}{0.1863-0.039}$$

Calculating $r-g$:

$$0.1863-0.039=0.1473$$

Now, substituting into the Price formula:

$$P_0=\frac{2.10}{0.1473}\approx 14.24$$

Final Result

The new price of the stock after the announcement is approximately $14.24 per share.