Question

Big Time Cell Phone Corporation just announced a cut in their annual dividend from $3.14 to $2.09 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 $18.88. After the announcement, the expectation is that dividends will now grow at a 4.16% rate.

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

Answer 1

To determine the new price of the stock after the announcement, we can use the Gordon Growth Model (Dividend Discount Model) which states:

\[
P_0 = \frac{D_1}{r - g}
\]

Where:
- \( P_0 \) = price of the stock today
- \( D_1 \) = dividend in year 1
- \( r \) = required rate of return
- \( g \) = growth rate of dividends

From the information provided:
- The new dividend \( D_1 \) is $2.09 (which is the dividend in year 1).
- The new growth rate \( g \) is 4.16% or 0.0416.

To use the formula, we first need the required rate of return \( r \). We can estimate it using the previous dividend and growth information. Initially, dividends were expected to grow at 2.50% (or 0.025) and the dividend was $3.14. The price was $18.88. We can arrange the Gordon Growth Model to find \( r \):

\[
P_0 = \frac{D_0(1+g)}{r - g}
\]

Substituting in the known values for \( P_0 = 18.88 \), \( D_0 = 3.14 \), and \( g = 0.025 \):

\[
18.88 = \frac{3.14(1 + 0.025)}{r - 0.025}
\]

Calculating \( D_1 \):

\[
D_1 = 3.14(1 + 0.025) = 3.14 \times 1.025 = 3.2155
\]

Now substitute back into the equation:

\[
18.88 = \frac{3.2155}{r - 0.025}
\]

Cross-multiplying gives:

\[
18.88(r - 0.025) = 3.2155
\]

Simplifying:

\[
18.88r - 0.472 = 3.2155
\]

\[
18.88r = 3.2155 + 0.472
\]

\[
18.88r = 3.6875
\]

\[
r = \frac{3.6875}{18.88} \approx 0.1954 \text{ or } 19.54\%
\]

Now with the new growth rate \( g = 4.16\% \) or \( 0.0416 \) and the new \( D_1 = 2.09 \):

\[
P_0 = \frac{2.09}{0.1954 - 0.0416}
\]

Calculating the denominator:

\[
0.1954 - 0.0416 = 0.1538
\]

Now substituting into the formula:

\[
P_0 = \frac{2.09}{0.1538} \approx 13.59
\]

Therefore, the new price of the stock after the announcement is approximately **$13.59**.