Big Time Cell Phone Corporation just announced a cut in their annual dividend from $3.06 to $2.14 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 $18.04. After the announcement, the expectation is that dividends will now grow at a 4.23% 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 by Big Time Cell Phone Corporation, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The model is given by the formula:

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

where:

• \( P_0 \) is the price of the stock today,
• \( D_1 \) is the dividend expected next year,
• \( r \) is the required rate of return,
• \( g \) is the growth rate of the dividends.

Step 1: Identify \( D_1 \), \( g \), and \( r \)

From the information provided:

• The new dividend, \( D_1 \), after the announcement is \( 2.14 \).
• The new growth rate \( g \) is \( 4.23% = 0.0423 \).

Step 2: Estimate the required rate of return \( r \)

To compute the new price, we need the required rate of return \( r \). Since we don't have \( r \) directly, we can use the previous stock price and the former growth rate to approximate it.

We can rearrange the Gordon Growth Model to solve for \( r \) based on the previous situation where the dividend was expected to grow at \( 2.50% \):

1. Calculate the expected next dividend before the cut:

   • \( D_0 = 3.06 \)
   • The expected next dividend, \( D_1 \), prior to the announcement (using the growth rate of \( 2.5% \)): \[ D_1 = D_0 \times (1 + g) = 3.06 \times (1 + 0.025) = 3.06 \times 1.025 = 3.13 \text{ (approximately)} \]

2. Using the previous stock price of \( 18.04 \) to estimate \( r \): \[ 18.04 = \frac{3.13}{r - 0.025} \]

Rearranging and solving for \( r \): \[ r - 0.025 = \frac{3.13}{18.04} \] \[ r - 0.025 \approx 0.1730 \] \[ r \approx 0.1730 + 0.025 = 0.198 \text{ or } 19.8% \]

Step 3: Calculate the new price using the new parameters

Now we can use the new dividend \( D_1 = 2.14 \) and the new growth rate \( g = 0.0423 \) in the Gordon Growth Model:

\[ P_0 = \frac{2.14}{0.198 - 0.0423} \]

Calculating \( r - g \): \[ r - g = 0.198 - 0.0423 = 0.1557 \]

Now substituting back into the formula: \[ P_0 = \frac{2.14}{0.1557} \approx 13.72 \]

Conclusion

After the announcement, the new price of Big Time Cell Phone Corporation’s stock is approximately $13.72.