Question

Big Time Cell Phone Corporation just announced a cut in their annual dividend from $3.01 to $2.19 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 $18.73. After the announcement, the expectation is that dividends will now grow at a 3.56% rate.

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

Answer 1

To calculate the new price of the stock after the announcement, we can use the Gordon Growth Model (Dividend Discount Model), which is given by the formula:

\[
P = \frac{D_1}{r - g}
\]

where:
- \( P \) = price of the stock
- \( D_1 \) = dividend in year 1
- \( r \) = required rate of return
- \( g \) = growth rate of dividends

Here are the steps to find the new price of the stock:

1. **Calculate the required rate of return (r):**
Since we have the previous stock price, dividend, and growth rate, we can rearrange the formula to find \( r \) before the announcement:

\[
P = \frac{D_0(1 + g)}{r - g}
\]

Before the dividend cut, the dividend was $3.01 per share, and \( g \) was 2.50% or 0.025.

Calculating \( D_1 \) (the dividend for year 1 before the cut):

\[
D_1 = D_0(1 + g) = 3.01 \times (1 + 0.025) = 3.01 \times 1.025 = 3.08025
\]

Now using the original stock price ($18.73):

\[
18.73 = \frac{3.08025}{r - 0.025}
\]

Rearranging gives:

\[
r - 0.025 = \frac{3.08025}{18.73}
\]

\[
r - 0.025 = 0.164
\]

\[
r = 0.164 + 0.025 = 0.189 = 18.9\%
\]

2. **Calculate the new price after the announcement:**
The new dividend \( D_1 \) after the cut is $2.19 per share, and the new growth rate \( g \) is 3.56% or 0.0356.

Now, using the Gordon Growth Model again with the new parameters:

\[
P = \frac{D_1}{r - g} = \frac{2.19}{0.189 - 0.0356}
\]

First, compute \( r - g \):

\[
r - g = 0.189 - 0.0356 = 0.1534
\]

Now substitute back into the formula:

\[
P = \frac{2.19}{0.1534} \approx 14.27
\]

Thus, the new price of the stock after the announcement is approximately **$14.27**.