Time Cell Phone Corporation just announced a cut in their annual dividend from $3.10 to $2.11 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 $16.43. After the announcement, the expectation is that dividends will now grow at a 4.09% rate.

Question

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

Answer 1

To determine the new price of Time Cell Phone Corporation's stock after the dividend cut and the updated growth rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model, DDM). This model calculates the stock price based on the expected future dividends and the growth rate of those dividends.

The formula for the Gordon Growth Model is:

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

Where:

• \(P_0\) = Price of the stock today
• \(D_1\) = Expected dividend next year
• \(r\) = Required rate of return
• \(g\) = Growth rate of dividends

Step 1: Calculate Expected Dividend for Next Year (\(D_1\))

After the announced cut, the new dividend is \(D_1 = 2.11\).

Step 2: Determine the Growth Rate (\(g\))

The new growth rate is \(g = 4.09% = 0.0409\).

Step 3: Calculate the Required Rate of Return (\(r\))

The required rate of return typically isn't provided directly in the problem. However, we can estimate it based on the original stock price and dividend growth assumption. Originally, dividends were expected to grow at \(2.50%\) with a dividend of \(3.10\). Using the original price of \(16.43\), we can estimate the required rate of return \(r\) using the model.

Initially, before the dividend cut:

1. Calculate the original expected dividend next year as \(D_1 = 3.10 \times (1 + 0.025) = 3.10 \times 1.025 = 3.175\).
2. Using the original price of \(16.43\):

\[ r_{old} = \frac{D_1}{P_0} + g = \frac{3.175}{16.43} + 0.025 \]

Calculating \(r_{old}\):

\[ r_{old} = 0.193 \text{ (approximately)} + 0.025 \approx 0.218 = 21.8% \]

Step 4: Estimate the Required Rate of Return (\(r\)) Post Announcement

Since the company is investing in a new indestructible smartphone, let's assume this investment might not change the required rate of return drastically. We could use the original estimated required rate.

Thus, we will use:

• \(r \approx 0.218\) (or 21.8%).

Step 5: Calculate New Price of the Stock (\(P_0\))

Now we can calculate the new stock price:

\[ P_0 = \frac{2.11}{0.218 - 0.0409} \]

Calculating the denominator:

\[ r - g = 0.218 - 0.0409 = 0.1771 \]

Now, substitute this into the price formula:

\[ P_0 = \frac{2.11}{0.1771} \approx 11.91 \]

Conclusion

The new price of Time Cell Phone Corporation's stock after the announcement is approximately $11.91.